| 0 | →𝜑→𝜓𝜑 | Axiom | ax-1 |
| 1 | →→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Axiom | ax-2 |
| 2 | →→¬𝜑¬𝜓→𝜓𝜑 | Axiom | ax-3, con4 |
| 3 | ¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Axiom | df-bi |
| 4 | ↔⋀𝜑𝜓¬→𝜑¬𝜓 | Axiom | df-an |
| 5 | →𝜑→𝜑𝜑 | Subs [𝜓↗𝜑] into ax-1 | |
| 6 | →𝜑→→𝜑𝜑𝜑 | Subs [𝜓↗→𝜑𝜑] into ax-1 | |
| 7 | →→𝜑→→𝜑𝜑𝜑→→𝜑→𝜑𝜑→𝜑𝜑 | Subs [𝜓↗→𝜑𝜑, 𝜒↗𝜑] into ax-2 | |
| 8 | →→𝜑→𝜑𝜑→𝜑𝜑 | Modus ponens 6, 7 | |
| 9 | →𝜑𝜑 | Modus ponens 5, 8 | id |
| 10 | →𝜓𝜓 | Subs [𝜑↗𝜓] into id | |
| 11 | →→𝜓𝜓→𝜑→𝜓𝜓 | Subs [𝜑↗→𝜓𝜓, 𝜓↗𝜑] into ax-1 | |
| 12 | →𝜑→𝜓𝜓 | Modus ponens 10, 11 | idd |
| 13 | →𝜑→𝜒𝜑 | Subs [𝜓↗𝜒] into ax-1 | |
| 14 | →→𝜑→𝜒𝜑→𝜑→𝜑→𝜒𝜑 | Subs [𝜑↗→𝜑→𝜒𝜑, 𝜓↗𝜑] into ax-1 | |
| 15 | →𝜑→𝜑→𝜒𝜑 | Modus ponens 13, 14 | |
| 16 | →→𝜑→𝜑→𝜒𝜑→→𝜑𝜑→𝜑→𝜒𝜑 | Subs [𝜓↗𝜑, 𝜒↗→𝜒𝜑] into ax-2 | |
| 17 | →→𝜑𝜑→𝜑→𝜒𝜑 | Modus ponens 15, 16 | |
| 18 | →→𝜒𝜑→𝜓→𝜒𝜑 | Subs [𝜑↗→𝜒𝜑] into ax-1 | |
| 19 | →→→𝜒𝜑→𝜓→𝜒𝜑→𝜑→→𝜒𝜑→𝜓→𝜒𝜑 | Subs [𝜑↗→→𝜒𝜑→𝜓→𝜒𝜑, 𝜓↗𝜑] into ax-1 | |
| 20 | →𝜑→→𝜒𝜑→𝜓→𝜒𝜑 | Modus ponens 18, 19 | |
| 21 | →→𝜑→→𝜒𝜑→𝜓→𝜒𝜑→→𝜑→𝜒𝜑→𝜑→𝜓→𝜒𝜑 | Subs [𝜓↗→𝜒𝜑, 𝜒↗→𝜓→𝜒𝜑] into ax-2 | |
| 22 | →→𝜑→𝜒𝜑→𝜑→𝜓→𝜒𝜑 | Modus ponens 20, 21 | |
| 23 | →𝜑→𝜓→𝜒𝜑 | Modus ponens 13, 22 | 2a1 |
| 24 | →→𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓] into id | |
| 25 | →𝜑→→𝜑𝜓𝜑 | Subs [𝜓↗→𝜑𝜓] into ax-1 | |
| 26 | →→𝜑→→𝜑𝜓𝜑→𝜑→𝜑→→𝜑𝜓𝜑 | Subs [𝜑↗→𝜑→→𝜑𝜓𝜑, 𝜓↗𝜑] into ax-1 | |
| 27 | →𝜑→𝜑→→𝜑𝜓𝜑 | Modus ponens 25, 26 | |
| 28 | →→𝜑→𝜑→→𝜑𝜓𝜑→→𝜑𝜑→𝜑→→𝜑𝜓𝜑 | Subs [𝜓↗𝜑, 𝜒↗→→𝜑𝜓𝜑] into ax-2 | |
| 29 | →→𝜑𝜑→𝜑→→𝜑𝜓𝜑 | Modus ponens 27, 28 | |
| 30 | →→→𝜑𝜓→𝜑𝜓→→→𝜑𝜓𝜑→→𝜑𝜓𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2 | |
| 31 | →→→𝜑𝜓𝜑→→𝜑𝜓𝜓 | Modus ponens 24, 30 | |
| 32 | →→→→𝜑𝜓𝜑→→𝜑𝜓𝜓→𝜑→→→𝜑𝜓𝜑→→𝜑𝜓𝜓 | Subs [𝜑↗→→→𝜑𝜓𝜑→→𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1 | |
| 33 | →𝜑→→→𝜑𝜓𝜑→→𝜑𝜓𝜓 | Modus ponens 31, 32 | |
| 34 | →→𝜑→→→𝜑𝜓𝜑→→𝜑𝜓𝜓→→𝜑→→𝜑𝜓𝜑→𝜑→→𝜑𝜓𝜓 | Subs [𝜓↗→→𝜑𝜓𝜑, 𝜒↗→→𝜑𝜓𝜓] into ax-2 | |
| 35 | →→𝜑→→𝜑𝜓𝜑→𝜑→→𝜑𝜓𝜓 | Modus ponens 33, 34 | |
| 36 | →𝜑→→𝜑𝜓𝜓 | Modus ponens 25, 35 | pm2.27 |
| 37 | →→𝜑→→𝜑𝜓𝜓→→𝜑→𝜑𝜓→𝜑𝜓 | Subs [𝜓↗→𝜑𝜓, 𝜒↗𝜓] into ax-2 | |
| 38 | →→𝜑→𝜑𝜓→𝜑𝜓 | Modus ponens pm2.27, 37 | pm2.43 |
| 39 | →→𝜑𝜓→𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒] into ax-1 | |
| 40 | →→→𝜑𝜓→𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 41 | →→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓 | Modus ponens 39, 40 | |
| 42 | →→→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜒→𝜑𝜓] into ax-2 | |
| 43 | →→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓 | Modus ponens 41, 42 | |
| 44 | →→𝜒→𝜑𝜓→→𝜒𝜑→𝜒𝜓 | Subs [𝜑↗𝜒, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2 | |
| 45 | →→→𝜒→𝜑𝜓→→𝜒𝜑→𝜒𝜓→→𝜑𝜓→→𝜒→𝜑𝜓→→𝜒𝜑→𝜒𝜓 | Subs [𝜑↗→→𝜒→𝜑𝜓→→𝜒𝜑→𝜒𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 46 | →→𝜑𝜓→→𝜒→𝜑𝜓→→𝜒𝜑→𝜒𝜓 | Modus ponens 44, 45 | |
| 47 | →→→𝜑𝜓→→𝜒→𝜑𝜓→→𝜒𝜑→𝜒𝜓→→→𝜑𝜓→𝜒→𝜑𝜓→→𝜑𝜓→→𝜒𝜑→𝜒𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→𝜑𝜓, 𝜒↗→→𝜒𝜑→𝜒𝜓] into ax-2 | |
| 48 | →→→𝜑𝜓→𝜒→𝜑𝜓→→𝜑𝜓→→𝜒𝜑→𝜒𝜓 | Modus ponens 46, 47 | |
| 49 | →→𝜑𝜓→→𝜒𝜑→𝜒𝜓 | Modus ponens 39, 48 | imim2 |
| 50 | →→𝜑𝜓→𝜒𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒] into idd | |
| 51 | →→𝜒𝜒→𝜓→𝜒𝜒 | Subs [𝜑↗→𝜒𝜒] into ax-1 | |
| 52 | →→→𝜒𝜒→𝜓→𝜒𝜒→→𝜑𝜓→→𝜒𝜒→𝜓→𝜒𝜒 | Subs [𝜑↗→→𝜒𝜒→𝜓→𝜒𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 53 | →→𝜑𝜓→→𝜒𝜒→𝜓→𝜒𝜒 | Modus ponens 51, 52 | |
| 54 | →→→𝜑𝜓→→𝜒𝜒→𝜓→𝜒𝜒→→→𝜑𝜓→𝜒𝜒→→𝜑𝜓→𝜓→𝜒𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒𝜒, 𝜒↗→𝜓→𝜒𝜒] into ax-2 | |
| 55 | →→→𝜑𝜓→𝜒𝜒→→𝜑𝜓→𝜓→𝜒𝜒 | Modus ponens 53, 54 | |
| 56 | →→𝜑𝜓→𝜓→𝜒𝜒 | Modus ponens 50, 55 | |
| 57 | →→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗𝜒] into ax-2 | |
| 58 | →→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒→→𝜑𝜓→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒 | Subs [𝜑↗→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 59 | →→𝜑𝜓→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒 | Modus ponens 57, 58 | |
| 60 | →→→𝜑𝜓→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒→→→𝜑𝜓→𝜓→𝜒𝜒→→𝜑𝜓→→𝜓𝜒→𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓→𝜒𝜒, 𝜒↗→→𝜓𝜒→𝜓𝜒] into ax-2 | |
| 61 | →→→𝜑𝜓→𝜓→𝜒𝜒→→𝜑𝜓→→𝜓𝜒→𝜓𝜒 | Modus ponens 59, 60 | |
| 62 | →→𝜑𝜓→→𝜓𝜒→𝜓𝜒 | Modus ponens 56, 61 | |
| 63 | →→𝜑𝜓→→𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜒] into ax-1 | |
| 64 | →→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→→𝜓𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 65 | →→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓 | Modus ponens 63, 64 | |
| 66 | →→→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜓] into ax-2 | |
| 67 | →→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓 | Modus ponens 65, 66 | |
| 68 | →→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗𝜑] into imim2 | |
| 69 | →→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜓𝜒] into ax-1 | |
| 70 | →→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 68, 69 | |
| 71 | →→→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜓𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 72 | →→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 70, 71 | |
| 73 | →→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 74 | →→𝜑𝜓→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 72, 73 | |
| 75 | →→→𝜑𝜓→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→→𝜓𝜒→𝜓𝜒→→𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜓𝜒→𝜓𝜒, 𝜒↗→→𝜓𝜒→→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 76 | →→→𝜑𝜓→→𝜓𝜒→𝜓𝜒→→𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 74, 75 | |
| 77 | →→𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 62, 76 | |
| 78 | →→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→𝜓𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜒] into ax-2 | |
| 79 | →→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→𝜑𝜓→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 80 | →→𝜑𝜓→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Modus ponens 78, 79 | |
| 81 | →→→𝜑𝜓→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→→𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜒↗→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒] into ax-2 | |
| 82 | →→→𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Modus ponens 80, 81 | |
| 83 | →→𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Modus ponens 77, 82 | |
| 84 | →→→𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜓𝜒→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜒] into ax-2 | |
| 85 | →→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Modus ponens 83, 84 | |
| 86 | →→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Modus ponens 63, 85 | imim1 |
| 87 | →→𝜓𝜒→→𝜒𝜃→𝜓𝜃 | Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗𝜃] into imim1 | |
| 88 | →→→𝜓𝜒→→𝜒𝜃→𝜓𝜃→𝜑→→𝜓𝜒→→𝜒𝜃→𝜓𝜃 | Subs [𝜑↗→→𝜓𝜒→→𝜒𝜃→𝜓𝜃, 𝜓↗𝜑] into ax-1 | |
| 89 | →𝜑→→𝜓𝜒→→𝜒𝜃→𝜓𝜃 | Modus ponens 87, 88 | |
| 90 | →→𝜑→→𝜓𝜒→→𝜒𝜃→𝜓𝜃→→𝜑→𝜓𝜒→𝜑→→𝜒𝜃→𝜓𝜃 | Subs [𝜓↗→𝜓𝜒, 𝜒↗→→𝜒𝜃→𝜓𝜃] into ax-2 | |
| 91 | →→𝜑→𝜓𝜒→𝜑→→𝜒𝜃→𝜓𝜃 | Modus ponens 89, 90 | |
| 92 | →→𝜑→→𝜒𝜃→𝜓𝜃→→𝜑→𝜒𝜃→𝜑→𝜓𝜃 | Subs [𝜓↗→𝜒𝜃, 𝜒↗→𝜓𝜃] into ax-2 | |
| 93 | →→→𝜑→→𝜒𝜃→𝜓𝜃→→𝜑→𝜒𝜃→𝜑→𝜓𝜃→→𝜑→𝜓𝜒→→𝜑→→𝜒𝜃→𝜓𝜃→→𝜑→𝜒𝜃→𝜑→𝜓𝜃 | Subs [𝜑↗→→𝜑→→𝜒𝜃→𝜓𝜃→→𝜑→𝜒𝜃→𝜑→𝜓𝜃, 𝜓↗→𝜑→𝜓𝜒] into ax-1 | |
| 94 | →→𝜑→𝜓𝜒→→𝜑→→𝜒𝜃→𝜓𝜃→→𝜑→𝜒𝜃→𝜑→𝜓𝜃 | Modus ponens 92, 93 | |
| 95 | →→→𝜑→𝜓𝜒→→𝜑→→𝜒𝜃→𝜓𝜃→→𝜑→𝜒𝜃→𝜑→𝜓𝜃→→→𝜑→𝜓𝜒→𝜑→→𝜒𝜃→𝜓𝜃→→𝜑→𝜓𝜒→→𝜑→𝜒𝜃→𝜑→𝜓𝜃 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→→𝜒𝜃→𝜓𝜃, 𝜒↗→→𝜑→𝜒𝜃→𝜑→𝜓𝜃] into ax-2 | |
| 96 | →→→𝜑→𝜓𝜒→𝜑→→𝜒𝜃→𝜓𝜃→→𝜑→𝜓𝜒→→𝜑→𝜒𝜃→𝜑→𝜓𝜃 | Modus ponens 94, 95 | |
| 97 | →→𝜑→𝜓𝜒→→𝜑→𝜒𝜃→𝜑→𝜓𝜃 | Modus ponens 91, 96 | pm2.83 |
| 98 | →→→𝜑𝜓𝜒→→𝜒𝜑→→𝜑𝜓𝜑 | Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒, 𝜒↗𝜑] into imim1 | |
| 99 | →→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑 | Subs [𝜑↗→→→𝜑𝜓𝜑𝜑] into id | |
| 100 | →→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑 | Subs [𝜑↗→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑, 𝜓↗→→𝜑𝜓𝜒] into ax-1 | |
| 101 | →→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑 | Modus ponens 99, 100 | |
| 102 | →→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑 | Subs [𝜑↗→→𝜒𝜑→→𝜑𝜓𝜑, 𝜓↗→→→𝜑𝜓𝜑𝜑] into ax-1 | |
| 103 | →→→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜒→→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑 | Subs [𝜑↗→→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑, 𝜓↗→→𝜑𝜓𝜒] into ax-1 | |
| 104 | →→→𝜑𝜓𝜒→→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑 | Modus ponens 102, 103 | |
| 105 | →→→→𝜑𝜓𝜒→→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜒→→𝜒𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑 | Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→→𝜒𝜑→→𝜑𝜓𝜑, 𝜒↗→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑] into ax-2 | |
| 106 | →→→→𝜑𝜓𝜒→→𝜒𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑 | Modus ponens 104, 105 | |
| 107 | →→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑 | Modus ponens 98, 106 | |
| 108 | →→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑 | Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗𝜑, 𝜒↗→𝜒𝜑] into imim2 | |
| 109 | →→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑 | Subs [𝜑↗→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑, 𝜓↗→→→𝜑𝜓𝜑𝜑] into ax-1 | |
| 110 | →→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑 | Modus ponens 108, 109 | |
| 111 | →→→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑 | Subs [𝜑↗→→→𝜑𝜓𝜑𝜑, 𝜓↗→→→𝜑𝜓𝜑𝜑, 𝜒↗→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑] into ax-2 | |
| 112 | →→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑 | Modus ponens 110, 111 | |
| 113 | →→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑 | Subs [𝜑↗→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑, 𝜓↗→→𝜑𝜓𝜒] into ax-1 | |
| 114 | →→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑 | Modus ponens 112, 113 | |
| 115 | →→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑 | Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑, 𝜒↗→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑] into ax-2 | |
| 116 | →→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑 | Modus ponens 114, 115 | |
| 117 | →→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑 | Modus ponens 101, 116 | |
| 118 | →→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑 | Subs [𝜑↗→→→𝜑𝜓𝜑𝜑, 𝜓↗→→𝜒𝜑→→𝜑𝜓𝜑, 𝜒↗→→𝜒𝜑𝜑] into ax-2 | |
| 119 | →→→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑 | Subs [𝜑↗→→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑, 𝜓↗→→𝜑𝜓𝜒] into ax-1 | |
| 120 | →→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑 | Modus ponens 118, 119 | |
| 121 | →→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑→→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑 | Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑, 𝜒↗→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑] into ax-2 | |
| 122 | →→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑 | Modus ponens 120, 121 | |
| 123 | →→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑 | Modus ponens 117, 122 | |
| 124 | →→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑→→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑 | Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑, 𝜒↗→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑] into ax-2 | |
| 125 | →→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑 | Modus ponens 123, 124 | |
| 126 | →→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑 | Modus ponens 107, 125 | |
| 127 | →→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑 | Subs [𝜑↗→→→𝜑𝜓𝜑𝜑, 𝜓↗→→𝜑𝜓𝜒] into ax-1 | |
| 128 | →→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑 | Subs [𝜑↗→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑, 𝜓↗→→→𝜑𝜓𝜑𝜑] into ax-1 | |
| 129 | →→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑 | Modus ponens 127, 128 | |
| 130 | →→→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑 | Subs [𝜑↗→→→𝜑𝜓𝜑𝜑, 𝜓↗→→→𝜑𝜓𝜑𝜑, 𝜒↗→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑] into ax-2 | |
| 131 | →→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑 | Modus ponens 129, 130 | |
| 132 | →→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑→→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑 | Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→→→𝜑𝜓𝜑𝜑, 𝜒↗→→𝜒𝜑𝜑] into ax-2 | |
| 133 | →→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑 | Modus ponens 126, 132 | |
| 134 | →→→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑 | Subs [𝜑↗→→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑, 𝜓↗→→→𝜑𝜓𝜑𝜑] into ax-1 | |
| 135 | →→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑 | Modus ponens 133, 134 | |
| 136 | →→→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑 | Subs [𝜑↗→→→𝜑𝜓𝜑𝜑, 𝜓↗→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑, 𝜒↗→→→𝜑𝜓𝜒→→𝜒𝜑𝜑] into ax-2 | |
| 137 | →→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑 | Modus ponens 135, 136 | |
| 138 | →→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑 | Modus ponens 127, 137 | peirceroll |
| 139 | →→𝜑→𝜓𝜒→𝜑→𝜓𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒] into id | |
| 140 | →𝜓→→𝜓𝜒𝜒 | Subs [𝜑↗𝜓, 𝜓↗𝜒] into pm2.27 | |
| 141 | →→𝜓→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜓→→𝜓𝜒𝜒 | Subs [𝜑↗→𝜓→→𝜓𝜒𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1 | |
| 142 | →→𝜑→𝜓𝜒→𝜓→→𝜓𝜒𝜒 | Modus ponens 140, 141 | |
| 143 | →→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒] into ax-1 | |
| 144 | →→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒 | Subs [𝜑↗→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1 | |
| 145 | →→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒 | Modus ponens 143, 144 | |
| 146 | →→→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒→→→𝜑→𝜓𝜒→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→𝜓→𝜑→𝜓𝜒] into ax-2 | |
| 147 | →→→𝜑→𝜓𝜒→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒 | Modus ponens 145, 146 | |
| 148 | →→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→𝜓𝜒, 𝜓↗𝜒, 𝜒↗𝜑] into imim2 | |
| 149 | →→→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜑𝜒→𝜓→→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜑𝜒] into ax-1 | |
| 150 | →𝜓→→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜑𝜒 | Modus ponens 148, 149 | |
| 151 | →→𝜓→→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→→𝜓𝜒𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗𝜓, 𝜓↗→→𝜓𝜒𝜒, 𝜒↗→→𝜑→𝜓𝜒→𝜑𝜒] into ax-2 | |
| 152 | →→𝜓→→𝜓𝜒𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒 | Modus ponens 150, 151 | |
| 153 | →→→𝜓→→𝜓𝜒𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒→→𝜓→→𝜓𝜒𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→→𝜓→→𝜓𝜒𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1 | |
| 154 | →→𝜑→𝜓𝜒→→𝜓→→𝜓𝜒𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒 | Modus ponens 152, 153 | |
| 155 | →→→𝜑→𝜓𝜒→→𝜓→→𝜓𝜒𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→→𝜑→𝜓𝜒→𝜓→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜓→→𝜓𝜒𝜒, 𝜒↗→𝜓→→𝜑→𝜓𝜒→𝜑𝜒] into ax-2 | |
| 156 | →→→𝜑→𝜓𝜒→𝜓→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒 | Modus ponens 154, 155 | |
| 157 | →→𝜑→𝜓𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒 | Modus ponens 142, 156 | |
| 158 | →→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒 | Subs [𝜑↗𝜓, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→𝜑𝜒] into ax-2 | |
| 159 | →→→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒→→𝜑→𝜓𝜒→→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1 | |
| 160 | →→𝜑→𝜓𝜒→→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒 | Modus ponens 158, 159 | |
| 161 | →→→𝜑→𝜓𝜒→→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒→→→𝜑→𝜓𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜓→→𝜑→𝜓𝜒→𝜑𝜒, 𝜒↗→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒] into ax-2 | |
| 162 | →→→𝜑→𝜓𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒 | Modus ponens 160, 161 | |
| 163 | →→𝜑→𝜓𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒 | Modus ponens 157, 162 | |
| 164 | →→→𝜑→𝜓𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒→→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜓→𝜑→𝜓𝜒, 𝜒↗→𝜓→𝜑𝜒] into ax-2 | |
| 165 | →→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→𝜓→𝜑𝜒 | Modus ponens 163, 164 | |
| 166 | →→𝜑→𝜓𝜒→𝜓→𝜑𝜒 | Modus ponens 143, 165 | pm2.04 |
| 167 | →→𝜒𝜃→→𝜓𝜒→𝜓𝜃 | Subs [𝜑↗𝜒, 𝜓↗𝜃, 𝜒↗𝜓] into imim2 | |
| 168 | →→𝜑𝜓→→𝜓𝜃→𝜑𝜃 | Subs [𝜒↗𝜃] into imim1 | |
| 169 | →→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜒𝜃→→𝜑𝜓→→𝜓𝜃→𝜑𝜃 | Subs [𝜑↗→→𝜑𝜓→→𝜓𝜃→𝜑𝜃, 𝜓↗→𝜒𝜃] into ax-1 | |
| 170 | →→𝜒𝜃→→𝜑𝜓→→𝜓𝜃→𝜑𝜃 | Modus ponens 168, 169 | |
| 171 | →→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃 | Subs [𝜑↗→→𝜓𝜒→𝜓𝜃, 𝜓↗→𝜑𝜓] into ax-1 | |
| 172 | →→→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜒𝜃→→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃 | Subs [𝜑↗→→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃, 𝜓↗→𝜒𝜃] into ax-1 | |
| 173 | →→𝜒𝜃→→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃 | Modus ponens 171, 172 | |
| 174 | →→→𝜒𝜃→→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→→𝜒𝜃→→𝜓𝜒→𝜓𝜃→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃 | Subs [𝜑↗→𝜒𝜃, 𝜓↗→→𝜓𝜒→𝜓𝜃, 𝜒↗→→𝜑𝜓→→𝜓𝜒→𝜓𝜃] into ax-2 | |
| 175 | →→→𝜒𝜃→→𝜓𝜒→𝜓𝜃→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃 | Modus ponens 173, 174 | |
| 176 | →→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃 | Modus ponens 167, 175 | |
| 177 | →→→𝜓𝜃→𝜑𝜃→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃 | Subs [𝜑↗→𝜓𝜃, 𝜓↗→𝜑𝜃, 𝜒↗→𝜓𝜒] into imim2 | |
| 178 | →→→→𝜓𝜃→𝜑𝜃→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→𝜑𝜓→→→𝜓𝜃→𝜑𝜃→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃 | Subs [𝜑↗→→→𝜓𝜃→𝜑𝜃→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃, 𝜓↗→𝜑𝜓] into ax-1 | |
| 179 | →→𝜑𝜓→→→𝜓𝜃→𝜑𝜃→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃 | Modus ponens 177, 178 | |
| 180 | →→→𝜑𝜓→→→𝜓𝜃→𝜑𝜃→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜓𝜃→𝜑𝜃, 𝜒↗→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃] into ax-2 | |
| 181 | →→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃 | Modus ponens 179, 180 | |
| 182 | →→→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→𝜒𝜃→→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃 | Subs [𝜑↗→→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃, 𝜓↗→𝜒𝜃] into ax-1 | |
| 183 | →→𝜒𝜃→→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃 | Modus ponens 181, 182 | |
| 184 | →→→𝜒𝜃→→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→→𝜒𝜃→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜒𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃 | Subs [𝜑↗→𝜒𝜃, 𝜓↗→→𝜑𝜓→→𝜓𝜃→𝜑𝜃, 𝜒↗→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃] into ax-2 | |
| 185 | →→→𝜒𝜃→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜒𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃 | Modus ponens 183, 184 | |
| 186 | →→𝜒𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃 | Modus ponens 170, 185 | |
| 187 | →→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜓𝜒→𝜓𝜃, 𝜒↗→→𝜓𝜒→𝜑𝜃] into ax-2 | |
| 188 | →→→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃→→𝜒𝜃→→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃 | Subs [𝜑↗→→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃, 𝜓↗→𝜒𝜃] into ax-1 | |
| 189 | →→𝜒𝜃→→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃 | Modus ponens 187, 188 | |
| 190 | →→→𝜒𝜃→→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃→→→𝜒𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→𝜒𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃 | Subs [𝜑↗→𝜒𝜃, 𝜓↗→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃, 𝜒↗→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃] into ax-2 | |
| 191 | →→→𝜒𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→𝜒𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃 | Modus ponens 189, 190 | |
| 192 | →→𝜒𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃 | Modus ponens 186, 191 | |
| 193 | →→→𝜒𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃→→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃 | Subs [𝜑↗→𝜒𝜃, 𝜓↗→→𝜑𝜓→→𝜓𝜒→𝜓𝜃, 𝜒↗→→𝜑𝜓→→𝜓𝜒→𝜑𝜃] into ax-2 | |
| 194 | →→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃 | Modus ponens 192, 193 | |
| 195 | →→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃 | Modus ponens 176, 194 | |
| 196 | →→𝜑𝜓→→𝜒𝜃→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒𝜃] into ax-1 | |
| 197 | →→→𝜑𝜓→→𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→→𝜒𝜃→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 198 | →→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→𝜑𝜓 | Modus ponens 196, 197 | |
| 199 | →→→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜒𝜃→𝜑𝜓] into ax-2 | |
| 200 | →→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→𝜑𝜓 | Modus ponens 198, 199 | |
| 201 | →→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃 | Subs [𝜑↗→𝜒𝜃, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜃] into ax-2 | |
| 202 | →→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃 | Modus ponens 195, 201 | |
| 203 | →→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃→→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃 | Subs [𝜑↗→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃, 𝜓↗→𝜑𝜓] into ax-1 | |
| 204 | →→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃 | Modus ponens 202, 203 | |
| 205 | →→→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃→→→𝜑𝜓→→𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜒𝜃→𝜑𝜓, 𝜒↗→→𝜒𝜃→→𝜓𝜒→𝜑𝜃] into ax-2 | |
| 206 | →→→𝜑𝜓→→𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃 | Modus ponens 204, 205 | |
| 207 | →→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃 | Modus ponens 196, 206 | imim12 |
| 208 | →𝜓→𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜑] into ax-1 | |
| 209 | →𝜒𝜒 | Subs [𝜑↗𝜒] into id | |
| 210 | →→𝜒𝜒→→𝜑𝜓→𝜒𝜒 | Subs [𝜑↗→𝜒𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 211 | →→→𝜑𝜓→𝜒𝜒→→→𝜑𝜓𝜒→→𝜑𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒] into ax-2 | |
| 212 | →→→𝜑𝜓𝜒→→𝜑𝜓𝜒 | Modus ponens 50, 211 | |
| 213 | →→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜑𝜓𝜒] into ax-1 | |
| 214 | →→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓→𝜓→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓] into ax-1 | |
| 215 | →𝜓→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓 | Modus ponens 213, 214 | |
| 216 | →→𝜓→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓→→𝜓→𝜑𝜓→𝜓→→→𝜑𝜓𝜒→𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→→𝜑𝜓𝜒→𝜑𝜓] into ax-2 | |
| 217 | →→𝜓→𝜑𝜓→𝜓→→→𝜑𝜓𝜒→𝜑𝜓 | Modus ponens 215, 216 | |
| 218 | →𝜓→→→𝜑𝜓𝜒→𝜑𝜓 | Modus ponens 208, 217 | |
| 219 | →→→→𝜑𝜓𝜒→→𝜑𝜓𝜒→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒 | Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-2 | |
| 220 | →→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒 | Modus ponens 212, 219 | |
| 221 | →→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒→𝜓→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒 | Subs [𝜑↗→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒] into ax-1 | |
| 222 | →𝜓→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒 | Modus ponens 220, 221 | |
| 223 | →→𝜓→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒→→𝜓→→→𝜑𝜓𝜒→𝜑𝜓→𝜓→→→𝜑𝜓𝜒𝜒 | Subs [𝜑↗𝜓, 𝜓↗→→→𝜑𝜓𝜒→𝜑𝜓, 𝜒↗→→→𝜑𝜓𝜒𝜒] into ax-2 | |
| 224 | →→𝜓→→→𝜑𝜓𝜒→𝜑𝜓→𝜓→→→𝜑𝜓𝜒𝜒 | Modus ponens 222, 223 | |
| 225 | →𝜓→→→𝜑𝜓𝜒𝜒 | Modus ponens 218, 224 | |
| 226 | →→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓𝜒] into ax-1 | |
| 227 | →→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒, 𝜓↗→→𝜑𝜓𝜒] into ax-1 | |
| 228 | →→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒 | Modus ponens 226, 227 | |
| 229 | →→→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒→→→→𝜑𝜓𝜒→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→→𝜑𝜓𝜒, 𝜒↗→𝜓→→𝜑𝜓𝜒] into ax-2 | |
| 230 | →→→→𝜑𝜓𝜒→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒 | Modus ponens 228, 229 | |
| 231 | →→𝜓→→→𝜑𝜓𝜒𝜒→→𝜓→→𝜑𝜓𝜒→𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜓𝜒] into ax-2 | |
| 232 | →→𝜓→→𝜑𝜓𝜒→𝜓𝜒 | Modus ponens 225, 231 | |
| 233 | →→→𝜓→→𝜑𝜓𝜒→𝜓𝜒→→→𝜑𝜓𝜒→→𝜓→→𝜑𝜓𝜒→𝜓𝜒 | Subs [𝜑↗→→𝜓→→𝜑𝜓𝜒→𝜓𝜒, 𝜓↗→→𝜑𝜓𝜒] into ax-1 | |
| 234 | →→→𝜑𝜓𝜒→→𝜓→→𝜑𝜓𝜒→𝜓𝜒 | Modus ponens 232, 233 | |
| 235 | →→→→𝜑𝜓𝜒→→𝜓→→𝜑𝜓𝜒→𝜓𝜒→→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→𝜓→→𝜑𝜓𝜒, 𝜒↗→𝜓𝜒] into ax-2 | |
| 236 | →→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→𝜓𝜒 | Modus ponens 234, 235 | |
| 237 | →→→𝜑𝜓𝜒→𝜓𝜒 | Modus ponens 226, 236 | jarr |
| 238 | →→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜑𝜒] into id | |
| 239 | →→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 240 | →→→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→𝜓→→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓] into ax-1 | |
| 241 | →𝜓→→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓 | Modus ponens 239, 240 | |
| 242 | →→𝜓→→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→→𝜓→𝜑𝜓→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→→𝜑𝜓→𝜑𝜒→𝜑𝜓] into ax-2 | |
| 243 | →→𝜓→𝜑𝜓→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓 | Modus ponens 241, 242 | |
| 244 | →𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓 | Modus ponens 208, 243 | |
| 245 | →→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜒] into ax-2 | |
| 246 | →→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒 | Modus ponens 238, 245 | |
| 247 | →→→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒→𝜓→→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒 | Subs [𝜑↗→→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒] into ax-1 | |
| 248 | →𝜓→→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒 | Modus ponens 246, 247 | |
| 249 | →→𝜓→→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒→→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒 | Subs [𝜑↗𝜓, 𝜓↗→→→𝜑𝜓→𝜑𝜒→𝜑𝜓, 𝜒↗→→→𝜑𝜓→𝜑𝜒→𝜑𝜒] into ax-2 | |
| 250 | →→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒 | Modus ponens 248, 249 | |
| 251 | →𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒 | Modus ponens 244, 250 | |
| 252 | →→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 253 | →→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 254 | →→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒 | Modus ponens 252, 253 | |
| 255 | →→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜓→→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 256 | →→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒 | Modus ponens 254, 255 | |
| 257 | →→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒→→𝜓→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒 | Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜑𝜒] into ax-2 | |
| 258 | →→𝜓→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒 | Modus ponens 251, 257 | |
| 259 | →→→𝜓→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜓→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜓→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 260 | →→→𝜑𝜓→𝜑𝜒→→𝜓→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒 | Modus ponens 258, 259 | |
| 261 | →→→→𝜑𝜓→𝜑𝜒→→𝜓→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜓→→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜓→𝜑𝜒] into ax-2 | |
| 262 | →→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒 | Modus ponens 260, 261 | |
| 263 | →→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒 | Modus ponens 252, 262 | |
| 264 | →𝜑→→𝜑𝜒𝜒 | Subs [𝜓↗𝜒] into pm2.27 | |
| 265 | →→𝜑→→𝜑𝜒𝜒→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜒𝜒 | Subs [𝜑↗→𝜑→→𝜑𝜒𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 266 | →→→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜒𝜒 | Modus ponens 264, 265 | |
| 267 | →→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒 | Subs [𝜑↗→𝜓→𝜑𝜒, 𝜓↗𝜑] into ax-1 | |
| 268 | →→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 269 | →→→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒 | Modus ponens 267, 268 | |
| 270 | →→→→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜓→𝜑𝜒, 𝜒↗→𝜑→𝜓→𝜑𝜒] into ax-2 | |
| 271 | →→→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒 | Modus ponens 269, 270 | |
| 272 | →→→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒 | Modus ponens 263, 271 | |
| 273 | →→→𝜑𝜒𝜒→→𝜓→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→𝜑𝜒, 𝜓↗𝜒, 𝜒↗𝜓] into imim2 | |
| 274 | →→→→𝜑𝜒𝜒→→𝜓→𝜑𝜒→𝜓𝜒→𝜑→→→𝜑𝜒𝜒→→𝜓→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜒𝜒→→𝜓→𝜑𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 275 | →𝜑→→→𝜑𝜒𝜒→→𝜓→𝜑𝜒→𝜓𝜒 | Modus ponens 273, 274 | |
| 276 | →→𝜑→→→𝜑𝜒𝜒→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒 | Subs [𝜓↗→→𝜑𝜒𝜒, 𝜒↗→→𝜓→𝜑𝜒→𝜓𝜒] into ax-2 | |
| 277 | →→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒 | Modus ponens 275, 276 | |
| 278 | →→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 279 | →→→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒 | Modus ponens 277, 278 | |
| 280 | →→→→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜒𝜒→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→→𝜑𝜒𝜒, 𝜒↗→𝜑→→𝜓→𝜑𝜒→𝜓𝜒] into ax-2 | |
| 281 | →→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜒𝜒→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒 | Modus ponens 279, 280 | |
| 282 | →→→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒 | Modus ponens 266, 281 | |
| 283 | →→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒 | Subs [𝜓↗→𝜓→𝜑𝜒, 𝜒↗→𝜓𝜒] into ax-2 | |
| 284 | →→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒 | Subs [𝜑↗→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 285 | →→→𝜑𝜓→𝜑𝜒→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒 | Modus ponens 283, 284 | |
| 286 | →→→→𝜑𝜓→𝜑𝜒→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒→→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→→𝜓→𝜑𝜒→𝜓𝜒, 𝜒↗→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒] into ax-2 | |
| 287 | →→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒 | Modus ponens 285, 286 | |
| 288 | →→→𝜑𝜓→𝜑𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒 | Modus ponens 282, 287 | |
| 289 | →→→→𝜑𝜓→𝜑𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒→→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→𝜓→𝜑𝜒, 𝜒↗→𝜑→𝜓𝜒] into ax-2 | |
| 290 | →→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒 | Modus ponens 288, 289 | |
| 291 | →→→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒 | Modus ponens 272, 290 | pm2.86 |
| 292 | →→→𝜑𝜓→𝜓𝜑→𝜓→𝜓𝜑 | Subs [𝜒↗→𝜓𝜑] into jarr | |
| 293 | →→𝜓𝜓→→→𝜑𝜓→𝜓𝜑→𝜓𝜓 | Subs [𝜑↗→𝜓𝜓, 𝜓↗→→𝜑𝜓→𝜓𝜑] into ax-1 | |
| 294 | →→→𝜑𝜓→𝜓𝜑→𝜓𝜓 | Modus ponens 10, 293 | |
| 295 | →→𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑 | Subs [𝜑↗𝜓, 𝜒↗𝜑] into ax-2 | |
| 296 | →→→𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑→→→𝜑𝜓→𝜓𝜑→→𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑 | Subs [𝜑↗→→𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑, 𝜓↗→→𝜑𝜓→𝜓𝜑] into ax-1 | |
| 297 | →→→𝜑𝜓→𝜓𝜑→→𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑 | Modus ponens 295, 296 | |
| 298 | →→→→𝜑𝜓→𝜓𝜑→→𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑→→→→𝜑𝜓→𝜓𝜑→𝜓→𝜓𝜑→→→𝜑𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑 | Subs [𝜑↗→→𝜑𝜓→𝜓𝜑, 𝜓↗→𝜓→𝜓𝜑, 𝜒↗→→𝜓𝜓→𝜓𝜑] into ax-2 | |
| 299 | →→→→𝜑𝜓→𝜓𝜑→𝜓→𝜓𝜑→→→𝜑𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑 | Modus ponens 297, 298 | |
| 300 | →→→𝜑𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑 | Modus ponens 292, 299 | |
| 301 | →→→→𝜑𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑→→→→𝜑𝜓→𝜓𝜑→𝜓𝜓→→→𝜑𝜓→𝜓𝜑→𝜓𝜑 | Subs [𝜑↗→→𝜑𝜓→𝜓𝜑, 𝜓↗→𝜓𝜓, 𝜒↗→𝜓𝜑] into ax-2 | |
| 302 | →→→→𝜑𝜓→𝜓𝜑→𝜓𝜓→→→𝜑𝜓→𝜓𝜑→𝜓𝜑 | Modus ponens 300, 301 | |
| 303 | →→→𝜑𝜓→𝜓𝜑→𝜓𝜑 | Modus ponens 294, 302 | loolin |
| 304 | →→𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗𝜑] into ax-2 | |
| 305 | →→→𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒 | Subs [𝜑↗→→𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 306 | →→→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒 | Modus ponens 304, 305 | |
| 307 | →→→→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜓→𝜑𝜒, 𝜒↗→→𝜓𝜑→𝜓𝜒] into ax-2 | |
| 308 | →→→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒 | Modus ponens 306, 307 | |
| 309 | →→→𝜑𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒 | Modus ponens 263, 308 | loowoz |
| 310 | →¬𝜑¬𝜑 | Subs [𝜑↗¬𝜑] into id | |
| 311 | →¬𝜑→¬𝜓¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓] into ax-1 | |
| 312 | →→¬𝜑→¬𝜓¬𝜑→¬𝜑→¬𝜑→¬𝜓¬𝜑 | Subs [𝜑↗→¬𝜑→¬𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 313 | →¬𝜑→¬𝜑→¬𝜓¬𝜑 | Modus ponens 311, 312 | |
| 314 | →→¬𝜑→¬𝜑→¬𝜓¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬𝜓¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬𝜓¬𝜑] into ax-2 | |
| 315 | →→¬𝜑¬𝜑→¬𝜑→¬𝜓¬𝜑 | Modus ponens 313, 314 | |
| 316 | →→¬𝜓¬𝜑→𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜑] into ax-3 | |
| 317 | →→→¬𝜓¬𝜑→𝜑𝜓→¬𝜑→→¬𝜓¬𝜑→𝜑𝜓 | Subs [𝜑↗→→¬𝜓¬𝜑→𝜑𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 318 | →¬𝜑→→¬𝜓¬𝜑→𝜑𝜓 | Modus ponens 316, 317 | |
| 319 | →→¬𝜑→→¬𝜓¬𝜑→𝜑𝜓→→¬𝜑→¬𝜓¬𝜑→¬𝜑→𝜑𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗→¬𝜓¬𝜑, 𝜒↗→𝜑𝜓] into ax-2 | |
| 320 | →→¬𝜑→¬𝜓¬𝜑→¬𝜑→𝜑𝜓 | Modus ponens 318, 319 | |
| 321 | →¬𝜑→𝜑𝜓 | Modus ponens 311, 320 | pm2.21 |
| 322 | →𝜑→¬𝜑𝜑 | Subs [𝜓↗¬𝜑] into ax-1 | |
| 323 | →→𝜑→¬𝜑𝜑→𝜑→𝜑→¬𝜑𝜑 | Subs [𝜑↗→𝜑→¬𝜑𝜑, 𝜓↗𝜑] into ax-1 | |
| 324 | →𝜑→𝜑→¬𝜑𝜑 | Modus ponens 322, 323 | |
| 325 | →→𝜑→𝜑→¬𝜑𝜑→→𝜑𝜑→𝜑→¬𝜑𝜑 | Subs [𝜓↗𝜑, 𝜒↗→¬𝜑𝜑] into ax-2 | |
| 326 | →→𝜑𝜑→𝜑→¬𝜑𝜑 | Modus ponens 324, 325 | |
| 327 | →→¬𝜑→𝜑𝜓→→¬𝜑𝜑→¬𝜑𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2 | |
| 328 | →→¬𝜑𝜑→¬𝜑𝜓 | Modus ponens pm2.21, 327 | |
| 329 | →→→¬𝜑𝜑→¬𝜑𝜓→𝜑→→¬𝜑𝜑→¬𝜑𝜓 | Subs [𝜑↗→→¬𝜑𝜑→¬𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 330 | →𝜑→→¬𝜑𝜑→¬𝜑𝜓 | Modus ponens 328, 329 | |
| 331 | →→𝜑→→¬𝜑𝜑→¬𝜑𝜓→→𝜑→¬𝜑𝜑→𝜑→¬𝜑𝜓 | Subs [𝜓↗→¬𝜑𝜑, 𝜒↗→¬𝜑𝜓] into ax-2 | |
| 332 | →→𝜑→¬𝜑𝜑→𝜑→¬𝜑𝜓 | Modus ponens 330, 331 | |
| 333 | →𝜑→¬𝜑𝜓 | Modus ponens 322, 332 | pm2.24 |
| 334 | →→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓→¬𝜑→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 335 | →¬𝜑→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓 | Modus ponens 213, 334 | |
| 336 | →→¬𝜑→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓→→¬𝜑→𝜑𝜓→¬𝜑→→→𝜑𝜓𝜒→𝜑𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗→𝜑𝜓, 𝜒↗→→→𝜑𝜓𝜒→𝜑𝜓] into ax-2 | |
| 337 | →→¬𝜑→𝜑𝜓→¬𝜑→→→𝜑𝜓𝜒→𝜑𝜓 | Modus ponens 335, 336 | |
| 338 | →¬𝜑→→→𝜑𝜓𝜒→𝜑𝜓 | Modus ponens pm2.21, 337 | |
| 339 | →→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒→¬𝜑→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒 | Subs [𝜑↗→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒, 𝜓↗¬𝜑] into ax-1 | |
| 340 | →¬𝜑→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒 | Modus ponens 220, 339 | |
| 341 | →→¬𝜑→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒→→¬𝜑→→→𝜑𝜓𝜒→𝜑𝜓→¬𝜑→→→𝜑𝜓𝜒𝜒 | Subs [𝜑↗¬𝜑, 𝜓↗→→→𝜑𝜓𝜒→𝜑𝜓, 𝜒↗→→→𝜑𝜓𝜒𝜒] into ax-2 | |
| 342 | →→¬𝜑→→→𝜑𝜓𝜒→𝜑𝜓→¬𝜑→→→𝜑𝜓𝜒𝜒 | Modus ponens 340, 341 | |
| 343 | →¬𝜑→→→𝜑𝜓𝜒𝜒 | Modus ponens 338, 342 | |
| 344 | →→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗¬𝜑] into ax-1 | |
| 345 | →→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒, 𝜓↗→→𝜑𝜓𝜒] into ax-1 | |
| 346 | →→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒 | Modus ponens 344, 345 | |
| 347 | →→→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒→→→→𝜑𝜓𝜒→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→→𝜑𝜓𝜒, 𝜒↗→¬𝜑→→𝜑𝜓𝜒] into ax-2 | |
| 348 | →→→→𝜑𝜓𝜒→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒 | Modus ponens 346, 347 | |
| 349 | →→¬𝜑→→→𝜑𝜓𝜒𝜒→→¬𝜑→→𝜑𝜓𝜒→¬𝜑𝜒 | Subs [𝜑↗¬𝜑, 𝜓↗→→𝜑𝜓𝜒] into ax-2 | |
| 350 | →→¬𝜑→→𝜑𝜓𝜒→¬𝜑𝜒 | Modus ponens 343, 349 | |
| 351 | →→→¬𝜑→→𝜑𝜓𝜒→¬𝜑𝜒→→→𝜑𝜓𝜒→→¬𝜑→→𝜑𝜓𝜒→¬𝜑𝜒 | Subs [𝜑↗→→¬𝜑→→𝜑𝜓𝜒→¬𝜑𝜒, 𝜓↗→→𝜑𝜓𝜒] into ax-1 | |
| 352 | →→→𝜑𝜓𝜒→→¬𝜑→→𝜑𝜓𝜒→¬𝜑𝜒 | Modus ponens 350, 351 | |
| 353 | →→→→𝜑𝜓𝜒→→¬𝜑→→𝜑𝜓𝜒→¬𝜑𝜒→→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→¬𝜑𝜒 | Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→¬𝜑→→𝜑𝜓𝜒, 𝜒↗→¬𝜑𝜒] into ax-2 | |
| 354 | →→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→¬𝜑𝜒 | Modus ponens 352, 353 | |
| 355 | →→→𝜑𝜓𝜒→¬𝜑𝜒 | Modus ponens 344, 354 | jarl |
| 356 | →→¬𝜑𝜑→¬𝜑𝜑 | Subs [𝜑↗→¬𝜑𝜑] into id | |
| 357 | →¬𝜑→𝜑¬→¬𝜑𝜑 | Subs [𝜓↗¬→¬𝜑𝜑] into pm2.21 | |
| 358 | →→¬𝜑→𝜑¬→¬𝜑𝜑→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗𝜑, 𝜒↗¬→¬𝜑𝜑] into ax-2 | |
| 359 | →→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑 | Modus ponens 357, 358 | |
| 360 | →→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑 | Subs [𝜑↗→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑, 𝜓↗→¬𝜑𝜑] into ax-1 | |
| 361 | →→¬𝜑𝜑→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑 | Modus ponens 359, 360 | |
| 362 | →→→¬𝜑𝜑→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑→→→¬𝜑𝜑→¬𝜑𝜑→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑 | Subs [𝜑↗→¬𝜑𝜑, 𝜓↗→¬𝜑𝜑, 𝜒↗→¬𝜑¬→¬𝜑𝜑] into ax-2 | |
| 363 | →→→¬𝜑𝜑→¬𝜑𝜑→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑 | Modus ponens 361, 362 | |
| 364 | →→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑𝜑 | Subs [𝜓↗→¬𝜑𝜑] into ax-3 | |
| 365 | →→→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑𝜑→→¬𝜑𝜑→→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑𝜑 | Subs [𝜑↗→→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑𝜑, 𝜓↗→¬𝜑𝜑] into ax-1 | |
| 366 | →→¬𝜑𝜑→→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑𝜑 | Modus ponens 364, 365 | |
| 367 | →→→¬𝜑𝜑→→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑𝜑→→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑→→¬𝜑𝜑𝜑 | Subs [𝜑↗→¬𝜑𝜑, 𝜓↗→¬𝜑¬→¬𝜑𝜑, 𝜒↗→→¬𝜑𝜑𝜑] into ax-2 | |
| 368 | →→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑→→¬𝜑𝜑𝜑 | Modus ponens 366, 367 | |
| 369 | →→¬𝜑𝜑→→¬𝜑𝜑𝜑 | Modus ponens 359, 368 | |
| 370 | →→→¬𝜑𝜑→→¬𝜑𝜑𝜑→→→¬𝜑𝜑→¬𝜑𝜑→→¬𝜑𝜑𝜑 | Subs [𝜑↗→¬𝜑𝜑, 𝜓↗→¬𝜑𝜑, 𝜒↗𝜑] into ax-2 | |
| 371 | →→→¬𝜑𝜑→¬𝜑𝜑→→¬𝜑𝜑𝜑 | Modus ponens 369, 370 | |
| 372 | →→¬𝜑𝜑𝜑 | Modus ponens 356, 371 | pm2.18 |
| 373 | →¬¬𝜑→¬𝜑𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗𝜑] into pm2.21 | |
| 374 | →→→¬𝜑𝜑𝜑→¬¬𝜑→→¬𝜑𝜑𝜑 | Subs [𝜑↗→→¬𝜑𝜑𝜑, 𝜓↗¬¬𝜑] into ax-1 | |
| 375 | →¬¬𝜑→→¬𝜑𝜑𝜑 | Modus ponens pm2.18, 374 | |
| 376 | →→¬¬𝜑→→¬𝜑𝜑𝜑→→¬¬𝜑→¬𝜑𝜑→¬¬𝜑𝜑 | Subs [𝜑↗¬¬𝜑, 𝜓↗→¬𝜑𝜑, 𝜒↗𝜑] into ax-2 | |
| 377 | →→¬¬𝜑→¬𝜑𝜑→¬¬𝜑𝜑 | Modus ponens 375, 376 | |
| 378 | →¬¬𝜑𝜑 | Modus ponens 373, 377 | notnotr |
| 379 | →→𝜑¬𝜓→𝜑¬𝜓 | Subs [𝜑↗→𝜑¬𝜓] into id | |
| 380 | →𝜑→→𝜑¬𝜓𝜑 | Subs [𝜓↗→𝜑¬𝜓] into ax-1 | |
| 381 | →→𝜑→→𝜑¬𝜓𝜑→¬¬𝜑→𝜑→→𝜑¬𝜓𝜑 | Subs [𝜑↗→𝜑→→𝜑¬𝜓𝜑, 𝜓↗¬¬𝜑] into ax-1 | |
| 382 | →¬¬𝜑→𝜑→→𝜑¬𝜓𝜑 | Modus ponens 380, 381 | |
| 383 | →→¬¬𝜑→𝜑→→𝜑¬𝜓𝜑→→¬¬𝜑𝜑→¬¬𝜑→→𝜑¬𝜓𝜑 | Subs [𝜑↗¬¬𝜑, 𝜓↗𝜑, 𝜒↗→→𝜑¬𝜓𝜑] into ax-2 | |
| 384 | →→¬¬𝜑𝜑→¬¬𝜑→→𝜑¬𝜓𝜑 | Modus ponens 382, 383 | |
| 385 | →¬¬𝜑→→𝜑¬𝜓𝜑 | Modus ponens notnotr, 384 | |
| 386 | →→→𝜑¬𝜓→𝜑¬𝜓→→→𝜑¬𝜓𝜑→→𝜑¬𝜓¬𝜓 | Subs [𝜑↗→𝜑¬𝜓, 𝜓↗𝜑, 𝜒↗¬𝜓] into ax-2 | |
| 387 | →→→𝜑¬𝜓𝜑→→𝜑¬𝜓¬𝜓 | Modus ponens 379, 386 | |
| 388 | →→→→𝜑¬𝜓𝜑→→𝜑¬𝜓¬𝜓→¬¬𝜑→→→𝜑¬𝜓𝜑→→𝜑¬𝜓¬𝜓 | Subs [𝜑↗→→→𝜑¬𝜓𝜑→→𝜑¬𝜓¬𝜓, 𝜓↗¬¬𝜑] into ax-1 | |
| 389 | →¬¬𝜑→→→𝜑¬𝜓𝜑→→𝜑¬𝜓¬𝜓 | Modus ponens 387, 388 | |
| 390 | →→¬¬𝜑→→→𝜑¬𝜓𝜑→→𝜑¬𝜓¬𝜓→→¬¬𝜑→→𝜑¬𝜓𝜑→¬¬𝜑→→𝜑¬𝜓¬𝜓 | Subs [𝜑↗¬¬𝜑, 𝜓↗→→𝜑¬𝜓𝜑, 𝜒↗→→𝜑¬𝜓¬𝜓] into ax-2 | |
| 391 | →→¬¬𝜑→→𝜑¬𝜓𝜑→¬¬𝜑→→𝜑¬𝜓¬𝜓 | Modus ponens 389, 390 | |
| 392 | →¬¬𝜑→→𝜑¬𝜓¬𝜓 | Modus ponens 385, 391 | |
| 393 | →→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓 | Subs [𝜑↗→𝜑¬𝜓, 𝜓↗¬¬𝜑] into ax-1 | |
| 394 | →→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓→→𝜑¬𝜓→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓 | Subs [𝜑↗→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓, 𝜓↗→𝜑¬𝜓] into ax-1 | |
| 395 | →→𝜑¬𝜓→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓 | Modus ponens 393, 394 | |
| 396 | →→→𝜑¬𝜓→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓→→→𝜑¬𝜓→𝜑¬𝜓→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓 | Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→𝜑¬𝜓, 𝜒↗→¬¬𝜑→𝜑¬𝜓] into ax-2 | |
| 397 | →→→𝜑¬𝜓→𝜑¬𝜓→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓 | Modus ponens 395, 396 | |
| 398 | →→¬¬𝜑→→𝜑¬𝜓¬𝜓→→¬¬𝜑→𝜑¬𝜓→¬¬𝜑¬𝜓 | Subs [𝜑↗¬¬𝜑, 𝜓↗→𝜑¬𝜓, 𝜒↗¬𝜓] into ax-2 | |
| 399 | →→¬¬𝜑→𝜑¬𝜓→¬¬𝜑¬𝜓 | Modus ponens 392, 398 | |
| 400 | →→→¬¬𝜑→𝜑¬𝜓→¬¬𝜑¬𝜓→→𝜑¬𝜓→→¬¬𝜑→𝜑¬𝜓→¬¬𝜑¬𝜓 | Subs [𝜑↗→→¬¬𝜑→𝜑¬𝜓→¬¬𝜑¬𝜓, 𝜓↗→𝜑¬𝜓] into ax-1 | |
| 401 | →→𝜑¬𝜓→→¬¬𝜑→𝜑¬𝜓→¬¬𝜑¬𝜓 | Modus ponens 399, 400 | |
| 402 | →→→𝜑¬𝜓→→¬¬𝜑→𝜑¬𝜓→¬¬𝜑¬𝜓→→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓→→𝜑¬𝜓→¬¬𝜑¬𝜓 | Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→¬¬𝜑→𝜑¬𝜓, 𝜒↗→¬¬𝜑¬𝜓] into ax-2 | |
| 403 | →→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓→→𝜑¬𝜓→¬¬𝜑¬𝜓 | Modus ponens 401, 402 | |
| 404 | →→𝜑¬𝜓→¬¬𝜑¬𝜓 | Modus ponens 393, 403 | |
| 405 | →→¬¬𝜑¬𝜓→𝜓¬𝜑 | Subs [𝜑↗¬𝜑] into ax-3 | |
| 406 | →→→¬¬𝜑¬𝜓→𝜓¬𝜑→→𝜑¬𝜓→→¬¬𝜑¬𝜓→𝜓¬𝜑 | Subs [𝜑↗→→¬¬𝜑¬𝜓→𝜓¬𝜑, 𝜓↗→𝜑¬𝜓] into ax-1 | |
| 407 | →→𝜑¬𝜓→→¬¬𝜑¬𝜓→𝜓¬𝜑 | Modus ponens 405, 406 | |
| 408 | →→→𝜑¬𝜓→→¬¬𝜑¬𝜓→𝜓¬𝜑→→→𝜑¬𝜓→¬¬𝜑¬𝜓→→𝜑¬𝜓→𝜓¬𝜑 | Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→¬¬𝜑¬𝜓, 𝜒↗→𝜓¬𝜑] into ax-2 | |
| 409 | →→→𝜑¬𝜓→¬¬𝜑¬𝜓→→𝜑¬𝜓→𝜓¬𝜑 | Modus ponens 407, 408 | |
| 410 | →→𝜑¬𝜓→𝜓¬𝜑 | Modus ponens 404, 409 | con2 |
| 411 | →→¬𝜑¬𝜑→𝜑→¬𝜑¬𝜑 | Subs [𝜑↗→¬𝜑¬𝜑, 𝜓↗𝜑] into ax-1 | |
| 412 | →𝜑→¬𝜑¬𝜑 | Modus ponens 310, 411 | |
| 413 | →¬¬¬𝜑¬𝜑 | Subs [𝜑↗¬𝜑] into notnotr | |
| 414 | →¬𝜑→𝜑¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗𝜑] into ax-1 | |
| 415 | →→¬𝜑→𝜑¬𝜑→¬¬¬𝜑→¬𝜑→𝜑¬𝜑 | Subs [𝜑↗→¬𝜑→𝜑¬𝜑, 𝜓↗¬¬¬𝜑] into ax-1 | |
| 416 | →¬¬¬𝜑→¬𝜑→𝜑¬𝜑 | Modus ponens 414, 415 | |
| 417 | →→¬¬¬𝜑→¬𝜑→𝜑¬𝜑→→¬¬¬𝜑¬𝜑→¬¬¬𝜑→𝜑¬𝜑 | Subs [𝜑↗¬¬¬𝜑, 𝜓↗¬𝜑, 𝜒↗→𝜑¬𝜑] into ax-2 | |
| 418 | →→¬¬¬𝜑¬𝜑→¬¬¬𝜑→𝜑¬𝜑 | Modus ponens 416, 417 | |
| 419 | →¬¬¬𝜑→𝜑¬𝜑 | Modus ponens 413, 418 | |
| 420 | →→𝜑→¬𝜑¬𝜑→→𝜑¬𝜑→𝜑¬𝜑 | Subs [𝜓↗¬𝜑, 𝜒↗¬𝜑] into ax-2 | |
| 421 | →→𝜑¬𝜑→𝜑¬𝜑 | Modus ponens 412, 420 | |
| 422 | →→→𝜑¬𝜑→𝜑¬𝜑→¬¬¬𝜑→→𝜑¬𝜑→𝜑¬𝜑 | Subs [𝜑↗→→𝜑¬𝜑→𝜑¬𝜑, 𝜓↗¬¬¬𝜑] into ax-1 | |
| 423 | →¬¬¬𝜑→→𝜑¬𝜑→𝜑¬𝜑 | Modus ponens 421, 422 | |
| 424 | →→¬¬¬𝜑→→𝜑¬𝜑→𝜑¬𝜑→→¬¬¬𝜑→𝜑¬𝜑→¬¬¬𝜑→𝜑¬𝜑 | Subs [𝜑↗¬¬¬𝜑, 𝜓↗→𝜑¬𝜑, 𝜒↗→𝜑¬𝜑] into ax-2 | |
| 425 | →→¬¬¬𝜑→𝜑¬𝜑→¬¬¬𝜑→𝜑¬𝜑 | Modus ponens 423, 424 | |
| 426 | →𝜑→¬¬¬𝜑𝜑 | Subs [𝜓↗¬¬¬𝜑] into ax-1 | |
| 427 | →→𝜑→¬¬¬𝜑𝜑→𝜑→𝜑→¬¬¬𝜑𝜑 | Subs [𝜑↗→𝜑→¬¬¬𝜑𝜑, 𝜓↗𝜑] into ax-1 | |
| 428 | →𝜑→𝜑→¬¬¬𝜑𝜑 | Modus ponens 426, 427 | |
| 429 | →→𝜑→𝜑→¬¬¬𝜑𝜑→→𝜑𝜑→𝜑→¬¬¬𝜑𝜑 | Subs [𝜓↗𝜑, 𝜒↗→¬¬¬𝜑𝜑] into ax-2 | |
| 430 | →→𝜑𝜑→𝜑→¬¬¬𝜑𝜑 | Modus ponens 428, 429 | |
| 431 | →→¬¬¬𝜑→𝜑¬𝜑→→¬¬¬𝜑𝜑→¬¬¬𝜑¬𝜑 | Subs [𝜑↗¬¬¬𝜑, 𝜓↗𝜑, 𝜒↗¬𝜑] into ax-2 | |
| 432 | →→¬¬¬𝜑𝜑→¬¬¬𝜑¬𝜑 | Modus ponens 419, 431 | |
| 433 | →→→¬¬¬𝜑𝜑→¬¬¬𝜑¬𝜑→𝜑→→¬¬¬𝜑𝜑→¬¬¬𝜑¬𝜑 | Subs [𝜑↗→→¬¬¬𝜑𝜑→¬¬¬𝜑¬𝜑, 𝜓↗𝜑] into ax-1 | |
| 434 | →𝜑→→¬¬¬𝜑𝜑→¬¬¬𝜑¬𝜑 | Modus ponens 432, 433 | |
| 435 | →→𝜑→→¬¬¬𝜑𝜑→¬¬¬𝜑¬𝜑→→𝜑→¬¬¬𝜑𝜑→𝜑→¬¬¬𝜑¬𝜑 | Subs [𝜓↗→¬¬¬𝜑𝜑, 𝜒↗→¬¬¬𝜑¬𝜑] into ax-2 | |
| 436 | →→𝜑→¬¬¬𝜑𝜑→𝜑→¬¬¬𝜑¬𝜑 | Modus ponens 434, 435 | |
| 437 | →𝜑→¬¬¬𝜑¬𝜑 | Modus ponens 426, 436 | |
| 438 | →→¬¬¬𝜑¬𝜑→𝜑¬¬𝜑 | Subs [𝜑↗¬¬𝜑, 𝜓↗𝜑] into ax-3 | |
| 439 | →→→¬¬¬𝜑¬𝜑→𝜑¬¬𝜑→𝜑→→¬¬¬𝜑¬𝜑→𝜑¬¬𝜑 | Subs [𝜑↗→→¬¬¬𝜑¬𝜑→𝜑¬¬𝜑, 𝜓↗𝜑] into ax-1 | |
| 440 | →𝜑→→¬¬¬𝜑¬𝜑→𝜑¬¬𝜑 | Modus ponens 438, 439 | |
| 441 | →→𝜑→→¬¬¬𝜑¬𝜑→𝜑¬¬𝜑→→𝜑→¬¬¬𝜑¬𝜑→𝜑→𝜑¬¬𝜑 | Subs [𝜓↗→¬¬¬𝜑¬𝜑, 𝜒↗→𝜑¬¬𝜑] into ax-2 | |
| 442 | →→𝜑→¬¬¬𝜑¬𝜑→𝜑→𝜑¬¬𝜑 | Modus ponens 440, 441 | |
| 443 | →𝜑→𝜑¬¬𝜑 | Modus ponens 437, 442 | |
| 444 | →→𝜑→𝜑¬¬𝜑→→𝜑𝜑→𝜑¬¬𝜑 | Subs [𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2 | |
| 445 | →→𝜑𝜑→𝜑¬¬𝜑 | Modus ponens 443, 444 | |
| 446 | →𝜑¬¬𝜑 | Modus ponens id, 445 | notnot |
| 447 | →→¬𝜑𝜓→¬𝜑𝜓 | Subs [𝜑↗→¬𝜑𝜓] into id | |
| 448 | →𝜓¬¬𝜓 | Subs [𝜑↗𝜓] into notnot | |
| 449 | →→𝜓¬¬𝜓→¬𝜑→𝜓¬¬𝜓 | Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 450 | →¬𝜑→𝜓¬¬𝜓 | Modus ponens 448, 449 | |
| 451 | →→¬𝜑→𝜓¬¬𝜓→→¬𝜑𝜓→¬𝜑¬¬𝜓 | Subs [𝜑↗¬𝜑, 𝜒↗¬¬𝜓] into ax-2 | |
| 452 | →→¬𝜑𝜓→¬𝜑¬¬𝜓 | Modus ponens 450, 451 | |
| 453 | →→→¬𝜑𝜓→¬𝜑¬¬𝜓→→¬𝜑𝜓→→¬𝜑𝜓→¬𝜑¬¬𝜓 | Subs [𝜑↗→→¬𝜑𝜓→¬𝜑¬¬𝜓, 𝜓↗→¬𝜑𝜓] into ax-1 | |
| 454 | →→¬𝜑𝜓→→¬𝜑𝜓→¬𝜑¬¬𝜓 | Modus ponens 452, 453 | |
| 455 | →→→¬𝜑𝜓→→¬𝜑𝜓→¬𝜑¬¬𝜓→→→¬𝜑𝜓→¬𝜑𝜓→→¬𝜑𝜓→¬𝜑¬¬𝜓 | Subs [𝜑↗→¬𝜑𝜓, 𝜓↗→¬𝜑𝜓, 𝜒↗→¬𝜑¬¬𝜓] into ax-2 | |
| 456 | →→→¬𝜑𝜓→¬𝜑𝜓→→¬𝜑𝜓→¬𝜑¬¬𝜓 | Modus ponens 454, 455 | |
| 457 | →→¬𝜑¬¬𝜓→¬𝜓𝜑 | Subs [𝜓↗¬𝜓] into ax-3 | |
| 458 | →→→¬𝜑¬¬𝜓→¬𝜓𝜑→→¬𝜑𝜓→→¬𝜑¬¬𝜓→¬𝜓𝜑 | Subs [𝜑↗→→¬𝜑¬¬𝜓→¬𝜓𝜑, 𝜓↗→¬𝜑𝜓] into ax-1 | |
| 459 | →→¬𝜑𝜓→→¬𝜑¬¬𝜓→¬𝜓𝜑 | Modus ponens 457, 458 | |
| 460 | →→→¬𝜑𝜓→→¬𝜑¬¬𝜓→¬𝜓𝜑→→→¬𝜑𝜓→¬𝜑¬¬𝜓→→¬𝜑𝜓→¬𝜓𝜑 | Subs [𝜑↗→¬𝜑𝜓, 𝜓↗→¬𝜑¬¬𝜓, 𝜒↗→¬𝜓𝜑] into ax-2 | |
| 461 | →→→¬𝜑𝜓→¬𝜑¬¬𝜓→→¬𝜑𝜓→¬𝜓𝜑 | Modus ponens 459, 460 | |
| 462 | →→¬𝜑𝜓→¬𝜓𝜑 | Modus ponens 452, 461 | con1 |
| 463 | →→𝜑→→𝜑𝜓𝜑→¬¬𝜑→𝜑→→𝜑𝜓𝜑 | Subs [𝜑↗→𝜑→→𝜑𝜓𝜑, 𝜓↗¬¬𝜑] into ax-1 | |
| 464 | →¬¬𝜑→𝜑→→𝜑𝜓𝜑 | Modus ponens 25, 463 | |
| 465 | →→¬¬𝜑→𝜑→→𝜑𝜓𝜑→→¬¬𝜑𝜑→¬¬𝜑→→𝜑𝜓𝜑 | Subs [𝜑↗¬¬𝜑, 𝜓↗𝜑, 𝜒↗→→𝜑𝜓𝜑] into ax-2 | |
| 466 | →→¬¬𝜑𝜑→¬¬𝜑→→𝜑𝜓𝜑 | Modus ponens 464, 465 | |
| 467 | →¬¬𝜑→→𝜑𝜓𝜑 | Modus ponens notnotr, 466 | |
| 468 | →→→→𝜑𝜓𝜑→→𝜑𝜓𝜓→¬¬𝜑→→→𝜑𝜓𝜑→→𝜑𝜓𝜓 | Subs [𝜑↗→→→𝜑𝜓𝜑→→𝜑𝜓𝜓, 𝜓↗¬¬𝜑] into ax-1 | |
| 469 | →¬¬𝜑→→→𝜑𝜓𝜑→→𝜑𝜓𝜓 | Modus ponens 31, 468 | |
| 470 | →→¬¬𝜑→→→𝜑𝜓𝜑→→𝜑𝜓𝜓→→¬¬𝜑→→𝜑𝜓𝜑→¬¬𝜑→→𝜑𝜓𝜓 | Subs [𝜑↗¬¬𝜑, 𝜓↗→→𝜑𝜓𝜑, 𝜒↗→→𝜑𝜓𝜓] into ax-2 | |
| 471 | →→¬¬𝜑→→𝜑𝜓𝜑→¬¬𝜑→→𝜑𝜓𝜓 | Modus ponens 469, 470 | |
| 472 | →¬¬𝜑→→𝜑𝜓𝜓 | Modus ponens 467, 471 | |
| 473 | →→𝜑𝜓→¬¬𝜑→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗¬¬𝜑] into ax-1 | |
| 474 | →→→𝜑𝜓→¬¬𝜑→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→¬¬𝜑→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→¬¬𝜑→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 475 | →→𝜑𝜓→→𝜑𝜓→¬¬𝜑→𝜑𝜓 | Modus ponens 473, 474 | |
| 476 | →→→𝜑𝜓→→𝜑𝜓→¬¬𝜑→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬𝜑→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→¬¬𝜑→𝜑𝜓] into ax-2 | |
| 477 | →→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬𝜑→𝜑𝜓 | Modus ponens 475, 476 | |
| 478 | →→¬¬𝜑→→𝜑𝜓𝜓→→¬¬𝜑→𝜑𝜓→¬¬𝜑𝜓 | Subs [𝜑↗¬¬𝜑, 𝜓↗→𝜑𝜓, 𝜒↗𝜓] into ax-2 | |
| 479 | →→¬¬𝜑→𝜑𝜓→¬¬𝜑𝜓 | Modus ponens 472, 478 | |
| 480 | →→→¬¬𝜑→𝜑𝜓→¬¬𝜑𝜓→→𝜑𝜓→→¬¬𝜑→𝜑𝜓→¬¬𝜑𝜓 | Subs [𝜑↗→→¬¬𝜑→𝜑𝜓→¬¬𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 481 | →→𝜑𝜓→→¬¬𝜑→𝜑𝜓→¬¬𝜑𝜓 | Modus ponens 479, 480 | |
| 482 | →→→𝜑𝜓→→¬¬𝜑→𝜑𝜓→¬¬𝜑𝜓→→→𝜑𝜓→¬¬𝜑→𝜑𝜓→→𝜑𝜓→¬¬𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬𝜑→𝜑𝜓, 𝜒↗→¬¬𝜑𝜓] into ax-2 | |
| 483 | →→→𝜑𝜓→¬¬𝜑→𝜑𝜓→→𝜑𝜓→¬¬𝜑𝜓 | Modus ponens 481, 482 | |
| 484 | →→𝜑𝜓→¬¬𝜑𝜓 | Modus ponens 473, 483 | |
| 485 | →→𝜓¬¬𝜓→¬¬𝜑→𝜓¬¬𝜓 | Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜑] into ax-1 | |
| 486 | →¬¬𝜑→𝜓¬¬𝜓 | Modus ponens 448, 485 | |
| 487 | →→¬¬𝜑→𝜓¬¬𝜓→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓 | Subs [𝜑↗¬¬𝜑, 𝜒↗¬¬𝜓] into ax-2 | |
| 488 | →→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓 | Modus ponens 486, 487 | |
| 489 | →→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓→→𝜑𝜓→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓 | Subs [𝜑↗→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 490 | →→𝜑𝜓→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓 | Modus ponens 488, 489 | |
| 491 | →→→𝜑𝜓→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓→→→𝜑𝜓→¬¬𝜑𝜓→→𝜑𝜓→¬¬𝜑¬¬𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬𝜑𝜓, 𝜒↗→¬¬𝜑¬¬𝜓] into ax-2 | |
| 492 | →→→𝜑𝜓→¬¬𝜑𝜓→→𝜑𝜓→¬¬𝜑¬¬𝜓 | Modus ponens 490, 491 | |
| 493 | →→𝜑𝜓→¬¬𝜑¬¬𝜓 | Modus ponens 484, 492 | |
| 494 | →→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓] into ax-3 | |
| 495 | →→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑→→𝜑𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑 | Subs [𝜑↗→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑, 𝜓↗→𝜑𝜓] into ax-1 | |
| 496 | →→𝜑𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑 | Modus ponens 494, 495 | |
| 497 | →→→𝜑𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑→→→𝜑𝜓→¬¬𝜑¬¬𝜓→→𝜑𝜓→¬𝜓¬𝜑 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬𝜑¬¬𝜓, 𝜒↗→¬𝜓¬𝜑] into ax-2 | |
| 498 | →→→𝜑𝜓→¬¬𝜑¬¬𝜓→→𝜑𝜓→¬𝜓¬𝜑 | Modus ponens 496, 497 | |
| 499 | →→𝜑𝜓→¬𝜓¬𝜑 | Modus ponens 493, 498 | con3 |
| 500 | →𝜑→→𝜑¬𝜓¬𝜓 | Subs [𝜓↗¬𝜓] into pm2.27 | |
| 501 | →¬¬→𝜑¬𝜓→𝜑¬𝜓 | Subs [𝜑↗→𝜑¬𝜓] into notnotr | |
| 502 | →→𝜑¬𝜓→𝜑→𝜑¬𝜓 | Subs [𝜑↗→𝜑¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 503 | →→→𝜑¬𝜓→𝜑→𝜑¬𝜓→¬¬→𝜑¬𝜓→→𝜑¬𝜓→𝜑→𝜑¬𝜓 | Subs [𝜑↗→→𝜑¬𝜓→𝜑→𝜑¬𝜓, 𝜓↗¬¬→𝜑¬𝜓] into ax-1 | |
| 504 | →¬¬→𝜑¬𝜓→→𝜑¬𝜓→𝜑→𝜑¬𝜓 | Modus ponens 502, 503 | |
| 505 | →→¬¬→𝜑¬𝜓→→𝜑¬𝜓→𝜑→𝜑¬𝜓→→¬¬→𝜑¬𝜓→𝜑¬𝜓→¬¬→𝜑¬𝜓→𝜑→𝜑¬𝜓 | Subs [𝜑↗¬¬→𝜑¬𝜓, 𝜓↗→𝜑¬𝜓, 𝜒↗→𝜑→𝜑¬𝜓] into ax-2 | |
| 506 | →→¬¬→𝜑¬𝜓→𝜑¬𝜓→¬¬→𝜑¬𝜓→𝜑→𝜑¬𝜓 | Modus ponens 504, 505 | |
| 507 | →¬¬→𝜑¬𝜓→𝜑→𝜑¬𝜓 | Modus ponens 501, 506 | |
| 508 | →→𝜑→→𝜑¬𝜓¬𝜓→→𝜑→𝜑¬𝜓→𝜑¬𝜓 | Subs [𝜓↗→𝜑¬𝜓, 𝜒↗¬𝜓] into ax-2 | |
| 509 | →→𝜑→𝜑¬𝜓→𝜑¬𝜓 | Modus ponens 500, 508 | |
| 510 | →→→𝜑→𝜑¬𝜓→𝜑¬𝜓→¬¬→𝜑¬𝜓→→𝜑→𝜑¬𝜓→𝜑¬𝜓 | Subs [𝜑↗→→𝜑→𝜑¬𝜓→𝜑¬𝜓, 𝜓↗¬¬→𝜑¬𝜓] into ax-1 | |
| 511 | →¬¬→𝜑¬𝜓→→𝜑→𝜑¬𝜓→𝜑¬𝜓 | Modus ponens 509, 510 | |
| 512 | →→¬¬→𝜑¬𝜓→→𝜑→𝜑¬𝜓→𝜑¬𝜓→→¬¬→𝜑¬𝜓→𝜑→𝜑¬𝜓→¬¬→𝜑¬𝜓→𝜑¬𝜓 | Subs [𝜑↗¬¬→𝜑¬𝜓, 𝜓↗→𝜑→𝜑¬𝜓, 𝜒↗→𝜑¬𝜓] into ax-2 | |
| 513 | →→¬¬→𝜑¬𝜓→𝜑→𝜑¬𝜓→¬¬→𝜑¬𝜓→𝜑¬𝜓 | Modus ponens 511, 512 | |
| 514 | →𝜑→¬¬→𝜑¬𝜓𝜑 | Subs [𝜓↗¬¬→𝜑¬𝜓] into ax-1 | |
| 515 | →→𝜑→¬¬→𝜑¬𝜓𝜑→𝜑→𝜑→¬¬→𝜑¬𝜓𝜑 | Subs [𝜑↗→𝜑→¬¬→𝜑¬𝜓𝜑, 𝜓↗𝜑] into ax-1 | |
| 516 | →𝜑→𝜑→¬¬→𝜑¬𝜓𝜑 | Modus ponens 514, 515 | |
| 517 | →→𝜑→𝜑→¬¬→𝜑¬𝜓𝜑→→𝜑𝜑→𝜑→¬¬→𝜑¬𝜓𝜑 | Subs [𝜓↗𝜑, 𝜒↗→¬¬→𝜑¬𝜓𝜑] into ax-2 | |
| 518 | →→𝜑𝜑→𝜑→¬¬→𝜑¬𝜓𝜑 | Modus ponens 516, 517 | |
| 519 | →→¬¬→𝜑¬𝜓→𝜑¬𝜓→→¬¬→𝜑¬𝜓𝜑→¬¬→𝜑¬𝜓¬𝜓 | Subs [𝜑↗¬¬→𝜑¬𝜓, 𝜓↗𝜑, 𝜒↗¬𝜓] into ax-2 | |
| 520 | →→¬¬→𝜑¬𝜓𝜑→¬¬→𝜑¬𝜓¬𝜓 | Modus ponens 501, 519 | |
| 521 | →→→¬¬→𝜑¬𝜓𝜑→¬¬→𝜑¬𝜓¬𝜓→𝜑→→¬¬→𝜑¬𝜓𝜑→¬¬→𝜑¬𝜓¬𝜓 | Subs [𝜑↗→→¬¬→𝜑¬𝜓𝜑→¬¬→𝜑¬𝜓¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 522 | →𝜑→→¬¬→𝜑¬𝜓𝜑→¬¬→𝜑¬𝜓¬𝜓 | Modus ponens 520, 521 | |
| 523 | →→𝜑→→¬¬→𝜑¬𝜓𝜑→¬¬→𝜑¬𝜓¬𝜓→→𝜑→¬¬→𝜑¬𝜓𝜑→𝜑→¬¬→𝜑¬𝜓¬𝜓 | Subs [𝜓↗→¬¬→𝜑¬𝜓𝜑, 𝜒↗→¬¬→𝜑¬𝜓¬𝜓] into ax-2 | |
| 524 | →→𝜑→¬¬→𝜑¬𝜓𝜑→𝜑→¬¬→𝜑¬𝜓¬𝜓 | Modus ponens 522, 523 | |
| 525 | →𝜑→¬¬→𝜑¬𝜓¬𝜓 | Modus ponens 514, 524 | |
| 526 | →→¬¬→𝜑¬𝜓¬𝜓→𝜓¬→𝜑¬𝜓 | Subs [𝜑↗¬→𝜑¬𝜓] into ax-3 | |
| 527 | →→→¬¬→𝜑¬𝜓¬𝜓→𝜓¬→𝜑¬𝜓→𝜑→→¬¬→𝜑¬𝜓¬𝜓→𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→→¬¬→𝜑¬𝜓¬𝜓→𝜓¬→𝜑¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 528 | →𝜑→→¬¬→𝜑¬𝜓¬𝜓→𝜓¬→𝜑¬𝜓 | Modus ponens 526, 527 | |
| 529 | →→𝜑→→¬¬→𝜑¬𝜓¬𝜓→𝜓¬→𝜑¬𝜓→→𝜑→¬¬→𝜑¬𝜓¬𝜓→𝜑→𝜓¬→𝜑¬𝜓 | Subs [𝜓↗→¬¬→𝜑¬𝜓¬𝜓, 𝜒↗→𝜓¬→𝜑¬𝜓] into ax-2 | |
| 530 | →→𝜑→¬¬→𝜑¬𝜓¬𝜓→𝜑→𝜓¬→𝜑¬𝜓 | Modus ponens 528, 529 | |
| 531 | →𝜑→𝜓¬→𝜑¬𝜓 | Modus ponens 525, 530 | pm3.2im |
| 532 | →¬¬→𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓] into notnotr | |
| 533 | →→𝜑𝜓→𝜑→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 534 | →→→𝜑𝜓→𝜑→𝜑𝜓→¬¬→𝜑𝜓→→𝜑𝜓→𝜑→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→𝜑→𝜑𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1 | |
| 535 | →¬¬→𝜑𝜓→→𝜑𝜓→𝜑→𝜑𝜓 | Modus ponens 533, 534 | |
| 536 | →→¬¬→𝜑𝜓→→𝜑𝜓→𝜑→𝜑𝜓→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→𝜑→𝜑𝜓 | Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑→𝜑𝜓] into ax-2 | |
| 537 | →→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→𝜑→𝜑𝜓 | Modus ponens 535, 536 | |
| 538 | →¬¬→𝜑𝜓→𝜑→𝜑𝜓 | Modus ponens 532, 537 | |
| 539 | →→→𝜑→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→→𝜑→𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→→𝜑→𝜑𝜓→𝜑𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1 | |
| 540 | →¬¬→𝜑𝜓→→𝜑→𝜑𝜓→𝜑𝜓 | Modus ponens pm2.43, 539 | |
| 541 | →→¬¬→𝜑𝜓→→𝜑→𝜑𝜓→𝜑𝜓→→¬¬→𝜑𝜓→𝜑→𝜑𝜓→¬¬→𝜑𝜓→𝜑𝜓 | Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑→𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2 | |
| 542 | →→¬¬→𝜑𝜓→𝜑→𝜑𝜓→¬¬→𝜑𝜓→𝜑𝜓 | Modus ponens 540, 541 | |
| 543 | →𝜑→¬¬→𝜑𝜓𝜑 | Subs [𝜓↗¬¬→𝜑𝜓] into ax-1 | |
| 544 | →→𝜑→¬¬→𝜑𝜓𝜑→𝜑→𝜑→¬¬→𝜑𝜓𝜑 | Subs [𝜑↗→𝜑→¬¬→𝜑𝜓𝜑, 𝜓↗𝜑] into ax-1 | |
| 545 | →𝜑→𝜑→¬¬→𝜑𝜓𝜑 | Modus ponens 543, 544 | |
| 546 | →→𝜑→𝜑→¬¬→𝜑𝜓𝜑→→𝜑𝜑→𝜑→¬¬→𝜑𝜓𝜑 | Subs [𝜓↗𝜑, 𝜒↗→¬¬→𝜑𝜓𝜑] into ax-2 | |
| 547 | →→𝜑𝜑→𝜑→¬¬→𝜑𝜓𝜑 | Modus ponens 545, 546 | |
| 548 | →→¬¬→𝜑𝜓→𝜑𝜓→→¬¬→𝜑𝜓𝜑→¬¬→𝜑𝜓𝜓 | Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2 | |
| 549 | →→¬¬→𝜑𝜓𝜑→¬¬→𝜑𝜓𝜓 | Modus ponens 532, 548 | |
| 550 | →→→¬¬→𝜑𝜓𝜑→¬¬→𝜑𝜓𝜓→𝜑→→¬¬→𝜑𝜓𝜑→¬¬→𝜑𝜓𝜓 | Subs [𝜑↗→→¬¬→𝜑𝜓𝜑→¬¬→𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1 | |
| 551 | →𝜑→→¬¬→𝜑𝜓𝜑→¬¬→𝜑𝜓𝜓 | Modus ponens 549, 550 | |
| 552 | →→𝜑→→¬¬→𝜑𝜓𝜑→¬¬→𝜑𝜓𝜓→→𝜑→¬¬→𝜑𝜓𝜑→𝜑→¬¬→𝜑𝜓𝜓 | Subs [𝜓↗→¬¬→𝜑𝜓𝜑, 𝜒↗→¬¬→𝜑𝜓𝜓] into ax-2 | |
| 553 | →→𝜑→¬¬→𝜑𝜓𝜑→𝜑→¬¬→𝜑𝜓𝜓 | Modus ponens 551, 552 | |
| 554 | →𝜑→¬¬→𝜑𝜓𝜓 | Modus ponens 543, 553 | |
| 555 | →→𝜓¬¬𝜓→¬¬→𝜑𝜓→𝜓¬¬𝜓 | Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1 | |
| 556 | →¬¬→𝜑𝜓→𝜓¬¬𝜓 | Modus ponens 448, 555 | |
| 557 | →→¬¬→𝜑𝜓→𝜓¬¬𝜓→→¬¬→𝜑𝜓𝜓→¬¬→𝜑𝜓¬¬𝜓 | Subs [𝜑↗¬¬→𝜑𝜓, 𝜒↗¬¬𝜓] into ax-2 | |
| 558 | →→¬¬→𝜑𝜓𝜓→¬¬→𝜑𝜓¬¬𝜓 | Modus ponens 556, 557 | |
| 559 | →→→¬¬→𝜑𝜓𝜓→¬¬→𝜑𝜓¬¬𝜓→𝜑→→¬¬→𝜑𝜓𝜓→¬¬→𝜑𝜓¬¬𝜓 | Subs [𝜑↗→→¬¬→𝜑𝜓𝜓→¬¬→𝜑𝜓¬¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 560 | →𝜑→→¬¬→𝜑𝜓𝜓→¬¬→𝜑𝜓¬¬𝜓 | Modus ponens 558, 559 | |
| 561 | →→𝜑→→¬¬→𝜑𝜓𝜓→¬¬→𝜑𝜓¬¬𝜓→→𝜑→¬¬→𝜑𝜓𝜓→𝜑→¬¬→𝜑𝜓¬¬𝜓 | Subs [𝜓↗→¬¬→𝜑𝜓𝜓, 𝜒↗→¬¬→𝜑𝜓¬¬𝜓] into ax-2 | |
| 562 | →→𝜑→¬¬→𝜑𝜓𝜓→𝜑→¬¬→𝜑𝜓¬¬𝜓 | Modus ponens 560, 561 | |
| 563 | →𝜑→¬¬→𝜑𝜓¬¬𝜓 | Modus ponens 554, 562 | |
| 564 | →→¬¬→𝜑𝜓¬¬𝜓→¬𝜓¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬𝜓] into ax-3 | |
| 565 | →→→¬¬→𝜑𝜓¬¬𝜓→¬𝜓¬→𝜑𝜓→𝜑→→¬¬→𝜑𝜓¬¬𝜓→¬𝜓¬→𝜑𝜓 | Subs [𝜑↗→→¬¬→𝜑𝜓¬¬𝜓→¬𝜓¬→𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 566 | →𝜑→→¬¬→𝜑𝜓¬¬𝜓→¬𝜓¬→𝜑𝜓 | Modus ponens 564, 565 | |
| 567 | →→𝜑→→¬¬→𝜑𝜓¬¬𝜓→¬𝜓¬→𝜑𝜓→→𝜑→¬¬→𝜑𝜓¬¬𝜓→𝜑→¬𝜓¬→𝜑𝜓 | Subs [𝜓↗→¬¬→𝜑𝜓¬¬𝜓, 𝜒↗→¬𝜓¬→𝜑𝜓] into ax-2 | |
| 568 | →→𝜑→¬¬→𝜑𝜓¬¬𝜓→𝜑→¬𝜓¬→𝜑𝜓 | Modus ponens 566, 567 | |
| 569 | →𝜑→¬𝜓¬→𝜑𝜓 | Modus ponens 563, 568 | jcn |
| 570 | →¬¬𝜓𝜓 | Subs [𝜑↗𝜓] into notnotr | |
| 571 | →→𝜓→𝜑𝜓→¬¬𝜓→𝜓→𝜑𝜓 | Subs [𝜑↗→𝜓→𝜑𝜓, 𝜓↗¬¬𝜓] into ax-1 | |
| 572 | →¬¬𝜓→𝜓→𝜑𝜓 | Modus ponens 208, 571 | |
| 573 | →→¬¬𝜓→𝜓→𝜑𝜓→→¬¬𝜓𝜓→¬¬𝜓→𝜑𝜓 | Subs [𝜑↗¬¬𝜓, 𝜒↗→𝜑𝜓] into ax-2 | |
| 574 | →→¬¬𝜓𝜓→¬¬𝜓→𝜑𝜓 | Modus ponens 572, 573 | |
| 575 | →¬¬𝜓→𝜑𝜓 | Modus ponens 570, 574 | |
| 576 | →→𝜑→𝜓𝜓→→𝜑𝜓→𝜑𝜓 | Subs [𝜒↗𝜓] into ax-2 | |
| 577 | →→→𝜑𝜓→𝜑𝜓→¬¬𝜓→→𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→𝜑𝜓, 𝜓↗¬¬𝜓] into ax-1 | |
| 578 | →¬¬𝜓→→𝜑𝜓→𝜑𝜓 | Modus ponens 24, 577 | |
| 579 | →→¬¬𝜓→→𝜑𝜓→𝜑𝜓→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑𝜓 | Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2 | |
| 580 | →→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑𝜓 | Modus ponens 578, 579 | |
| 581 | →𝜑→¬¬𝜓𝜑 | Subs [𝜓↗¬¬𝜓] into ax-1 | |
| 582 | →→𝜑→¬¬𝜓𝜑→𝜑→𝜑→¬¬𝜓𝜑 | Subs [𝜑↗→𝜑→¬¬𝜓𝜑, 𝜓↗𝜑] into ax-1 | |
| 583 | →𝜑→𝜑→¬¬𝜓𝜑 | Modus ponens 581, 582 | |
| 584 | →→𝜑→𝜑→¬¬𝜓𝜑→→𝜑𝜑→𝜑→¬¬𝜓𝜑 | Subs [𝜓↗𝜑, 𝜒↗→¬¬𝜓𝜑] into ax-2 | |
| 585 | →→𝜑𝜑→𝜑→¬¬𝜓𝜑 | Modus ponens 583, 584 | |
| 586 | →→¬¬𝜓→𝜑𝜓→→¬¬𝜓𝜑→¬¬𝜓𝜓 | Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2 | |
| 587 | →→¬¬𝜓𝜑→¬¬𝜓𝜓 | Modus ponens 575, 586 | |
| 588 | →→→¬¬𝜓𝜑→¬¬𝜓𝜓→𝜑→→¬¬𝜓𝜑→¬¬𝜓𝜓 | Subs [𝜑↗→→¬¬𝜓𝜑→¬¬𝜓𝜓, 𝜓↗𝜑] into ax-1 | |
| 589 | →𝜑→→¬¬𝜓𝜑→¬¬𝜓𝜓 | Modus ponens 587, 588 | |
| 590 | →→𝜑→→¬¬𝜓𝜑→¬¬𝜓𝜓→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓𝜓 | Subs [𝜓↗→¬¬𝜓𝜑, 𝜒↗→¬¬𝜓𝜓] into ax-2 | |
| 591 | →→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓𝜓 | Modus ponens 589, 590 | |
| 592 | →𝜑→¬¬𝜓𝜓 | Modus ponens 581, 591 | |
| 593 | →→𝜓¬¬𝜓→¬¬𝜓→𝜓¬¬𝜓 | Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜓] into ax-1 | |
| 594 | →¬¬𝜓→𝜓¬¬𝜓 | Modus ponens 448, 593 | |
| 595 | →→¬¬𝜓→𝜓¬¬𝜓→→¬¬𝜓𝜓→¬¬𝜓¬¬𝜓 | Subs [𝜑↗¬¬𝜓, 𝜒↗¬¬𝜓] into ax-2 | |
| 596 | →→¬¬𝜓𝜓→¬¬𝜓¬¬𝜓 | Modus ponens 594, 595 | |
| 597 | →→→¬¬𝜓𝜓→¬¬𝜓¬¬𝜓→𝜑→→¬¬𝜓𝜓→¬¬𝜓¬¬𝜓 | Subs [𝜑↗→→¬¬𝜓𝜓→¬¬𝜓¬¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 598 | →𝜑→→¬¬𝜓𝜓→¬¬𝜓¬¬𝜓 | Modus ponens 596, 597 | |
| 599 | →→𝜑→→¬¬𝜓𝜓→¬¬𝜓¬¬𝜓→→𝜑→¬¬𝜓𝜓→𝜑→¬¬𝜓¬¬𝜓 | Subs [𝜓↗→¬¬𝜓𝜓, 𝜒↗→¬¬𝜓¬¬𝜓] into ax-2 | |
| 600 | →→𝜑→¬¬𝜓𝜓→𝜑→¬¬𝜓¬¬𝜓 | Modus ponens 598, 599 | |
| 601 | →𝜑→¬¬𝜓¬¬𝜓 | Modus ponens 592, 600 | |
| 602 | →→¬¬𝜓¬¬𝜓→¬𝜓¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓] into ax-3 | |
| 603 | →→→¬¬𝜓¬¬𝜓→¬𝜓¬𝜓→𝜑→→¬¬𝜓¬¬𝜓→¬𝜓¬𝜓 | Subs [𝜑↗→→¬¬𝜓¬¬𝜓→¬𝜓¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 604 | →𝜑→→¬¬𝜓¬¬𝜓→¬𝜓¬𝜓 | Modus ponens 602, 603 | |
| 605 | →→𝜑→→¬¬𝜓¬¬𝜓→¬𝜓¬𝜓→→𝜑→¬¬𝜓¬¬𝜓→𝜑→¬𝜓¬𝜓 | Subs [𝜓↗→¬¬𝜓¬¬𝜓, 𝜒↗→¬𝜓¬𝜓] into ax-2 | |
| 606 | →→𝜑→¬¬𝜓¬¬𝜓→𝜑→¬𝜓¬𝜓 | Modus ponens 604, 605 | |
| 607 | →𝜑→¬𝜓¬𝜓 | Modus ponens 601, 606 | |
| 608 | →¬𝜓¬𝜓 | Subs [𝜑↗¬𝜓] into id | |
| 609 | →¬𝜓→𝜑¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 610 | →→¬𝜓→𝜑¬𝜓→¬𝜓→¬𝜓→𝜑¬𝜓 | Subs [𝜑↗→¬𝜓→𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 611 | →¬𝜓→¬𝜓→𝜑¬𝜓 | Modus ponens 609, 610 | |
| 612 | →→¬𝜓→¬𝜓→𝜑¬𝜓→→¬𝜓¬𝜓→¬𝜓→𝜑¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→𝜑¬𝜓] into ax-2 | |
| 613 | →→¬𝜓¬𝜓→¬𝜓→𝜑¬𝜓 | Modus ponens 611, 612 | |
| 614 | →→𝜑→¬𝜓¬𝜓→→𝜑¬𝜓→𝜑¬𝜓 | Subs [𝜓↗¬𝜓, 𝜒↗¬𝜓] into ax-2 | |
| 615 | →→→𝜑¬𝜓→𝜑¬𝜓→¬𝜓→→𝜑¬𝜓→𝜑¬𝜓 | Subs [𝜑↗→→𝜑¬𝜓→𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 616 | →¬𝜓→→𝜑¬𝜓→𝜑¬𝜓 | Modus ponens 379, 615 | |
| 617 | →→¬𝜓→→𝜑¬𝜓→𝜑¬𝜓→→¬𝜓→𝜑¬𝜓→¬𝜓→𝜑¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗→𝜑¬𝜓, 𝜒↗→𝜑¬𝜓] into ax-2 | |
| 618 | →→¬𝜓→𝜑¬𝜓→¬𝜓→𝜑¬𝜓 | Modus ponens 616, 617 | |
| 619 | →¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗¬→𝜑¬𝜓] into id | |
| 620 | →→¬→𝜑¬𝜓¬→𝜑¬𝜓→¬𝜓→¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 621 | →¬𝜓→¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 619, 620 | |
| 622 | →¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗¬→𝜑¬𝜓] into notnotr | |
| 623 | →¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 624 | →→¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1 | |
| 625 | →¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓 | Modus ponens 623, 624 | |
| 626 | →→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→¬𝜓¬→𝜑¬𝜓] into ax-2 | |
| 627 | →→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓 | Modus ponens 625, 626 | |
| 628 | →¬¬¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓 | Modus ponens 622, 627 | |
| 629 | →→¬𝜓→¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬𝜓¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗¬→𝜑¬𝜓] into ax-2 | |
| 630 | →→¬𝜓¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓 | Modus ponens 621, 629 | |
| 631 | →→→¬𝜓¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→→¬𝜓¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→→¬𝜓¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1 | |
| 632 | →¬¬¬→𝜑¬𝜓→→¬𝜓¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓 | Modus ponens 630, 631 | |
| 633 | →→¬¬¬→𝜑¬𝜓→→¬𝜓¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗→¬𝜓¬→𝜑¬𝜓, 𝜒↗→¬𝜓¬→𝜑¬𝜓] into ax-2 | |
| 634 | →→¬¬¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓 | Modus ponens 632, 633 | |
| 635 | →¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1 | |
| 636 | →→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓→¬𝜓→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 637 | →¬𝜓→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓 | Modus ponens 635, 636 | |
| 638 | →→¬𝜓→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→𝜑¬𝜓¬𝜓] into ax-2 | |
| 639 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓 | Modus ponens 637, 638 | |
| 640 | →→¬¬¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬𝜓, 𝜒↗¬→𝜑¬𝜓] into ax-2 | |
| 641 | →→¬¬¬→𝜑¬𝜓¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 628, 640 | |
| 642 | →→→¬¬¬→𝜑¬𝜓¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬𝜓→→¬¬¬→𝜑¬𝜓¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 643 | →¬𝜓→→¬¬¬→𝜑¬𝜓¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 641, 642 | |
| 644 | →→¬𝜓→→¬¬¬→𝜑¬𝜓¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜑¬𝜓¬𝜓, 𝜒↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓] into ax-2 | |
| 645 | →→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 643, 644 | |
| 646 | →¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 635, 645 | |
| 647 | →→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Subs [𝜑↗¬¬→𝜑¬𝜓, 𝜓↗→𝜑¬𝜓] into ax-3 | |
| 648 | →→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 649 | →¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Modus ponens 647, 648 | |
| 650 | →→¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜒↗→→𝜑¬𝜓¬¬→𝜑¬𝜓] into ax-2 | |
| 651 | →→¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Modus ponens 649, 650 | |
| 652 | →¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Modus ponens 646, 651 | |
| 653 | →→¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬𝜓→𝜑¬𝜓→¬𝜓¬¬→𝜑¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗→𝜑¬𝜓, 𝜒↗¬¬→𝜑¬𝜓] into ax-2 | |
| 654 | →→¬𝜓→𝜑¬𝜓→¬𝜓¬¬→𝜑¬𝜓 | Modus ponens 652, 653 | |
| 655 | →¬𝜓¬¬→𝜑¬𝜓 | Modus ponens 609, 654 | |
| 656 | →→¬𝜓¬¬→𝜑¬𝜓→¬→𝜑¬𝜓𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→𝜑¬𝜓] into ax-3 | |
| 657 | →¬→𝜑¬𝜓𝜓 | Modus ponens 655, 656 | simprim |
| 658 | →¬→𝜑𝜓¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓] into id | |
| 659 | →→¬→𝜑𝜓¬→𝜑𝜓→¬𝜑→¬→𝜑𝜓¬→𝜑𝜓 | Subs [𝜑↗→¬→𝜑𝜓¬→𝜑𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 660 | →¬𝜑→¬→𝜑𝜓¬→𝜑𝜓 | Modus ponens 658, 659 | |
| 661 | →¬¬¬→𝜑𝜓¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓] into notnotr | |
| 662 | →¬→𝜑𝜓→¬𝜑¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 663 | →→¬→𝜑𝜓→¬𝜑¬→𝜑𝜓→¬¬¬→𝜑𝜓→¬→𝜑𝜓→¬𝜑¬→𝜑𝜓 | Subs [𝜑↗→¬→𝜑𝜓→¬𝜑¬→𝜑𝜓, 𝜓↗¬¬¬→𝜑𝜓] into ax-1 | |
| 664 | →¬¬¬→𝜑𝜓→¬→𝜑𝜓→¬𝜑¬→𝜑𝜓 | Modus ponens 662, 663 | |
| 665 | →→¬¬¬→𝜑𝜓→¬→𝜑𝜓→¬𝜑¬→𝜑𝜓→→¬¬¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜑𝜓→¬𝜑¬→𝜑𝜓 | Subs [𝜑↗¬¬¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗→¬𝜑¬→𝜑𝜓] into ax-2 | |
| 666 | →→¬¬¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜑𝜓→¬𝜑¬→𝜑𝜓 | Modus ponens 664, 665 | |
| 667 | →¬¬¬→𝜑𝜓→¬𝜑¬→𝜑𝜓 | Modus ponens 661, 666 | |
| 668 | →→¬𝜑→¬→𝜑𝜓¬→𝜑𝜓→→¬𝜑¬→𝜑𝜓→¬𝜑¬→𝜑𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗¬→𝜑𝜓, 𝜒↗¬→𝜑𝜓] into ax-2 | |
| 669 | →→¬𝜑¬→𝜑𝜓→¬𝜑¬→𝜑𝜓 | Modus ponens 660, 668 | |
| 670 | →→→¬𝜑¬→𝜑𝜓→¬𝜑¬→𝜑𝜓→¬¬¬→𝜑𝜓→→¬𝜑¬→𝜑𝜓→¬𝜑¬→𝜑𝜓 | Subs [𝜑↗→→¬𝜑¬→𝜑𝜓→¬𝜑¬→𝜑𝜓, 𝜓↗¬¬¬→𝜑𝜓] into ax-1 | |
| 671 | →¬¬¬→𝜑𝜓→→¬𝜑¬→𝜑𝜓→¬𝜑¬→𝜑𝜓 | Modus ponens 669, 670 | |
| 672 | →→¬¬¬→𝜑𝜓→→¬𝜑¬→𝜑𝜓→¬𝜑¬→𝜑𝜓→→¬¬¬→𝜑𝜓→¬𝜑¬→𝜑𝜓→¬¬¬→𝜑𝜓→¬𝜑¬→𝜑𝜓 | Subs [𝜑↗¬¬¬→𝜑𝜓, 𝜓↗→¬𝜑¬→𝜑𝜓, 𝜒↗→¬𝜑¬→𝜑𝜓] into ax-2 | |
| 673 | →→¬¬¬→𝜑𝜓→¬𝜑¬→𝜑𝜓→¬¬¬→𝜑𝜓→¬𝜑¬→𝜑𝜓 | Modus ponens 671, 672 | |
| 674 | →¬𝜑→¬¬¬→𝜑𝜓¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→𝜑𝜓] into ax-1 | |
| 675 | →→¬𝜑→¬¬¬→𝜑𝜓¬𝜑→¬𝜑→¬𝜑→¬¬¬→𝜑𝜓¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬→𝜑𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 676 | →¬𝜑→¬𝜑→¬¬¬→𝜑𝜓¬𝜑 | Modus ponens 674, 675 | |
| 677 | →→¬𝜑→¬𝜑→¬¬¬→𝜑𝜓¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→𝜑𝜓¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→𝜑𝜓¬𝜑] into ax-2 | |
| 678 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬→𝜑𝜓¬𝜑 | Modus ponens 676, 677 | |
| 679 | →→¬¬¬→𝜑𝜓→¬𝜑¬→𝜑𝜓→→¬¬¬→𝜑𝜓¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓 | Subs [𝜑↗¬¬¬→𝜑𝜓, 𝜓↗¬𝜑, 𝜒↗¬→𝜑𝜓] into ax-2 | |
| 680 | →→¬¬¬→𝜑𝜓¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓 | Modus ponens 667, 679 | |
| 681 | →→→¬¬¬→𝜑𝜓¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓→¬𝜑→→¬¬¬→𝜑𝜓¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓 | Subs [𝜑↗→→¬¬¬→𝜑𝜓¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 682 | →¬𝜑→→¬¬¬→𝜑𝜓¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓 | Modus ponens 680, 681 | |
| 683 | →→¬𝜑→→¬¬¬→𝜑𝜓¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓→→¬𝜑→¬¬¬→𝜑𝜓¬𝜑→¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→𝜑𝜓¬𝜑, 𝜒↗→¬¬¬→𝜑𝜓¬→𝜑𝜓] into ax-2 | |
| 684 | →→¬𝜑→¬¬¬→𝜑𝜓¬𝜑→¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓 | Modus ponens 682, 683 | |
| 685 | →¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓 | Modus ponens 674, 684 | |
| 686 | →→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓 | Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-3 | |
| 687 | →→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓→¬𝜑→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓 | Subs [𝜑↗→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 688 | →¬𝜑→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓 | Modus ponens 686, 687 | |
| 689 | →→¬𝜑→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓→→¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓→¬𝜑→→𝜑𝜓¬¬→𝜑𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→𝜑𝜓¬→𝜑𝜓, 𝜒↗→→𝜑𝜓¬¬→𝜑𝜓] into ax-2 | |
| 690 | →→¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓→¬𝜑→→𝜑𝜓¬¬→𝜑𝜓 | Modus ponens 688, 689 | |
| 691 | →¬𝜑→→𝜑𝜓¬¬→𝜑𝜓 | Modus ponens 685, 690 | |
| 692 | →→¬𝜑→→𝜑𝜓¬¬→𝜑𝜓→→¬𝜑→𝜑𝜓→¬𝜑¬¬→𝜑𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗→𝜑𝜓, 𝜒↗¬¬→𝜑𝜓] into ax-2 | |
| 693 | →→¬𝜑→𝜑𝜓→¬𝜑¬¬→𝜑𝜓 | Modus ponens 691, 692 | |
| 694 | →¬𝜑¬¬→𝜑𝜓 | Modus ponens pm2.21, 693 | |
| 695 | →→¬𝜑¬¬→𝜑𝜓→¬→𝜑𝜓𝜑 | Subs [𝜓↗¬→𝜑𝜓] into ax-3 | |
| 696 | →¬→𝜑𝜓𝜑 | Modus ponens 694, 695 | simplim |
| 697 | →𝜑→¬𝜒𝜑 | Subs [𝜓↗¬𝜒] into ax-1 | |
| 698 | →→𝜑→¬𝜒𝜑→¬→𝜑𝜓→𝜑→¬𝜒𝜑 | Subs [𝜑↗→𝜑→¬𝜒𝜑, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 699 | →¬→𝜑𝜓→𝜑→¬𝜒𝜑 | Modus ponens 697, 698 | |
| 700 | →→¬→𝜑𝜓→𝜑→¬𝜒𝜑→→¬→𝜑𝜓𝜑→¬→𝜑𝜓→¬𝜒𝜑 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗𝜑, 𝜒↗→¬𝜒𝜑] into ax-2 | |
| 701 | →→¬→𝜑𝜓𝜑→¬→𝜑𝜓→¬𝜒𝜑 | Modus ponens 699, 700 | |
| 702 | →¬→𝜑𝜓→¬𝜒𝜑 | Modus ponens simplim, 701 | |
| 703 | →→𝜑¬¬𝜑→¬𝜒→𝜑¬¬𝜑 | Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬𝜒] into ax-1 | |
| 704 | →¬𝜒→𝜑¬¬𝜑 | Modus ponens notnot, 703 | |
| 705 | →→¬𝜒→𝜑¬¬𝜑→→¬𝜒𝜑→¬𝜒¬¬𝜑 | Subs [𝜑↗¬𝜒, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2 | |
| 706 | →→¬𝜒𝜑→¬𝜒¬¬𝜑 | Modus ponens 704, 705 | |
| 707 | →→→¬𝜒𝜑→¬𝜒¬¬𝜑→¬→𝜑𝜓→→¬𝜒𝜑→¬𝜒¬¬𝜑 | Subs [𝜑↗→→¬𝜒𝜑→¬𝜒¬¬𝜑, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 708 | →¬→𝜑𝜓→→¬𝜒𝜑→¬𝜒¬¬𝜑 | Modus ponens 706, 707 | |
| 709 | →→¬→𝜑𝜓→→¬𝜒𝜑→¬𝜒¬¬𝜑→→¬→𝜑𝜓→¬𝜒𝜑→¬→𝜑𝜓→¬𝜒¬¬𝜑 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬𝜒𝜑, 𝜒↗→¬𝜒¬¬𝜑] into ax-2 | |
| 710 | →→¬→𝜑𝜓→¬𝜒𝜑→¬→𝜑𝜓→¬𝜒¬¬𝜑 | Modus ponens 708, 709 | |
| 711 | →¬→𝜑𝜓→¬𝜒¬¬𝜑 | Modus ponens 702, 710 | |
| 712 | →→¬𝜒¬¬𝜑→¬𝜑𝜒 | Subs [𝜑↗𝜒, 𝜓↗¬𝜑] into ax-3 | |
| 713 | →→→¬𝜒¬¬𝜑→¬𝜑𝜒→¬→𝜑𝜓→→¬𝜒¬¬𝜑→¬𝜑𝜒 | Subs [𝜑↗→→¬𝜒¬¬𝜑→¬𝜑𝜒, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 714 | →¬→𝜑𝜓→→¬𝜒¬¬𝜑→¬𝜑𝜒 | Modus ponens 712, 713 | |
| 715 | →→¬→𝜑𝜓→→¬𝜒¬¬𝜑→¬𝜑𝜒→→¬→𝜑𝜓→¬𝜒¬¬𝜑→¬→𝜑𝜓→¬𝜑𝜒 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬𝜒¬¬𝜑, 𝜒↗→¬𝜑𝜒] into ax-2 | |
| 716 | →→¬→𝜑𝜓→¬𝜒¬¬𝜑→¬→𝜑𝜓→¬𝜑𝜒 | Modus ponens 714, 715 | |
| 717 | →¬→𝜑𝜓→¬𝜑𝜒 | Modus ponens 711, 716 | pm2.5g |
| 718 | →¬→𝜑𝜓→¬𝜑𝜓 | Subs [𝜒↗𝜓] into pm2.5g | pm2.5 |
| 719 | →→¬→𝜑𝜓¬→𝜑𝜓→𝜓→¬→𝜑𝜓¬→𝜑𝜓 | Subs [𝜑↗→¬→𝜑𝜓¬→𝜑𝜓] into ax-1 | |
| 720 | →𝜓→¬→𝜑𝜓¬→𝜑𝜓 | Modus ponens 658, 719 | |
| 721 | →¬→𝜑𝜓→𝜓¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓] into ax-1 | |
| 722 | →→¬→𝜑𝜓→𝜓¬→𝜑𝜓→¬¬¬→𝜑𝜓→¬→𝜑𝜓→𝜓¬→𝜑𝜓 | Subs [𝜑↗→¬→𝜑𝜓→𝜓¬→𝜑𝜓, 𝜓↗¬¬¬→𝜑𝜓] into ax-1 | |
| 723 | →¬¬¬→𝜑𝜓→¬→𝜑𝜓→𝜓¬→𝜑𝜓 | Modus ponens 721, 722 | |
| 724 | →→¬¬¬→𝜑𝜓→¬→𝜑𝜓→𝜓¬→𝜑𝜓→→¬¬¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜑𝜓→𝜓¬→𝜑𝜓 | Subs [𝜑↗¬¬¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗→𝜓¬→𝜑𝜓] into ax-2 | |
| 725 | →→¬¬¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜑𝜓→𝜓¬→𝜑𝜓 | Modus ponens 723, 724 | |
| 726 | →¬¬¬→𝜑𝜓→𝜓¬→𝜑𝜓 | Modus ponens 661, 725 | |
| 727 | →→𝜓→¬→𝜑𝜓¬→𝜑𝜓→→𝜓¬→𝜑𝜓→𝜓¬→𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗¬→𝜑𝜓] into ax-2 | |
| 728 | →→𝜓¬→𝜑𝜓→𝜓¬→𝜑𝜓 | Modus ponens 720, 727 | |
| 729 | →→→𝜓¬→𝜑𝜓→𝜓¬→𝜑𝜓→¬¬¬→𝜑𝜓→→𝜓¬→𝜑𝜓→𝜓¬→𝜑𝜓 | Subs [𝜑↗→→𝜓¬→𝜑𝜓→𝜓¬→𝜑𝜓, 𝜓↗¬¬¬→𝜑𝜓] into ax-1 | |
| 730 | →¬¬¬→𝜑𝜓→→𝜓¬→𝜑𝜓→𝜓¬→𝜑𝜓 | Modus ponens 728, 729 | |
| 731 | →→¬¬¬→𝜑𝜓→→𝜓¬→𝜑𝜓→𝜓¬→𝜑𝜓→→¬¬¬→𝜑𝜓→𝜓¬→𝜑𝜓→¬¬¬→𝜑𝜓→𝜓¬→𝜑𝜓 | Subs [𝜑↗¬¬¬→𝜑𝜓, 𝜓↗→𝜓¬→𝜑𝜓, 𝜒↗→𝜓¬→𝜑𝜓] into ax-2 | |
| 732 | →→¬¬¬→𝜑𝜓→𝜓¬→𝜑𝜓→¬¬¬→𝜑𝜓→𝜓¬→𝜑𝜓 | Modus ponens 730, 731 | |
| 733 | →𝜓→¬¬¬→𝜑𝜓𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬¬¬→𝜑𝜓] into ax-1 | |
| 734 | →→𝜓→¬¬¬→𝜑𝜓𝜓→𝜓→𝜓→¬¬¬→𝜑𝜓𝜓 | Subs [𝜑↗→𝜓→¬¬¬→𝜑𝜓𝜓] into ax-1 | |
| 735 | →𝜓→𝜓→¬¬¬→𝜑𝜓𝜓 | Modus ponens 733, 734 | |
| 736 | →→𝜓→𝜓→¬¬¬→𝜑𝜓𝜓→→𝜓𝜓→𝜓→¬¬¬→𝜑𝜓𝜓 | Subs [𝜑↗𝜓, 𝜒↗→¬¬¬→𝜑𝜓𝜓] into ax-2 | |
| 737 | →→𝜓𝜓→𝜓→¬¬¬→𝜑𝜓𝜓 | Modus ponens 735, 736 | |
| 738 | →→¬¬¬→𝜑𝜓→𝜓¬→𝜑𝜓→→¬¬¬→𝜑𝜓𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓 | Subs [𝜑↗¬¬¬→𝜑𝜓, 𝜒↗¬→𝜑𝜓] into ax-2 | |
| 739 | →→¬¬¬→𝜑𝜓𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓 | Modus ponens 726, 738 | |
| 740 | →→→¬¬¬→𝜑𝜓𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓→𝜓→→¬¬¬→𝜑𝜓𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓 | Subs [𝜑↗→→¬¬¬→𝜑𝜓𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓] into ax-1 | |
| 741 | →𝜓→→¬¬¬→𝜑𝜓𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓 | Modus ponens 739, 740 | |
| 742 | →→𝜓→→¬¬¬→𝜑𝜓𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜓→¬¬¬→𝜑𝜓𝜓→𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗→¬¬¬→𝜑𝜓𝜓, 𝜒↗→¬¬¬→𝜑𝜓¬→𝜑𝜓] into ax-2 | |
| 743 | →→𝜓→¬¬¬→𝜑𝜓𝜓→𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓 | Modus ponens 741, 742 | |
| 744 | →𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓 | Modus ponens 733, 743 | |
| 745 | →→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓→𝜓→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓 | Subs [𝜑↗→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓] into ax-1 | |
| 746 | →𝜓→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓 | Modus ponens 686, 745 | |
| 747 | →→𝜓→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓→→𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓→𝜓→→𝜑𝜓¬¬→𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗→¬¬¬→𝜑𝜓¬→𝜑𝜓, 𝜒↗→→𝜑𝜓¬¬→𝜑𝜓] into ax-2 | |
| 748 | →→𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓→𝜓→→𝜑𝜓¬¬→𝜑𝜓 | Modus ponens 746, 747 | |
| 749 | →𝜓→→𝜑𝜓¬¬→𝜑𝜓 | Modus ponens 744, 748 | |
| 750 | →→𝜓→→𝜑𝜓¬¬→𝜑𝜓→→𝜓→𝜑𝜓→𝜓¬¬→𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗→𝜑𝜓, 𝜒↗¬¬→𝜑𝜓] into ax-2 | |
| 751 | →→𝜓→𝜑𝜓→𝜓¬¬→𝜑𝜓 | Modus ponens 749, 750 | |
| 752 | →𝜓¬¬→𝜑𝜓 | Modus ponens 208, 751 | |
| 753 | →→𝜓¬¬→𝜑𝜓→¬→𝜑𝜓→𝜓¬¬→𝜑𝜓 | Subs [𝜑↗→𝜓¬¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 754 | →¬→𝜑𝜓→𝜓¬¬→𝜑𝜓 | Modus ponens 752, 753 | |
| 755 | →𝜓→¬→𝜑𝜓𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 756 | →→𝜓→¬→𝜑𝜓𝜓→¬¬𝜓→𝜓→¬→𝜑𝜓𝜓 | Subs [𝜑↗→𝜓→¬→𝜑𝜓𝜓, 𝜓↗¬¬𝜓] into ax-1 | |
| 757 | →¬¬𝜓→𝜓→¬→𝜑𝜓𝜓 | Modus ponens 755, 756 | |
| 758 | →→¬¬𝜓→𝜓→¬→𝜑𝜓𝜓→→¬¬𝜓𝜓→¬¬𝜓→¬→𝜑𝜓𝜓 | Subs [𝜑↗¬¬𝜓, 𝜒↗→¬→𝜑𝜓𝜓] into ax-2 | |
| 759 | →→¬¬𝜓𝜓→¬¬𝜓→¬→𝜑𝜓𝜓 | Modus ponens 757, 758 | |
| 760 | →¬¬𝜓→¬→𝜑𝜓𝜓 | Modus ponens 570, 759 | |
| 761 | →→¬→𝜑𝜓→𝜓¬¬→𝜑𝜓→→¬→𝜑𝜓𝜓→¬→𝜑𝜓¬¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜒↗¬¬→𝜑𝜓] into ax-2 | |
| 762 | →→¬→𝜑𝜓𝜓→¬→𝜑𝜓¬¬→𝜑𝜓 | Modus ponens 754, 761 | |
| 763 | →→→¬→𝜑𝜓𝜓→¬→𝜑𝜓¬¬→𝜑𝜓→¬¬𝜓→→¬→𝜑𝜓𝜓→¬→𝜑𝜓¬¬→𝜑𝜓 | Subs [𝜑↗→→¬→𝜑𝜓𝜓→¬→𝜑𝜓¬¬→𝜑𝜓, 𝜓↗¬¬𝜓] into ax-1 | |
| 764 | →¬¬𝜓→→¬→𝜑𝜓𝜓→¬→𝜑𝜓¬¬→𝜑𝜓 | Modus ponens 762, 763 | |
| 765 | →→¬¬𝜓→→¬→𝜑𝜓𝜓→¬→𝜑𝜓¬¬→𝜑𝜓→→¬¬𝜓→¬→𝜑𝜓𝜓→¬¬𝜓→¬→𝜑𝜓¬¬→𝜑𝜓 | Subs [𝜑↗¬¬𝜓, 𝜓↗→¬→𝜑𝜓𝜓, 𝜒↗→¬→𝜑𝜓¬¬→𝜑𝜓] into ax-2 | |
| 766 | →→¬¬𝜓→¬→𝜑𝜓𝜓→¬¬𝜓→¬→𝜑𝜓¬¬→𝜑𝜓 | Modus ponens 764, 765 | |
| 767 | →¬¬𝜓→¬→𝜑𝜓¬¬→𝜑𝜓 | Modus ponens 760, 766 | |
| 768 | →¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬¬𝜓] into ax-1 | |
| 769 | →→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓 | Subs [𝜑↗→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 770 | →¬→𝜑𝜓→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓 | Modus ponens 768, 769 | |
| 771 | →→¬→𝜑𝜓→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗→¬¬𝜓¬→𝜑𝜓] into ax-2 | |
| 772 | →→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓 | Modus ponens 770, 771 | |
| 773 | →→¬¬𝜓→¬→𝜑𝜓¬¬→𝜑𝜓→→¬¬𝜓¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓 | Subs [𝜑↗¬¬𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗¬¬→𝜑𝜓] into ax-2 | |
| 774 | →→¬¬𝜓¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓 | Modus ponens 767, 773 | |
| 775 | →→→¬¬𝜓¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓→→¬¬𝜓¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓 | Subs [𝜑↗→→¬¬𝜓¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 776 | →¬→𝜑𝜓→→¬¬𝜓¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓 | Modus ponens 774, 775 | |
| 777 | →→¬→𝜑𝜓→→¬¬𝜓¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓→→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬¬𝜓¬→𝜑𝜓, 𝜒↗→¬¬𝜓¬¬→𝜑𝜓] into ax-2 | |
| 778 | →→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓 | Modus ponens 776, 777 | |
| 779 | →¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓 | Modus ponens 768, 778 | |
| 780 | →→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬→𝜑𝜓] into ax-3 | |
| 781 | →→→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜓→¬→𝜑𝜓→→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜓 | Subs [𝜑↗→→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜓, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 782 | →¬→𝜑𝜓→→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜓 | Modus ponens 780, 781 | |
| 783 | →→¬→𝜑𝜓→→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜓→→¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓→¬→𝜑𝜓¬𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬¬𝜓¬¬→𝜑𝜓, 𝜒↗→¬→𝜑𝜓¬𝜓] into ax-2 | |
| 784 | →→¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓→¬→𝜑𝜓¬𝜓 | Modus ponens 782, 783 | |
| 785 | →¬→𝜑𝜓→¬→𝜑𝜓¬𝜓 | Modus ponens 779, 784 | |
| 786 | →→¬→𝜑𝜓→¬→𝜑𝜓¬𝜓→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓¬𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗¬𝜓] into ax-2 | |
| 787 | →→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓¬𝜓 | Modus ponens 785, 786 | |
| 788 | →¬→𝜑𝜓¬𝜓 | Modus ponens 658, 787 | conax1 |
| 789 | →¬𝜓→𝜒¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗𝜒] into ax-1 | |
| 790 | →→¬𝜓→𝜒¬𝜓→¬→𝜑𝜓→¬𝜓→𝜒¬𝜓 | Subs [𝜑↗→¬𝜓→𝜒¬𝜓, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 791 | →¬→𝜑𝜓→¬𝜓→𝜒¬𝜓 | Modus ponens 789, 790 | |
| 792 | →→¬→𝜑𝜓→¬𝜓→𝜒¬𝜓→→¬→𝜑𝜓¬𝜓→¬→𝜑𝜓→𝜒¬𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬𝜓, 𝜒↗→𝜒¬𝜓] into ax-2 | |
| 793 | →→¬→𝜑𝜓¬𝜓→¬→𝜑𝜓→𝜒¬𝜓 | Modus ponens 791, 792 | |
| 794 | →¬→𝜑𝜓→𝜒¬𝜓 | Modus ponens conax1, 793 | conax1k |
| 795 | →¬→𝜑𝜓→𝜑¬𝜓 | Subs [𝜒↗𝜑] into conax1k | pm2.51 |
| 796 | →¬→𝜑𝜓→¬𝜑¬𝜓 | Subs [𝜒↗¬𝜑] into conax1k | pm2.52 |
| 797 | →¬𝜓→¬𝜒¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜒] into ax-1 | |
| 798 | →→¬𝜓→¬𝜒¬𝜓→¬→𝜑𝜓→¬𝜓→¬𝜒¬𝜓 | Subs [𝜑↗→¬𝜓→¬𝜒¬𝜓, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 799 | →¬→𝜑𝜓→¬𝜓→¬𝜒¬𝜓 | Modus ponens 797, 798 | |
| 800 | →→¬→𝜑𝜓→¬𝜓→¬𝜒¬𝜓→→¬→𝜑𝜓¬𝜓→¬→𝜑𝜓→¬𝜒¬𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬𝜓, 𝜒↗→¬𝜒¬𝜓] into ax-2 | |
| 801 | →→¬→𝜑𝜓¬𝜓→¬→𝜑𝜓→¬𝜒¬𝜓 | Modus ponens 799, 800 | |
| 802 | →¬→𝜑𝜓→¬𝜒¬𝜓 | Modus ponens conax1, 801 | |
| 803 | →→¬𝜒¬𝜓→𝜓𝜒 | Subs [𝜑↗𝜒] into ax-3 | |
| 804 | →→→¬𝜒¬𝜓→𝜓𝜒→¬→𝜑𝜓→→¬𝜒¬𝜓→𝜓𝜒 | Subs [𝜑↗→→¬𝜒¬𝜓→𝜓𝜒, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 805 | →¬→𝜑𝜓→→¬𝜒¬𝜓→𝜓𝜒 | Modus ponens 803, 804 | |
| 806 | →→¬→𝜑𝜓→→¬𝜒¬𝜓→𝜓𝜒→→¬→𝜑𝜓→¬𝜒¬𝜓→¬→𝜑𝜓→𝜓𝜒 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬𝜒¬𝜓, 𝜒↗→𝜓𝜒] into ax-2 | |
| 807 | →→¬→𝜑𝜓→¬𝜒¬𝜓→¬→𝜑𝜓→𝜓𝜒 | Modus ponens 805, 806 | |
| 808 | →¬→𝜑𝜓→𝜓𝜒 | Modus ponens 802, 807 | pm2.521g |
| 809 | →→𝜑→𝜒𝜑→¬→𝜑𝜓→𝜑→𝜒𝜑 | Subs [𝜑↗→𝜑→𝜒𝜑, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 810 | →¬→𝜑𝜓→𝜑→𝜒𝜑 | Modus ponens 13, 809 | |
| 811 | →→¬→𝜑𝜓→𝜑→𝜒𝜑→→¬→𝜑𝜓𝜑→¬→𝜑𝜓→𝜒𝜑 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗𝜑, 𝜒↗→𝜒𝜑] into ax-2 | |
| 812 | →→¬→𝜑𝜓𝜑→¬→𝜑𝜓→𝜒𝜑 | Modus ponens 810, 811 | |
| 813 | →¬→𝜑𝜓→𝜒𝜑 | Modus ponens simplim, 812 | pm2.521g2 |
| 814 | →¬→𝜑𝜓→𝜓𝜑 | Subs [𝜒↗𝜑] into pm2.521g | pm2.521 |
| 815 | →𝜑→𝜒𝜒 | Subs [𝜓↗𝜒] into idd | |
| 816 | →→𝜒𝜒→¬→𝜑¬𝜓→𝜒𝜒 | Subs [𝜑↗→𝜒𝜒, 𝜓↗¬→𝜑¬𝜓] into ax-1 | |
| 817 | →→→𝜒𝜒→¬→𝜑¬𝜓→𝜒𝜒→𝜑→→𝜒𝜒→¬→𝜑¬𝜓→𝜒𝜒 | Subs [𝜑↗→→𝜒𝜒→¬→𝜑¬𝜓→𝜒𝜒, 𝜓↗𝜑] into ax-1 | |
| 818 | →𝜑→→𝜒𝜒→¬→𝜑¬𝜓→𝜒𝜒 | Modus ponens 816, 817 | |
| 819 | →→𝜑→→𝜒𝜒→¬→𝜑¬𝜓→𝜒𝜒→→𝜑→𝜒𝜒→𝜑→¬→𝜑¬𝜓→𝜒𝜒 | Subs [𝜓↗→𝜒𝜒, 𝜒↗→¬→𝜑¬𝜓→𝜒𝜒] into ax-2 | |
| 820 | →→𝜑→𝜒𝜒→𝜑→¬→𝜑¬𝜓→𝜒𝜒 | Modus ponens 818, 819 | |
| 821 | →𝜑→¬→𝜑¬𝜓→𝜒𝜒 | Modus ponens 815, 820 | |
| 822 | →→¬→𝜑¬𝜓→𝜒𝜒→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒 | Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗𝜒] into ax-2 | |
| 823 | →→→¬→𝜑¬𝜓→𝜒𝜒→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→𝜑→→¬→𝜑¬𝜓→𝜒𝜒→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒 | Subs [𝜑↗→→¬→𝜑¬𝜓→𝜒𝜒→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 824 | →𝜑→→¬→𝜑¬𝜓→𝜒𝜒→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒 | Modus ponens 822, 823 | |
| 825 | →→𝜑→→¬→𝜑¬𝜓→𝜒𝜒→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→𝜑→¬→𝜑¬𝜓→𝜒𝜒→𝜑→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒 | Subs [𝜓↗→¬→𝜑¬𝜓→𝜒𝜒, 𝜒↗→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒] into ax-2 | |
| 826 | →→𝜑→¬→𝜑¬𝜓→𝜒𝜒→𝜑→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒 | Modus ponens 824, 825 | |
| 827 | →𝜑→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒 | Modus ponens 821, 826 | |
| 828 | →→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→𝜓¬→𝜑¬𝜓, 𝜓↗→¬→𝜑¬𝜓𝜒] into ax-1 | |
| 829 | →→→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→𝜑→→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 830 | →𝜑→→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓 | Modus ponens 828, 829 | |
| 831 | →→𝜑→→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓 | Subs [𝜓↗→𝜓¬→𝜑¬𝜓, 𝜒↗→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓] into ax-2 | |
| 832 | →→𝜑→𝜓¬→𝜑¬𝜓→𝜑→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓 | Modus ponens 830, 831 | |
| 833 | →𝜑→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓 | Modus ponens pm3.2im, 832 | |
| 834 | →→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒 | Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗𝜒, 𝜒↗𝜓] into imim2 | |
| 835 | →→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒 | Subs [𝜑↗→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒, 𝜓↗→¬→𝜑¬𝜓𝜒] into ax-1 | |
| 836 | →→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒 | Modus ponens 834, 835 | |
| 837 | →→→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒 | Subs [𝜑↗→¬→𝜑¬𝜓𝜒, 𝜓↗→¬→𝜑¬𝜓𝜒, 𝜒↗→→𝜓¬→𝜑¬𝜓→𝜓𝜒] into ax-2 | |
| 838 | →→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒 | Modus ponens 836, 837 | |
| 839 | →→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→𝜑→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒 | Subs [𝜑↗→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 840 | →𝜑→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒 | Modus ponens 838, 839 | |
| 841 | →→𝜑→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→𝜑→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→𝜑→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒 | Subs [𝜓↗→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒, 𝜒↗→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒] into ax-2 | |
| 842 | →→𝜑→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→𝜑→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒 | Modus ponens 840, 841 | |
| 843 | →𝜑→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒 | Modus ponens 827, 842 | |
| 844 | →→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒 | Subs [𝜑↗→¬→𝜑¬𝜓𝜒, 𝜓↗→𝜓¬→𝜑¬𝜓, 𝜒↗→𝜓𝜒] into ax-2 | |
| 845 | →→→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒→𝜑→→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒 | Subs [𝜑↗→→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 846 | →𝜑→→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒 | Modus ponens 844, 845 | |
| 847 | →→𝜑→→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒→→𝜑→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→𝜑→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒 | Subs [𝜓↗→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒, 𝜒↗→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒] into ax-2 | |
| 848 | →→𝜑→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→𝜑→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒 | Modus ponens 846, 847 | |
| 849 | →𝜑→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒 | Modus ponens 843, 848 | |
| 850 | →→𝜑→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒→→𝜑→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→𝜑→→¬→𝜑¬𝜓𝜒→𝜓𝜒 | Subs [𝜓↗→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓, 𝜒↗→→¬→𝜑¬𝜓𝜒→𝜓𝜒] into ax-2 | |
| 851 | →→𝜑→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→𝜑→→¬→𝜑¬𝜓𝜒→𝜓𝜒 | Modus ponens 849, 850 | |
| 852 | →𝜑→→¬→𝜑¬𝜓𝜒→𝜓𝜒 | Modus ponens 833, 851 | |
| 853 | →→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒 | Subs [𝜑↗→¬→𝜑¬𝜓𝜒] into id | |
| 854 | →→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒 | Subs [𝜑↗→¬→𝜑¬𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 855 | →→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒 | Subs [𝜑↗→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒, 𝜓↗→¬→𝜑¬𝜓𝜒] into ax-1 | |
| 856 | →→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒 | Modus ponens 854, 855 | |
| 857 | →→→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒 | Subs [𝜑↗→¬→𝜑¬𝜓𝜒, 𝜓↗→¬→𝜑¬𝜓𝜒, 𝜒↗→𝜑→¬→𝜑¬𝜓𝜒] into ax-2 | |
| 858 | →→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒 | Modus ponens 856, 857 | |
| 859 | →→𝜑→→¬→𝜑¬𝜓𝜒→𝜓𝜒→→𝜑→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒 | Subs [𝜓↗→¬→𝜑¬𝜓𝜒, 𝜒↗→𝜓𝜒] into ax-2 | |
| 860 | →→𝜑→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒 | Modus ponens 852, 859 | |
| 861 | →→→𝜑→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜑→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒 | Subs [𝜑↗→→𝜑→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒, 𝜓↗→¬→𝜑¬𝜓𝜒] into ax-1 | |
| 862 | →→¬→𝜑¬𝜓𝜒→→𝜑→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒 | Modus ponens 860, 861 | |
| 863 | →→→¬→𝜑¬𝜓𝜒→→𝜑→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒→→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒 | Subs [𝜑↗→¬→𝜑¬𝜓𝜒, 𝜓↗→𝜑→¬→𝜑¬𝜓𝜒, 𝜒↗→𝜑→𝜓𝜒] into ax-2 | |
| 864 | →→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒 | Modus ponens 862, 863 | |
| 865 | →→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒 | Modus ponens 854, 864 | expt |
| 866 | →¬→𝜑¬𝜓𝜑 | Subs [𝜓↗¬𝜓] into simplim | |
| 867 | →→𝜓𝜒→𝜓𝜒 | Subs [𝜑↗→𝜓𝜒] into id | |
| 868 | →→→𝜓𝜒→𝜓𝜒→𝜑→→𝜓𝜒→𝜓𝜒 | Subs [𝜑↗→→𝜓𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 869 | →𝜑→→𝜓𝜒→𝜓𝜒 | Modus ponens 867, 868 | |
| 870 | →→𝜑→→𝜓𝜒→𝜓𝜒→→𝜑→𝜓𝜒→𝜑→𝜓𝜒 | Subs [𝜓↗→𝜓𝜒, 𝜒↗→𝜓𝜒] into ax-2 | |
| 871 | →𝜑→→𝜑→𝜓𝜒𝜑 | Subs [𝜓↗→𝜑→𝜓𝜒] into ax-1 | |
| 872 | →→𝜑→→𝜑→𝜓𝜒𝜑→¬→𝜑¬𝜓→𝜑→→𝜑→𝜓𝜒𝜑 | Subs [𝜑↗→𝜑→→𝜑→𝜓𝜒𝜑, 𝜓↗¬→𝜑¬𝜓] into ax-1 | |
| 873 | →¬→𝜑¬𝜓→𝜑→→𝜑→𝜓𝜒𝜑 | Modus ponens 871, 872 | |
| 874 | →→¬→𝜑¬𝜓→𝜑→→𝜑→𝜓𝜒𝜑→→¬→𝜑¬𝜓𝜑→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜑 | Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗𝜑, 𝜒↗→→𝜑→𝜓𝜒𝜑] into ax-2 | |
| 875 | →→¬→𝜑¬𝜓𝜑→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜑 | Modus ponens 873, 874 | |
| 876 | →¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜑 | Modus ponens 866, 875 | |
| 877 | →→→𝜑→𝜓𝜒→𝜑→𝜓𝜒→→→𝜑→𝜓𝜒𝜑→→𝜑→𝜓𝜒→𝜓𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗𝜑, 𝜒↗→𝜓𝜒] into ax-2 | |
| 878 | →→→𝜑→𝜓𝜒𝜑→→𝜑→𝜓𝜒→𝜓𝜒 | Modus ponens 139, 877 | |
| 879 | →→→→𝜑→𝜓𝜒𝜑→→𝜑→𝜓𝜒→𝜓𝜒→¬→𝜑¬𝜓→→→𝜑→𝜓𝜒𝜑→→𝜑→𝜓𝜒→𝜓𝜒 | Subs [𝜑↗→→→𝜑→𝜓𝜒𝜑→→𝜑→𝜓𝜒→𝜓𝜒, 𝜓↗¬→𝜑¬𝜓] into ax-1 | |
| 880 | →¬→𝜑¬𝜓→→→𝜑→𝜓𝜒𝜑→→𝜑→𝜓𝜒→𝜓𝜒 | Modus ponens 878, 879 | |
| 881 | →→¬→𝜑¬𝜓→→→𝜑→𝜓𝜒𝜑→→𝜑→𝜓𝜒→𝜓𝜒→→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜑→¬→𝜑¬𝜓→→𝜑→𝜓𝜒→𝜓𝜒 | Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗→→𝜑→𝜓𝜒𝜑, 𝜒↗→→𝜑→𝜓𝜒→𝜓𝜒] into ax-2 | |
| 882 | →→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜑→¬→𝜑¬𝜓→→𝜑→𝜓𝜒→𝜓𝜒 | Modus ponens 880, 881 | |
| 883 | →¬→𝜑¬𝜓→→𝜑→𝜓𝜒→𝜓𝜒 | Modus ponens 876, 882 | |
| 884 | →→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗¬→𝜑¬𝜓] into ax-1 | |
| 885 | →→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒 | Subs [𝜑↗→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1 | |
| 886 | →→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒 | Modus ponens 884, 885 | |
| 887 | →→→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒→→→𝜑→𝜓𝜒→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→¬→𝜑¬𝜓→𝜑→𝜓𝜒] into ax-2 | |
| 888 | →→→𝜑→𝜓𝜒→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒 | Modus ponens 886, 887 | |
| 889 | →→¬→𝜑¬𝜓→→𝜑→𝜓𝜒→𝜓𝜒→→¬→𝜑¬𝜓→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒 | Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→𝜓𝜒] into ax-2 | |
| 890 | →→¬→𝜑¬𝜓→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒 | Modus ponens 883, 889 | |
| 891 | →→→¬→𝜑¬𝜓→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒 | Subs [𝜑↗→→¬→𝜑¬𝜓→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1 | |
| 892 | →→𝜑→𝜓𝜒→→¬→𝜑¬𝜓→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒 | Modus ponens 890, 891 | |
| 893 | →→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒→→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→¬→𝜑¬𝜓→𝜑→𝜓𝜒, 𝜒↗→¬→𝜑¬𝜓→𝜓𝜒] into ax-2 | |
| 894 | →→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒 | Modus ponens 892, 893 | |
| 895 | →→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒 | Modus ponens 884, 894 | |
| 896 | →→¬→𝜑¬𝜓𝜓→→𝜑→𝜓𝜒→¬→𝜑¬𝜓𝜓 | Subs [𝜑↗→¬→𝜑¬𝜓𝜓, 𝜓↗→𝜑→𝜓𝜒] into ax-1 | |
| 897 | →→𝜑→𝜓𝜒→¬→𝜑¬𝜓𝜓 | Modus ponens simprim, 896 | |
| 898 | →→¬→𝜑¬𝜓→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒 | Subs [𝜑↗¬→𝜑¬𝜓] into ax-2 | |
| 899 | →→→¬→𝜑¬𝜓→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒 | Subs [𝜑↗→→¬→𝜑¬𝜓→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1 | |
| 900 | →→𝜑→𝜓𝜒→→¬→𝜑¬𝜓→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒 | Modus ponens 898, 899 | |
| 901 | →→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒→→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→¬→𝜑¬𝜓→𝜓𝜒, 𝜒↗→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒] into ax-2 | |
| 902 | →→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒 | Modus ponens 900, 901 | |
| 903 | →→𝜑→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒 | Modus ponens 895, 902 | |
| 904 | →→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒→→→𝜑→𝜓𝜒→¬→𝜑¬𝜓𝜓→→𝜑→𝜓𝜒→¬→𝜑¬𝜓𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→¬→𝜑¬𝜓𝜓, 𝜒↗→¬→𝜑¬𝜓𝜒] into ax-2 | |
| 905 | →→→𝜑→𝜓𝜒→¬→𝜑¬𝜓𝜓→→𝜑→𝜓𝜒→¬→𝜑¬𝜓𝜒 | Modus ponens 903, 904 | |
| 906 | →→𝜑→𝜓𝜒→¬→𝜑¬𝜓𝜒 | Modus ponens 897, 905 | impt |
| 907 | →→¬𝜑¬𝜑→→𝜑¬𝜑→¬𝜑¬𝜑 | Subs [𝜑↗→¬𝜑¬𝜑, 𝜓↗→𝜑¬𝜑] into ax-1 | |
| 908 | →→𝜑¬𝜑→¬𝜑¬𝜑 | Modus ponens 310, 907 | |
| 909 | →¬𝜑¬¬¬𝜑 | Subs [𝜑↗¬𝜑] into notnot | |
| 910 | →→¬𝜑¬¬¬𝜑→¬𝜑→¬𝜑¬¬¬𝜑 | Subs [𝜑↗→¬𝜑¬¬¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 911 | →¬𝜑→¬𝜑¬¬¬𝜑 | Modus ponens 909, 910 | |
| 912 | →→¬𝜑→¬𝜑¬¬¬𝜑→→¬𝜑¬𝜑→¬𝜑¬¬¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗¬¬¬𝜑] into ax-2 | |
| 913 | →→¬𝜑¬𝜑→¬𝜑¬¬¬𝜑 | Modus ponens 911, 912 | |
| 914 | →→→¬𝜑¬𝜑→¬𝜑¬¬¬𝜑→→𝜑¬𝜑→→¬𝜑¬𝜑→¬𝜑¬¬¬𝜑 | Subs [𝜑↗→→¬𝜑¬𝜑→¬𝜑¬¬¬𝜑, 𝜓↗→𝜑¬𝜑] into ax-1 | |
| 915 | →→𝜑¬𝜑→→¬𝜑¬𝜑→¬𝜑¬¬¬𝜑 | Modus ponens 913, 914 | |
| 916 | →→→𝜑¬𝜑→→¬𝜑¬𝜑→¬𝜑¬¬¬𝜑→→→𝜑¬𝜑→¬𝜑¬𝜑→→𝜑¬𝜑→¬𝜑¬¬¬𝜑 | Subs [𝜑↗→𝜑¬𝜑, 𝜓↗→¬𝜑¬𝜑, 𝜒↗→¬𝜑¬¬¬𝜑] into ax-2 | |
| 917 | →→→𝜑¬𝜑→¬𝜑¬𝜑→→𝜑¬𝜑→¬𝜑¬¬¬𝜑 | Modus ponens 915, 916 | |
| 918 | →→𝜑¬𝜑→¬𝜑¬¬¬𝜑 | Modus ponens 908, 917 | |
| 919 | →→¬𝜑¬¬¬𝜑→¬¬𝜑𝜑 | Subs [𝜓↗¬¬𝜑] into ax-3 | |
| 920 | →→→¬𝜑¬¬¬𝜑→¬¬𝜑𝜑→→𝜑¬𝜑→→¬𝜑¬¬¬𝜑→¬¬𝜑𝜑 | Subs [𝜑↗→→¬𝜑¬¬¬𝜑→¬¬𝜑𝜑, 𝜓↗→𝜑¬𝜑] into ax-1 | |
| 921 | →→𝜑¬𝜑→→¬𝜑¬¬¬𝜑→¬¬𝜑𝜑 | Modus ponens 919, 920 | |
| 922 | →→→𝜑¬𝜑→→¬𝜑¬¬¬𝜑→¬¬𝜑𝜑→→→𝜑¬𝜑→¬𝜑¬¬¬𝜑→→𝜑¬𝜑→¬¬𝜑𝜑 | Subs [𝜑↗→𝜑¬𝜑, 𝜓↗→¬𝜑¬¬¬𝜑, 𝜒↗→¬¬𝜑𝜑] into ax-2 | |
| 923 | →→→𝜑¬𝜑→¬𝜑¬¬¬𝜑→→𝜑¬𝜑→¬¬𝜑𝜑 | Modus ponens 921, 922 | |
| 924 | →→𝜑¬𝜑→¬¬𝜑𝜑 | Modus ponens 918, 923 | |
| 925 | →→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑 | Subs [𝜑↗→𝜑¬𝜑, 𝜓↗¬¬𝜑] into ax-1 | |
| 926 | →→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑→→𝜑¬𝜑→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑 | Subs [𝜑↗→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑, 𝜓↗→𝜑¬𝜑] into ax-1 | |
| 927 | →→𝜑¬𝜑→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑 | Modus ponens 925, 926 | |
| 928 | →→→𝜑¬𝜑→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑→→→𝜑¬𝜑→𝜑¬𝜑→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑 | Subs [𝜑↗→𝜑¬𝜑, 𝜓↗→𝜑¬𝜑, 𝜒↗→¬¬𝜑→𝜑¬𝜑] into ax-2 | |
| 929 | →→→𝜑¬𝜑→𝜑¬𝜑→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑 | Modus ponens 927, 928 | |
| 930 | →→¬¬𝜑→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑 | Subs [𝜑↗¬¬𝜑, 𝜓↗𝜑, 𝜒↗¬𝜑] into ax-2 | |
| 931 | →→→¬¬𝜑→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑→→𝜑¬𝜑→→¬¬𝜑→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑 | Subs [𝜑↗→→¬¬𝜑→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑, 𝜓↗→𝜑¬𝜑] into ax-1 | |
| 932 | →→𝜑¬𝜑→→¬¬𝜑→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑 | Modus ponens 930, 931 | |
| 933 | →→→𝜑¬𝜑→→¬¬𝜑→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑→→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑→→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑 | Subs [𝜑↗→𝜑¬𝜑, 𝜓↗→¬¬𝜑→𝜑¬𝜑, 𝜒↗→→¬¬𝜑𝜑→¬¬𝜑¬𝜑] into ax-2 | |
| 934 | →→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑→→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑 | Modus ponens 932, 933 | |
| 935 | →→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑 | Modus ponens 925, 934 | |
| 936 | →→→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑→→→𝜑¬𝜑→¬¬𝜑𝜑→→𝜑¬𝜑→¬¬𝜑¬𝜑 | Subs [𝜑↗→𝜑¬𝜑, 𝜓↗→¬¬𝜑𝜑, 𝜒↗→¬¬𝜑¬𝜑] into ax-2 | |
| 937 | →→→𝜑¬𝜑→¬¬𝜑𝜑→→𝜑¬𝜑→¬¬𝜑¬𝜑 | Modus ponens 935, 936 | |
| 938 | →→𝜑¬𝜑→¬¬𝜑¬𝜑 | Modus ponens 924, 937 | |
| 939 | →¬¬𝜑→¬𝜑¬→𝜑¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬→𝜑¬𝜑] into pm2.21 | |
| 940 | →→¬¬𝜑→¬𝜑¬→𝜑¬𝜑→→¬¬𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑 | Subs [𝜑↗¬¬𝜑, 𝜓↗¬𝜑, 𝜒↗¬→𝜑¬𝜑] into ax-2 | |
| 941 | →→¬¬𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑 | Modus ponens 939, 940 | |
| 942 | →→→¬¬𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑→→¬¬𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑 | Subs [𝜑↗→→¬¬𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑, 𝜓↗→𝜑¬𝜑] into ax-1 | |
| 943 | →→𝜑¬𝜑→→¬¬𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑 | Modus ponens 941, 942 | |
| 944 | →→→𝜑¬𝜑→→¬¬𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑→→→𝜑¬𝜑→¬¬𝜑¬𝜑→→𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑 | Subs [𝜑↗→𝜑¬𝜑, 𝜓↗→¬¬𝜑¬𝜑, 𝜒↗→¬¬𝜑¬→𝜑¬𝜑] into ax-2 | |
| 945 | →→→𝜑¬𝜑→¬¬𝜑¬𝜑→→𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑 | Modus ponens 943, 944 | |
| 946 | →→𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑 | Modus ponens 938, 945 | |
| 947 | →→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗→𝜑¬𝜑] into ax-3 | |
| 948 | →→→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑¬𝜑→→𝜑¬𝜑→→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑¬𝜑 | Subs [𝜑↗→→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑¬𝜑, 𝜓↗→𝜑¬𝜑] into ax-1 | |
| 949 | →→𝜑¬𝜑→→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑¬𝜑 | Modus ponens 947, 948 | |
| 950 | →→→𝜑¬𝜑→→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑¬𝜑→→→𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑→→𝜑¬𝜑¬𝜑 | Subs [𝜑↗→𝜑¬𝜑, 𝜓↗→¬¬𝜑¬→𝜑¬𝜑, 𝜒↗→→𝜑¬𝜑¬𝜑] into ax-2 | |
| 951 | →→→𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑→→𝜑¬𝜑¬𝜑 | Modus ponens 949, 950 | |
| 952 | →→𝜑¬𝜑→→𝜑¬𝜑¬𝜑 | Modus ponens 946, 951 | |
| 953 | →→→𝜑¬𝜑→→𝜑¬𝜑¬𝜑→→→𝜑¬𝜑→𝜑¬𝜑→→𝜑¬𝜑¬𝜑 | Subs [𝜑↗→𝜑¬𝜑, 𝜓↗→𝜑¬𝜑, 𝜒↗¬𝜑] into ax-2 | |
| 954 | →→→𝜑¬𝜑→𝜑¬𝜑→→𝜑¬𝜑¬𝜑 | Modus ponens 952, 953 | |
| 955 | →→𝜑¬𝜑¬𝜑 | Modus ponens 421, 954 | pm2.01 |
| 956 | →→¬𝜑𝜓→𝜓𝜓 | Subs [𝜑↗→¬𝜑𝜓] into idd | |
| 957 | →¬𝜑→→¬𝜑𝜓¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗→¬𝜑𝜓] into ax-1 | |
| 958 | →→¬𝜑→→¬𝜑𝜓¬𝜑→¬𝜑→¬𝜑→→¬𝜑𝜓¬𝜑 | Subs [𝜑↗→¬𝜑→→¬𝜑𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 959 | →¬𝜑→¬𝜑→→¬𝜑𝜓¬𝜑 | Modus ponens 957, 958 | |
| 960 | →→¬𝜑→¬𝜑→→¬𝜑𝜓¬𝜑→→¬𝜑¬𝜑→¬𝜑→→¬𝜑𝜓¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→→¬𝜑𝜓¬𝜑] into ax-2 | |
| 961 | →→¬𝜑¬𝜑→¬𝜑→→¬𝜑𝜓¬𝜑 | Modus ponens 959, 960 | |
| 962 | →→→¬𝜑𝜓→¬𝜑𝜓→→→¬𝜑𝜓¬𝜑→→¬𝜑𝜓𝜓 | Subs [𝜑↗→¬𝜑𝜓, 𝜓↗¬𝜑, 𝜒↗𝜓] into ax-2 | |
| 963 | →→→¬𝜑𝜓¬𝜑→→¬𝜑𝜓𝜓 | Modus ponens 447, 962 | |
| 964 | →→→→¬𝜑𝜓¬𝜑→→¬𝜑𝜓𝜓→¬𝜑→→→¬𝜑𝜓¬𝜑→→¬𝜑𝜓𝜓 | Subs [𝜑↗→→→¬𝜑𝜓¬𝜑→→¬𝜑𝜓𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 965 | →¬𝜑→→→¬𝜑𝜓¬𝜑→→¬𝜑𝜓𝜓 | Modus ponens 963, 964 | |
| 966 | →→¬𝜑→→→¬𝜑𝜓¬𝜑→→¬𝜑𝜓𝜓→→¬𝜑→→¬𝜑𝜓¬𝜑→¬𝜑→→¬𝜑𝜓𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗→→¬𝜑𝜓¬𝜑, 𝜒↗→→¬𝜑𝜓𝜓] into ax-2 | |
| 967 | →→¬𝜑→→¬𝜑𝜓¬𝜑→¬𝜑→→¬𝜑𝜓𝜓 | Modus ponens 965, 966 | |
| 968 | →¬𝜑→→¬𝜑𝜓𝜓 | Modus ponens 957, 967 | |
| 969 | →𝜓→→¬𝜑𝜓𝜓 | Subs [𝜑↗𝜓, 𝜓↗→¬𝜑𝜓] into ax-1 | |
| 970 | →→𝜓→→¬𝜑𝜓𝜓→𝜓→𝜓→→¬𝜑𝜓𝜓 | Subs [𝜑↗→𝜓→→¬𝜑𝜓𝜓] into ax-1 | |
| 971 | →𝜓→𝜓→→¬𝜑𝜓𝜓 | Modus ponens 969, 970 | |
| 972 | →→𝜓→𝜓→→¬𝜑𝜓𝜓→→𝜓𝜓→𝜓→→¬𝜑𝜓𝜓 | Subs [𝜑↗𝜓, 𝜒↗→→¬𝜑𝜓𝜓] into ax-2 | |
| 973 | →→𝜓𝜓→𝜓→→¬𝜑𝜓𝜓 | Modus ponens 971, 972 | |
| 974 | →→→¬𝜑𝜓→𝜓𝜓→→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓 | Subs [𝜑↗→¬𝜑𝜓, 𝜒↗𝜓] into ax-2 | |
| 975 | →→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓 | Modus ponens 956, 974 | |
| 976 | →→→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→𝜓→→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓 | Subs [𝜑↗→→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓] into ax-1 | |
| 977 | →𝜓→→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓 | Modus ponens 975, 976 | |
| 978 | →→𝜓→→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→→𝜓→→¬𝜑𝜓𝜓→𝜓→→¬𝜑𝜓𝜓 | Subs [𝜑↗𝜓, 𝜓↗→→¬𝜑𝜓𝜓, 𝜒↗→→¬𝜑𝜓𝜓] into ax-2 | |
| 979 | →→𝜓→→¬𝜑𝜓𝜓→𝜓→→¬𝜑𝜓𝜓 | Modus ponens 977, 978 | |
| 980 | →→𝜓→→¬𝜑𝜓𝜓→𝜑→𝜓→→¬𝜑𝜓𝜓 | Subs [𝜑↗→𝜓→→¬𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1 | |
| 981 | →𝜑→𝜓→→¬𝜑𝜓𝜓 | Modus ponens 969, 980 | |
| 982 | →→𝜑→𝜓→→¬𝜑𝜓𝜓→→𝜑𝜓→𝜑→→¬𝜑𝜓𝜓 | Subs [𝜒↗→→¬𝜑𝜓𝜓] into ax-2 | |
| 983 | →→𝜑𝜓→𝜑→→¬𝜑𝜓𝜓 | Modus ponens 981, 982 | |
| 984 | →→¬𝜑→→¬𝜑𝜓𝜓→→𝜑𝜓→¬𝜑→→¬𝜑𝜓𝜓 | Subs [𝜑↗→¬𝜑→→¬𝜑𝜓𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 985 | →→𝜑𝜓→¬𝜑→→¬𝜑𝜓𝜓 | Modus ponens 968, 984 | |
| 986 | →→→¬𝜑𝜓𝜓¬¬→→¬𝜑𝜓𝜓 | Subs [𝜑↗→→¬𝜑𝜓𝜓] into notnot | |
| 987 | →→→→¬𝜑𝜓𝜓¬¬→→¬𝜑𝜓𝜓→¬𝜑→→→¬𝜑𝜓𝜓¬¬→→¬𝜑𝜓𝜓 | Subs [𝜑↗→→→¬𝜑𝜓𝜓¬¬→→¬𝜑𝜓𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 988 | →¬𝜑→→→¬𝜑𝜓𝜓¬¬→→¬𝜑𝜓𝜓 | Modus ponens 986, 987 | |
| 989 | →→¬𝜑→→→¬𝜑𝜓𝜓¬¬→→¬𝜑𝜓𝜓→→¬𝜑→→¬𝜑𝜓𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗→→¬𝜑𝜓𝜓, 𝜒↗¬¬→→¬𝜑𝜓𝜓] into ax-2 | |
| 990 | →→¬𝜑→→¬𝜑𝜓𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓 | Modus ponens 988, 989 | |
| 991 | →→→¬𝜑→→¬𝜑𝜓𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓→→𝜑𝜓→→¬𝜑→→¬𝜑𝜓𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓 | Subs [𝜑↗→→¬𝜑→→¬𝜑𝜓𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 992 | →→𝜑𝜓→→¬𝜑→→¬𝜑𝜓𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓 | Modus ponens 990, 991 | |
| 993 | →→→𝜑𝜓→→¬𝜑→→¬𝜑𝜓𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓→→→𝜑𝜓→¬𝜑→→¬𝜑𝜓𝜓→→𝜑𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬𝜑→→¬𝜑𝜓𝜓, 𝜒↗→¬𝜑¬¬→→¬𝜑𝜓𝜓] into ax-2 | |
| 994 | →→→𝜑𝜓→¬𝜑→→¬𝜑𝜓𝜓→→𝜑𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓 | Modus ponens 992, 993 | |
| 995 | →→𝜑𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓 | Modus ponens 985, 994 | |
| 996 | →→¬𝜑¬¬→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓𝜑 | Subs [𝜓↗¬→→¬𝜑𝜓𝜓] into ax-3 | |
| 997 | →→→¬𝜑¬¬→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓𝜑→→𝜑𝜓→→¬𝜑¬¬→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓𝜑 | Subs [𝜑↗→→¬𝜑¬¬→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓𝜑, 𝜓↗→𝜑𝜓] into ax-1 | |
| 998 | →→𝜑𝜓→→¬𝜑¬¬→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓𝜑 | Modus ponens 996, 997 | |
| 999 | →→→𝜑𝜓→→¬𝜑¬¬→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓𝜑→→→𝜑𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓→→𝜑𝜓→¬→→¬𝜑𝜓𝜓𝜑 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬𝜑¬¬→→¬𝜑𝜓𝜓, 𝜒↗→¬→→¬𝜑𝜓𝜓𝜑] into ax-2 | |
| 1000 | →→→𝜑𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓→→𝜑𝜓→¬→→¬𝜑𝜓𝜓𝜑 | Modus ponens 998, 999 | |
| 1001 | →→𝜑𝜓→¬→→¬𝜑𝜓𝜓𝜑 | Modus ponens 995, 1000 | |
| 1002 | →→𝜑→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓 | Subs [𝜑↗→𝜑→→¬𝜑𝜓𝜓, 𝜓↗¬→→¬𝜑𝜓𝜓] into ax-1 | |
| 1003 | →→→𝜑→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→𝜑𝜓→→𝜑→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓 | Subs [𝜑↗→→𝜑→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 1004 | →→𝜑𝜓→→𝜑→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓 | Modus ponens 1002, 1003 | |
| 1005 | →→→𝜑𝜓→→𝜑→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→→𝜑𝜓→𝜑→→¬𝜑𝜓𝜓→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑→→¬𝜑𝜓𝜓, 𝜒↗→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓] into ax-2 | |
| 1006 | →→→𝜑𝜓→𝜑→→¬𝜑𝜓𝜓→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓 | Modus ponens 1004, 1005 | |
| 1007 | →→𝜑𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓 | Modus ponens 983, 1006 | |
| 1008 | →→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓 | Subs [𝜑↗¬→→¬𝜑𝜓𝜓, 𝜓↗𝜑, 𝜒↗→→¬𝜑𝜓𝜓] into ax-2 | |
| 1009 | →→→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓 | Subs [𝜑↗→→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 1010 | →→𝜑𝜓→→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓 | Modus ponens 1008, 1009 | |
| 1011 | →→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓, 𝜒↗→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓] into ax-2 | |
| 1012 | →→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓 | Modus ponens 1010, 1011 | |
| 1013 | →→𝜑𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓 | Modus ponens 1007, 1012 | |
| 1014 | →→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→→→𝜑𝜓→¬→→¬𝜑𝜓𝜓𝜑→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬→→¬𝜑𝜓𝜓𝜑, 𝜒↗→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓] into ax-2 | |
| 1015 | →→→𝜑𝜓→¬→→¬𝜑𝜓𝜓𝜑→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓 | Modus ponens 1013, 1014 | |
| 1016 | →→𝜑𝜓→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓 | Modus ponens 1001, 1015 | |
| 1017 | →¬→→¬𝜑𝜓𝜓→→→¬𝜑𝜓𝜓¬→𝜑𝜓 | Subs [𝜑↗→→¬𝜑𝜓𝜓, 𝜓↗¬→𝜑𝜓] into pm2.21 | |
| 1018 | →→¬→→¬𝜑𝜓𝜓→→→¬𝜑𝜓𝜓¬→𝜑𝜓→→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓 | Subs [𝜑↗¬→→¬𝜑𝜓𝜓, 𝜓↗→→¬𝜑𝜓𝜓, 𝜒↗¬→𝜑𝜓] into ax-2 | |
| 1019 | →→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓 | Modus ponens 1017, 1018 | |
| 1020 | →→→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓 | Subs [𝜑↗→→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 1021 | →→𝜑𝜓→→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓 | Modus ponens 1019, 1020 | |
| 1022 | →→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→→𝜑𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓, 𝜒↗→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓] into ax-2 | |
| 1023 | →→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→→𝜑𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓 | Modus ponens 1021, 1022 | |
| 1024 | →→𝜑𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓 | Modus ponens 1016, 1023 | |
| 1025 | →→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓 | Subs [𝜑↗→→¬𝜑𝜓𝜓, 𝜓↗→𝜑𝜓] into ax-3 | |
| 1026 | →→→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓 | Subs [𝜑↗→→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 1027 | →→𝜑𝜓→→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓 | Modus ponens 1025, 1026 | |
| 1028 | →→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓→→→𝜑𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓, 𝜒↗→→𝜑𝜓→→¬𝜑𝜓𝜓] into ax-2 | |
| 1029 | →→→𝜑𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓 | Modus ponens 1027, 1028 | |
| 1030 | →→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓 | Modus ponens 1024, 1029 | |
| 1031 | →→→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→¬𝜑𝜓𝜓] into ax-2 | |
| 1032 | →→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓 | Modus ponens 1030, 1031 | |
| 1033 | →→𝜑𝜓→→¬𝜑𝜓𝜓 | Modus ponens 24, 1032 | pm2.61 |
| 1034 | →→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓 | Subs [𝜑↗→¬𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 1035 | →→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓→→¬𝜑𝜓→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓 | Subs [𝜑↗→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓, 𝜓↗→¬𝜑𝜓] into ax-1 | |
| 1036 | →→¬𝜑𝜓→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓 | Modus ponens 1034, 1035 | |
| 1037 | →→→¬𝜑𝜓→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓→→→¬𝜑𝜓→¬𝜑𝜓→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓 | Subs [𝜑↗→¬𝜑𝜓, 𝜓↗→¬𝜑𝜓, 𝜒↗→→𝜑𝜓→¬𝜑𝜓] into ax-2 | |
| 1038 | →→→¬𝜑𝜓→¬𝜑𝜓→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓 | Modus ponens 1036, 1037 | |
| 1039 | →→→𝜑𝜓→→¬𝜑𝜓𝜓→→→𝜑𝜓→¬𝜑𝜓→→𝜑𝜓𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬𝜑𝜓, 𝜒↗𝜓] into ax-2 | |
| 1040 | →→→𝜑𝜓→¬𝜑𝜓→→𝜑𝜓𝜓 | Modus ponens pm2.61, 1039 | |
| 1041 | →→→→𝜑𝜓→¬𝜑𝜓→→𝜑𝜓𝜓→→¬𝜑𝜓→→→𝜑𝜓→¬𝜑𝜓→→𝜑𝜓𝜓 | Subs [𝜑↗→→→𝜑𝜓→¬𝜑𝜓→→𝜑𝜓𝜓, 𝜓↗→¬𝜑𝜓] into ax-1 | |
| 1042 | →→¬𝜑𝜓→→→𝜑𝜓→¬𝜑𝜓→→𝜑𝜓𝜓 | Modus ponens 1040, 1041 | |
| 1043 | →→→¬𝜑𝜓→→→𝜑𝜓→¬𝜑𝜓→→𝜑𝜓𝜓→→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓→→¬𝜑𝜓→→𝜑𝜓𝜓 | Subs [𝜑↗→¬𝜑𝜓, 𝜓↗→→𝜑𝜓→¬𝜑𝜓, 𝜒↗→→𝜑𝜓𝜓] into ax-2 | |
| 1044 | →→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓→→¬𝜑𝜓→→𝜑𝜓𝜓 | Modus ponens 1042, 1043 | |
| 1045 | →→¬𝜑𝜓→→𝜑𝜓𝜓 | Modus ponens 1034, 1044 | pm2.6 |
| 1046 | →→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬𝜑𝜓] into ax-1 | |
| 1047 | →→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 1048 | →→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓 | Modus ponens 1046, 1047 | |
| 1049 | →→→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→¬𝜑𝜓→𝜑𝜓] into ax-2 | |
| 1050 | →→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓 | Modus ponens 1048, 1049 | |
| 1051 | →→→¬𝜑𝜓→→𝜑𝜓𝜓→→→¬𝜑𝜓→𝜑𝜓→→¬𝜑𝜓𝜓 | Subs [𝜑↗→¬𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗𝜓] into ax-2 | |
| 1052 | →→→¬𝜑𝜓→𝜑𝜓→→¬𝜑𝜓𝜓 | Modus ponens pm2.6, 1051 | |
| 1053 | →→→→¬𝜑𝜓→𝜑𝜓→→¬𝜑𝜓𝜓→→𝜑𝜓→→→¬𝜑𝜓→𝜑𝜓→→¬𝜑𝜓𝜓 | Subs [𝜑↗→→→¬𝜑𝜓→𝜑𝜓→→¬𝜑𝜓𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 1054 | →→𝜑𝜓→→→¬𝜑𝜓→𝜑𝜓→→¬𝜑𝜓𝜓 | Modus ponens 1052, 1053 | |
| 1055 | →→→𝜑𝜓→→→¬𝜑𝜓→𝜑𝜓→→¬𝜑𝜓𝜓→→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→→¬𝜑𝜓→𝜑𝜓, 𝜒↗→→¬𝜑𝜓𝜓] into ax-2 | |
| 1056 | →→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓 | Modus ponens 1054, 1055 | |
| 1057 | →→𝜑𝜓→¬𝜑¬𝜑 | Subs [𝜑↗→𝜑𝜓, 𝜓↗¬𝜑] into idd | |
| 1058 | →¬𝜑→→𝜑𝜓¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗→𝜑𝜓] into ax-1 | |
| 1059 | →→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑→¬𝜑→→𝜑𝜓¬𝜑 | Subs [𝜑↗→¬𝜑→→𝜑𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 1060 | →¬𝜑→¬𝜑→→𝜑𝜓¬𝜑 | Modus ponens 1058, 1059 | |
| 1061 | →→¬𝜑→¬𝜑→→𝜑𝜓¬𝜑→→¬𝜑¬𝜑→¬𝜑→→𝜑𝜓¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→→𝜑𝜓¬𝜑] into ax-2 | |
| 1062 | →→¬𝜑¬𝜑→¬𝜑→→𝜑𝜓¬𝜑 | Modus ponens 1060, 1061 | |
| 1063 | →→→𝜑𝜓→¬𝜑¬𝜑→→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑 | Subs [𝜑↗→𝜑𝜓, 𝜓↗¬𝜑, 𝜒↗¬𝜑] into ax-2 | |
| 1064 | →→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑 | Modus ponens 1057, 1063 | |
| 1065 | →→→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→¬𝜑→→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑 | Subs [𝜑↗→→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 1066 | →¬𝜑→→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑 | Modus ponens 1064, 1065 | |
| 1067 | →→¬𝜑→→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑→→𝜑𝜓¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗→→𝜑𝜓¬𝜑, 𝜒↗→→𝜑𝜓¬𝜑] into ax-2 | |
| 1068 | →→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑→→𝜑𝜓¬𝜑 | Modus ponens 1066, 1067 | |
| 1069 | →¬𝜓→→𝜑𝜓¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 1070 | →→¬𝜓→→𝜑𝜓¬𝜓→¬𝜓→¬𝜓→→𝜑𝜓¬𝜓 | Subs [𝜑↗→¬𝜓→→𝜑𝜓¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 1071 | →¬𝜓→¬𝜓→→𝜑𝜓¬𝜓 | Modus ponens 1069, 1070 | |
| 1072 | →→¬𝜓→¬𝜓→→𝜑𝜓¬𝜓→→¬𝜓¬𝜓→¬𝜓→→𝜑𝜓¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→→𝜑𝜓¬𝜓] into ax-2 | |
| 1073 | →→¬𝜓¬𝜓→¬𝜓→→𝜑𝜓¬𝜓 | Modus ponens 1071, 1072 | |
| 1074 | →→→𝜑𝜓→¬𝜓¬𝜑→→→𝜑𝜓¬𝜓→→𝜑𝜓¬𝜑 | Subs [𝜑↗→𝜑𝜓, 𝜓↗¬𝜓, 𝜒↗¬𝜑] into ax-2 | |
| 1075 | →→→𝜑𝜓¬𝜓→→𝜑𝜓¬𝜑 | Modus ponens con3, 1074 | |
| 1076 | →→→→𝜑𝜓¬𝜓→→𝜑𝜓¬𝜑→¬𝜓→→→𝜑𝜓¬𝜓→→𝜑𝜓¬𝜑 | Subs [𝜑↗→→→𝜑𝜓¬𝜓→→𝜑𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1 | |
| 1077 | →¬𝜓→→→𝜑𝜓¬𝜓→→𝜑𝜓¬𝜑 | Modus ponens 1075, 1076 | |
| 1078 | →→¬𝜓→→→𝜑𝜓¬𝜓→→𝜑𝜓¬𝜑→→¬𝜓→→𝜑𝜓¬𝜓→¬𝜓→→𝜑𝜓¬𝜑 | Subs [𝜑↗¬𝜓, 𝜓↗→→𝜑𝜓¬𝜓, 𝜒↗→→𝜑𝜓¬𝜑] into ax-2 | |
| 1079 | →→¬𝜓→→𝜑𝜓¬𝜓→¬𝜓→→𝜑𝜓¬𝜑 | Modus ponens 1077, 1078 | |
| 1080 | →¬𝜓→→𝜑𝜓¬𝜑 | Modus ponens 1069, 1079 | |
| 1081 | →→¬𝜓→→𝜑𝜓¬𝜑→𝜑→¬𝜓→→𝜑𝜓¬𝜑 | Subs [𝜑↗→¬𝜓→→𝜑𝜓¬𝜑, 𝜓↗𝜑] into ax-1 | |
| 1082 | →𝜑→¬𝜓→→𝜑𝜓¬𝜑 | Modus ponens 1080, 1081 | |
| 1083 | →→𝜑→¬𝜓→→𝜑𝜓¬𝜑→→𝜑¬𝜓→𝜑→→𝜑𝜓¬𝜑 | Subs [𝜓↗¬𝜓, 𝜒↗→→𝜑𝜓¬𝜑] into ax-2 | |
| 1084 | →→𝜑¬𝜓→𝜑→→𝜑𝜓¬𝜑 | Modus ponens 1082, 1083 | |
| 1085 | →→¬𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬𝜑→→𝜑𝜓¬𝜑 | Subs [𝜑↗→¬𝜑→→𝜑𝜓¬𝜑, 𝜓↗→𝜑¬𝜓] into ax-1 | |
| 1086 | →→𝜑¬𝜓→¬𝜑→→𝜑𝜓¬𝜑 | Modus ponens 1058, 1085 | |
| 1087 | →→→𝜑𝜓¬𝜑¬¬→→𝜑𝜓¬𝜑 | Subs [𝜑↗→→𝜑𝜓¬𝜑] into notnot | |
| 1088 | →→→→𝜑𝜓¬𝜑¬¬→→𝜑𝜓¬𝜑→¬𝜑→→→𝜑𝜓¬𝜑¬¬→→𝜑𝜓¬𝜑 | Subs [𝜑↗→→→𝜑𝜓¬𝜑¬¬→→𝜑𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 1089 | →¬𝜑→→→𝜑𝜓¬𝜑¬¬→→𝜑𝜓¬𝜑 | Modus ponens 1087, 1088 | |
| 1090 | →→¬𝜑→→→𝜑𝜓¬𝜑¬¬→→𝜑𝜓¬𝜑→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑¬¬→→𝜑𝜓¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗→→𝜑𝜓¬𝜑, 𝜒↗¬¬→→𝜑𝜓¬𝜑] into ax-2 | |
| 1091 | →→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑¬¬→→𝜑𝜓¬𝜑 | Modus ponens 1089, 1090 | |
| 1092 | →→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑¬¬→→𝜑𝜓¬𝜑→→𝜑¬𝜓→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑¬¬→→𝜑𝜓¬𝜑 | Subs [𝜑↗→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑¬¬→→𝜑𝜓¬𝜑, 𝜓↗→𝜑¬𝜓] into ax-1 | |
| 1093 | →→𝜑¬𝜓→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑¬¬→→𝜑𝜓¬𝜑 | Modus ponens 1091, 1092 | |
| 1094 | →→→𝜑¬𝜓→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑¬¬→→𝜑𝜓¬𝜑→→→𝜑¬𝜓→¬𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬𝜑¬¬→→𝜑𝜓¬𝜑 | Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→¬𝜑→→𝜑𝜓¬𝜑, 𝜒↗→¬𝜑¬¬→→𝜑𝜓¬𝜑] into ax-2 | |
| 1095 | →→→𝜑¬𝜓→¬𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬𝜑¬¬→→𝜑𝜓¬𝜑 | Modus ponens 1093, 1094 | |
| 1096 | →→𝜑¬𝜓→¬𝜑¬¬→→𝜑𝜓¬𝜑 | Modus ponens 1086, 1095 | |
| 1097 | →→¬𝜑¬¬→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑𝜑 | Subs [𝜓↗¬→→𝜑𝜓¬𝜑] into ax-3 | |
| 1098 | →→→¬𝜑¬¬→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑𝜑→→𝜑¬𝜓→→¬𝜑¬¬→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑𝜑 | Subs [𝜑↗→→¬𝜑¬¬→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑𝜑, 𝜓↗→𝜑¬𝜓] into ax-1 | |
| 1099 | →→𝜑¬𝜓→→¬𝜑¬¬→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑𝜑 | Modus ponens 1097, 1098 | |
| 1100 | →→→𝜑¬𝜓→→¬𝜑¬¬→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑𝜑→→→𝜑¬𝜓→¬𝜑¬¬→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑𝜑 | Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→¬𝜑¬¬→→𝜑𝜓¬𝜑, 𝜒↗→¬→→𝜑𝜓¬𝜑𝜑] into ax-2 | |
| 1101 | →→→𝜑¬𝜓→¬𝜑¬¬→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑𝜑 | Modus ponens 1099, 1100 | |
| 1102 | →→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑𝜑 | Modus ponens 1096, 1101 | |
| 1103 | →→𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑 | Subs [𝜑↗→𝜑→→𝜑𝜓¬𝜑, 𝜓↗¬→→𝜑𝜓¬𝜑] into ax-1 | |
| 1104 | →→→𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→→𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑 | Subs [𝜑↗→→𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑, 𝜓↗→𝜑¬𝜓] into ax-1 | |
| 1105 | →→𝜑¬𝜓→→𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑 | Modus ponens 1103, 1104 | |
| 1106 | →→→𝜑¬𝜓→→𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→→𝜑¬𝜓→𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑 | Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→𝜑→→𝜑𝜓¬𝜑, 𝜒↗→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑] into ax-2 | |
| 1107 | →→→𝜑¬𝜓→𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑 | Modus ponens 1105, 1106 | |
| 1108 | →→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑 | Modus ponens 1084, 1107 | |
| 1109 | →→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑 | Subs [𝜑↗¬→→𝜑𝜓¬𝜑, 𝜓↗𝜑, 𝜒↗→→𝜑𝜓¬𝜑] into ax-2 | |
| 1110 | →→→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑 | Subs [𝜑↗→→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑, 𝜓↗→𝜑¬𝜓] into ax-1 | |
| 1111 | →→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑 | Modus ponens 1109, 1110 | |
| 1112 | →→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑 | Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑, 𝜒↗→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑] into ax-2 | |
| 1113 | →→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑 | Modus ponens 1111, 1112 | |
| 1114 | →→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑 | Modus ponens 1108, 1113 | |
| 1115 | →→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑𝜑→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑 | Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→¬→→𝜑𝜓¬𝜑𝜑, 𝜒↗→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑] into ax-2 | |
| 1116 | →→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑𝜑→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑 | Modus ponens 1114, 1115 | |
| 1117 | →→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑 | Modus ponens 1102, 1116 | |
| 1118 | →¬→→𝜑𝜓¬𝜑→→→𝜑𝜓¬𝜑¬→𝜑¬𝜓 | Subs [𝜑↗→→𝜑𝜓¬𝜑, 𝜓↗¬→𝜑¬𝜓] into pm2.21 | |
| 1119 | →→¬→→𝜑𝜓¬𝜑→→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓 | Subs [𝜑↗¬→→𝜑𝜓¬𝜑, 𝜓↗→→𝜑𝜓¬𝜑, 𝜒↗¬→𝜑¬𝜓] into ax-2 | |
| 1120 | →→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓 | Modus ponens 1118, 1119 | |
| 1121 | →→→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓 | Subs [𝜑↗→→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓, 𝜓↗→𝜑¬𝜓] into ax-1 | |
| 1122 | →→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓 | Modus ponens 1120, 1121 | |
| 1123 | →→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓 | Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑, 𝜒↗→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓] into ax-2 | |
| 1124 | →→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓 | Modus ponens 1122, 1123 | |
| 1125 | →→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓 | Modus ponens 1117, 1124 | |
| 1126 | →→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑 | Subs [𝜑↗→→𝜑𝜓¬𝜑, 𝜓↗→𝜑¬𝜓] into ax-3 | |
| 1127 | →→→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑 | Subs [𝜑↗→→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑, 𝜓↗→𝜑¬𝜓] into ax-1 | |
| 1128 | →→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑 | Modus ponens 1126, 1127 | |
| 1129 | →→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑→→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑 | Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓, 𝜒↗→→𝜑¬𝜓→→𝜑𝜓¬𝜑] into ax-2 | |
| 1130 | →→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑 | Modus ponens 1128, 1129 | |
| 1131 | →→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑 | Modus ponens 1125, 1130 | |
| 1132 | →→→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑→→→𝜑¬𝜓→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑 | Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→𝜑¬𝜓, 𝜒↗→→𝜑𝜓¬𝜑] into ax-2 | |
| 1133 | →→→𝜑¬𝜓→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑 | Modus ponens 1131, 1132 | |
| 1134 | →→𝜑¬𝜓→→𝜑𝜓¬𝜑 | Modus ponens 379, 1133 | |
| 1135 | →→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑¬𝜓] into ax-1 | |
| 1136 | →→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 1137 | →→𝜑𝜓→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓 | Modus ponens 1135, 1136 | |
| 1138 | →→→𝜑𝜓→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜑¬𝜓→𝜑𝜓] into ax-2 | |
| 1139 | →→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓 | Modus ponens 1137, 1138 | |
| 1140 | →→→𝜑¬𝜓→→𝜑𝜓¬𝜑→→→𝜑¬𝜓→𝜑𝜓→→𝜑¬𝜓¬𝜑 | Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗¬𝜑] into ax-2 | |
| 1141 | →→→𝜑¬𝜓→𝜑𝜓→→𝜑¬𝜓¬𝜑 | Modus ponens 1134, 1140 | |
| 1142 | →→→→𝜑¬𝜓→𝜑𝜓→→𝜑¬𝜓¬𝜑→→𝜑𝜓→→→𝜑¬𝜓→𝜑𝜓→→𝜑¬𝜓¬𝜑 | Subs [𝜑↗→→→𝜑¬𝜓→𝜑𝜓→→𝜑¬𝜓¬𝜑, 𝜓↗→𝜑𝜓] into ax-1 | |
| 1143 | →→𝜑𝜓→→→𝜑¬𝜓→𝜑𝜓→→𝜑¬𝜓¬𝜑 | Modus ponens 1141, 1142 | |
| 1144 | →→→𝜑𝜓→→→𝜑¬𝜓→𝜑𝜓→→𝜑¬𝜓¬𝜑→→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓→→𝜑𝜓→→𝜑¬𝜓¬𝜑 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜑¬𝜓→𝜑𝜓, 𝜒↗→→𝜑¬𝜓¬𝜑] into ax-2 | |
| 1145 | →→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓→→𝜑𝜓→→𝜑¬𝜓¬𝜑 | Modus ponens 1143, 1144 | |
| 1146 | →→𝜑𝜓→→𝜑¬𝜓¬𝜑 | Modus ponens 1135, 1145 | pm2.65 |
| 1147 | →→𝜑𝜑→→𝜑𝜓→𝜑𝜑 | Subs [𝜑↗→𝜑𝜑, 𝜓↗→𝜑𝜓] into ax-1 | |
| 1148 | →→𝜑𝜓→𝜑𝜑 | Modus ponens id, 1147 | |
| 1149 | →→→𝜑𝜓→𝜑𝜑→→→𝜑𝜓𝜑→→𝜑𝜓𝜑 | Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜑, 𝜒↗𝜑] into ax-2 | |
| 1150 | →→→𝜑𝜓𝜑→→𝜑𝜓𝜑 | Modus ponens 1148, 1149 | |
| 1151 | →→¬→𝜑𝜓𝜑→→→𝜑𝜓𝜑→¬→𝜑𝜓𝜑 | Subs [𝜑↗→¬→𝜑𝜓𝜑, 𝜓↗→→𝜑𝜓𝜑] into ax-1 | |
| 1152 | →→→𝜑𝜓𝜑→¬→𝜑𝜓𝜑 | Modus ponens simplim, 1151 | |
| 1153 | →→𝜑¬¬𝜑→¬→𝜑𝜓→𝜑¬¬𝜑 | Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 1154 | →¬→𝜑𝜓→𝜑¬¬𝜑 | Modus ponens notnot, 1153 | |
| 1155 | →→¬→𝜑𝜓→𝜑¬¬𝜑→→¬→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2 | |
| 1156 | →→¬→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑 | Modus ponens 1154, 1155 | |
| 1157 | →→→¬→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑→→→𝜑𝜓𝜑→→¬→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑 | Subs [𝜑↗→→¬→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑, 𝜓↗→→𝜑𝜓𝜑] into ax-1 | |
| 1158 | →→→𝜑𝜓𝜑→→¬→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑 | Modus ponens 1156, 1157 | |
| 1159 | →→→→𝜑𝜓𝜑→→¬→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑→→→→𝜑𝜓𝜑→¬→𝜑𝜓𝜑→→→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑 | Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗→¬→𝜑𝜓𝜑, 𝜒↗→¬→𝜑𝜓¬¬𝜑] into ax-2 | |
| 1160 | →→→→𝜑𝜓𝜑→¬→𝜑𝜓𝜑→→→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑 | Modus ponens 1158, 1159 | |
| 1161 | →→→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑 | Modus ponens 1152, 1160 | |
| 1162 | →→¬→𝜑𝜓¬¬𝜑→¬𝜑→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗¬𝜑] into ax-3 | |
| 1163 | →→→¬→𝜑𝜓¬¬𝜑→¬𝜑→𝜑𝜓→→→𝜑𝜓𝜑→→¬→𝜑𝜓¬¬𝜑→¬𝜑→𝜑𝜓 | Subs [𝜑↗→→¬→𝜑𝜓¬¬𝜑→¬𝜑→𝜑𝜓, 𝜓↗→→𝜑𝜓𝜑] into ax-1 | |
| 1164 | →→→𝜑𝜓𝜑→→¬→𝜑𝜓¬¬𝜑→¬𝜑→𝜑𝜓 | Modus ponens 1162, 1163 | |
| 1165 | →→→→𝜑𝜓𝜑→→¬→𝜑𝜓¬¬𝜑→¬𝜑→𝜑𝜓→→→→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑→→→𝜑𝜓𝜑→¬𝜑→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗→¬→𝜑𝜓¬¬𝜑, 𝜒↗→¬𝜑→𝜑𝜓] into ax-2 | |
| 1166 | →→→→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑→→→𝜑𝜓𝜑→¬𝜑→𝜑𝜓 | Modus ponens 1164, 1165 | |
| 1167 | →→→𝜑𝜓𝜑→¬𝜑→𝜑𝜓 | Modus ponens 1161, 1166 | |
| 1168 | →→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑 | Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 1169 | →→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑 | Subs [𝜑↗→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑, 𝜓↗→→𝜑𝜓𝜑] into ax-1 | |
| 1170 | →→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑 | Modus ponens 1168, 1169 | |
| 1171 | →→→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑 | Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗→→𝜑𝜓𝜑, 𝜒↗→¬𝜑→→𝜑𝜓𝜑] into ax-2 | |
| 1172 | →→→→𝜑𝜓𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑 | Modus ponens 1170, 1171 | |
| 1173 | →→¬𝜑→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗→𝜑𝜓, 𝜒↗𝜑] into ax-2 | |
| 1174 | →→→¬𝜑→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑→→→𝜑𝜓𝜑→→¬𝜑→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑 | Subs [𝜑↗→→¬𝜑→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑, 𝜓↗→→𝜑𝜓𝜑] into ax-1 | |
| 1175 | →→→𝜑𝜓𝜑→→¬𝜑→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑 | Modus ponens 1173, 1174 | |
| 1176 | →→→→𝜑𝜓𝜑→→¬𝜑→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑→→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑 | Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗→¬𝜑→→𝜑𝜓𝜑, 𝜒↗→→¬𝜑→𝜑𝜓→¬𝜑𝜑] into ax-2 | |
| 1177 | →→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑 | Modus ponens 1175, 1176 | |
| 1178 | →→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑 | Modus ponens 1168, 1177 | |
| 1179 | →→→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑→→→→𝜑𝜓𝜑→¬𝜑→𝜑𝜓→→→𝜑𝜓𝜑→¬𝜑𝜑 | Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗→¬𝜑→𝜑𝜓, 𝜒↗→¬𝜑𝜑] into ax-2 | |
| 1180 | →→→→𝜑𝜓𝜑→¬𝜑→𝜑𝜓→→→𝜑𝜓𝜑→¬𝜑𝜑 | Modus ponens 1178, 1179 | |
| 1181 | →→→𝜑𝜓𝜑→¬𝜑𝜑 | Modus ponens 1167, 1180 | |
| 1182 | →¬𝜑→𝜑¬→→𝜑𝜓𝜑 | Subs [𝜓↗¬→→𝜑𝜓𝜑] into pm2.21 | |
| 1183 | →→¬𝜑→𝜑¬→→𝜑𝜓𝜑→→¬𝜑𝜑→¬𝜑¬→→𝜑𝜓𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗𝜑, 𝜒↗¬→→𝜑𝜓𝜑] into ax-2 | |
| 1184 | →→¬𝜑𝜑→¬𝜑¬→→𝜑𝜓𝜑 | Modus ponens 1182, 1183 | |
| 1185 | →→→¬𝜑𝜑→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→→¬𝜑𝜑→¬𝜑¬→→𝜑𝜓𝜑 | Subs [𝜑↗→→¬𝜑𝜑→¬𝜑¬→→𝜑𝜓𝜑, 𝜓↗→→𝜑𝜓𝜑] into ax-1 | |
| 1186 | →→→𝜑𝜓𝜑→→¬𝜑𝜑→¬𝜑¬→→𝜑𝜓𝜑 | Modus ponens 1184, 1185 | |
| 1187 | →→→→𝜑𝜓𝜑→→¬𝜑𝜑→¬𝜑¬→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑→¬𝜑𝜑→→→𝜑𝜓𝜑→¬𝜑¬→→𝜑𝜓𝜑 | Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗→¬𝜑𝜑, 𝜒↗→¬𝜑¬→→𝜑𝜓𝜑] into ax-2 | |
| 1188 | →→→→𝜑𝜓𝜑→¬𝜑𝜑→→→𝜑𝜓𝜑→¬𝜑¬→→𝜑𝜓𝜑 | Modus ponens 1186, 1187 | |
| 1189 | →→→𝜑𝜓𝜑→¬𝜑¬→→𝜑𝜓𝜑 | Modus ponens 1181, 1188 | |
| 1190 | →→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑 | Subs [𝜓↗→→𝜑𝜓𝜑] into ax-3 | |
| 1191 | →→→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑→→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑 | Subs [𝜑↗→→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑, 𝜓↗→→𝜑𝜓𝜑] into ax-1 | |
| 1192 | →→→𝜑𝜓𝜑→→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑 | Modus ponens 1190, 1191 | |
| 1193 | →→→→𝜑𝜓𝜑→→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑 | Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗→¬𝜑¬→→𝜑𝜓𝜑, 𝜒↗→→→𝜑𝜓𝜑𝜑] into ax-2 | |
| 1194 | →→→→𝜑𝜓𝜑→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑 | Modus ponens 1192, 1193 | |
| 1195 | →→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑 | Modus ponens 1189, 1194 | |
| 1196 | →→→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑 | Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗→→𝜑𝜓𝜑, 𝜒↗𝜑] into ax-2 | |
| 1197 | →→→→𝜑𝜓𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑 | Modus ponens 1195, 1196 | |
| 1198 | →→→𝜑𝜓𝜑𝜑 | Modus ponens 1150, 1197 | peirce |
| 1199 | →→→𝜑𝜓𝜓→→𝜓𝜑→→𝜑𝜓𝜑 | Subs [𝜑↗→𝜑𝜓, 𝜒↗𝜑] into imim1 | |
| 1200 | →→→→𝜑𝜓𝜑𝜑→→𝜓𝜑→→→𝜑𝜓𝜑𝜑 | Subs [𝜑↗→→→𝜑𝜓𝜑𝜑, 𝜓↗→𝜓𝜑] into ax-1 | |
| 1201 | →→𝜓𝜑→→→𝜑𝜓𝜑𝜑 | Modus ponens peirce, 1200 | |
| 1202 | →→→𝜓𝜑→→→𝜑𝜓𝜑𝜑→→→𝜓𝜑→→𝜑𝜓𝜑→→𝜓𝜑𝜑 | Subs [𝜑↗→𝜓𝜑, 𝜓↗→→𝜑𝜓𝜑, 𝜒↗𝜑] into ax-2 | |
| 1203 | →→→𝜓𝜑→→𝜑𝜓𝜑→→𝜓𝜑𝜑 | Modus ponens 1201, 1202 | |
| 1204 | →→→→𝜓𝜑→→𝜑𝜓𝜑→→𝜓𝜑𝜑→→→𝜑𝜓𝜓→→→𝜓𝜑→→𝜑𝜓𝜑→→𝜓𝜑𝜑 | Subs [𝜑↗→→→𝜓𝜑→→𝜑𝜓𝜑→→𝜓𝜑𝜑, 𝜓↗→→𝜑𝜓𝜓] into ax-1 | |
| 1205 | →→→𝜑𝜓𝜓→→→𝜓𝜑→→𝜑𝜓𝜑→→𝜓𝜑𝜑 | Modus ponens 1203, 1204 | |
| 1206 | →→→→𝜑𝜓𝜓→→→𝜓𝜑→→𝜑𝜓𝜑→→𝜓𝜑𝜑→→→→𝜑𝜓𝜓→→𝜓𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜓→→𝜓𝜑𝜑 | Subs [𝜑↗→→𝜑𝜓𝜓, 𝜓↗→→𝜓𝜑→→𝜑𝜓𝜑, 𝜒↗→→𝜓𝜑𝜑] into ax-2 | |
| 1207 | →→→→𝜑𝜓𝜓→→𝜓𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜓→→𝜓𝜑𝜑 | Modus ponens 1205, 1206 | |
| 1208 | →→→𝜑𝜓𝜓→→𝜓𝜑𝜑 | Modus ponens 1199, 1207 | looinv |
| 1209 | →→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→𝜑𝜑] into pm2.01 | |
| 1210 | →→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑 | Subs [𝜑↗→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑] into ax-1 | |
| 1211 | →→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑 | Modus ponens id, 1210 | |
| 1212 | →→𝜑𝜑→𝜑𝜑 | Subs [𝜑↗→𝜑𝜑] into id | |
| 1213 | →→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜓↗→𝜑𝜑] into ax-1 | |
| 1214 | →→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1209, 1213 | |
| 1215 | →¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑] into notnotr | |
| 1216 | →→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→𝜑𝜑] into ax-1 | |
| 1217 | →→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1 | |
| 1218 | →¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1216, 1217 | |
| 1219 | →→¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑] into ax-2 | |
| 1220 | →→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1218, 1219 | |
| 1221 | →¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1215, 1220 | |
| 1222 | →→→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑, 𝜒↗¬→𝜑𝜑] into ax-2 | |
| 1223 | →→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1214, 1222 | |
| 1224 | →→→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1 | |
| 1225 | →¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1223, 1224 | |
| 1226 | →→¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→→𝜑𝜑¬→𝜑𝜑] into ax-2 | |
| 1227 | →→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1225, 1226 | |
| 1228 | →→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑 | Subs [𝜑↗→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1 | |
| 1229 | →→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→→𝜑𝜑→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑 | Subs [𝜑↗→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑, 𝜓↗→𝜑𝜑] into ax-1 | |
| 1230 | →→𝜑𝜑→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑 | Modus ponens 1228, 1229 | |
| 1231 | →→→𝜑𝜑→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→→→𝜑𝜑→𝜑𝜑→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑 | Subs [𝜑↗→𝜑𝜑, 𝜓↗→𝜑𝜑, 𝜒↗→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑] into ax-2 | |
| 1232 | →→→𝜑𝜑→𝜑𝜑→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑 | Modus ponens 1230, 1231 | |
| 1233 | →→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→𝜑𝜑, 𝜒↗¬→𝜑𝜑] into ax-2 | |
| 1234 | →→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1215, 1233 | |
| 1235 | →→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜓↗→𝜑𝜑] into ax-1 | |
| 1236 | →→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1234, 1235 | |
| 1237 | →→→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→𝜑𝜑, 𝜓↗→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑, 𝜒↗→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑] into ax-2 | |
| 1238 | →→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1236, 1237 | |
| 1239 | →→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1228, 1238 | |
| 1240 | →→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→𝜑𝜑] into ax-3 | |
| 1241 | →→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→𝜑𝜑] into ax-1 | |
| 1242 | →→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1240, 1241 | |
| 1243 | →→→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→𝜑𝜑, 𝜓↗→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜒↗→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑] into ax-2 | |
| 1244 | →→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1242, 1243 | |
| 1245 | →→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1239, 1244 | |
| 1246 | →→→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→𝜑𝜑, 𝜓↗→𝜑𝜑, 𝜒↗¬→→𝜑𝜑¬→𝜑𝜑] into ax-2 | |
| 1247 | →→→𝜑𝜑→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1245, 1246 | |
| 1248 | →→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1212, 1247 | |
| 1249 | →¬→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬→𝜑𝜑] into id | |
| 1250 | →→¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→¬→𝜑𝜑¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑] into ax-1 | |
| 1251 | →→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1249, 1250 | |
| 1252 | →¬¬¬→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬→𝜑𝜑] into notnotr | |
| 1253 | →¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑] into ax-1 | |
| 1254 | →→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬¬→𝜑𝜑] into ax-1 | |
| 1255 | →¬¬¬→𝜑𝜑→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1253, 1254 | |
| 1256 | →→¬¬¬→𝜑𝜑→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬¬¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑, 𝜒↗→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑] into ax-2 | |
| 1257 | →→¬¬¬→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1255, 1256 | |
| 1258 | →¬¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1252, 1257 | |
| 1259 | →→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬→𝜑𝜑→→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑, 𝜒↗¬→𝜑𝜑] into ax-2 | |
| 1260 | →→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1251, 1259 | |
| 1261 | →→→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬¬→𝜑𝜑] into ax-1 | |
| 1262 | →¬¬¬→𝜑𝜑→→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1260, 1261 | |
| 1263 | →→¬¬¬→𝜑𝜑→→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬¬¬→𝜑𝜑, 𝜓↗→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜒↗→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑] into ax-2 | |
| 1264 | →→¬¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1262, 1263 | |
| 1265 | →→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑] into id | |
| 1266 | →→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬¬→𝜑𝜑] into ax-1 | |
| 1267 | →→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑] into ax-1 | |
| 1268 | →→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1266, 1267 | |
| 1269 | →→→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑] into ax-2 | |
| 1270 | →→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1268, 1269 | |
| 1271 | →→¬¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬¬¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑, 𝜒↗¬→𝜑𝜑] into ax-2 | |
| 1272 | →→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1258, 1271 | |
| 1273 | →→→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑] into ax-1 | |
| 1274 | →→→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1272, 1273 | |
| 1275 | →→→→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑→→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬¬¬→𝜑𝜑¬→𝜑𝜑] into ax-2 | |
| 1276 | →→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1274, 1275 | |
| 1277 | →→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1266, 1276 | |
| 1278 | →→¬¬¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑 | Subs [𝜑↗¬¬→𝜑𝜑, 𝜓↗→𝜑𝜑] into ax-3 | |
| 1279 | →→→¬¬¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑 | Subs [𝜑↗→→¬¬¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑] into ax-1 | |
| 1280 | →→→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑 | Modus ponens 1278, 1279 | |
| 1281 | →→→→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑→→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑 | Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→¬¬¬→𝜑𝜑¬→𝜑𝜑, 𝜒↗→→𝜑𝜑¬¬→𝜑𝜑] into ax-2 | |
| 1282 | →→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑 | Modus ponens 1280, 1281 | |
| 1283 | →→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑 | Modus ponens 1277, 1282 | |
| 1284 | →→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑→→→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑 | Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→𝜑𝜑, 𝜒↗¬¬→𝜑𝜑] into ax-2 | |
| 1285 | →→→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑 | Modus ponens 1283, 1284 | |
| 1286 | →→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑 | Modus ponens 1211, 1285 | |
| 1287 | →→→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑 | Subs [𝜑↗→→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1 | |
| 1288 | →¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑 | Modus ponens 1286, 1287 | |
| 1289 | →→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1 | |
| 1290 | →→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1 | |
| 1291 | →¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1289, 1290 | |
| 1292 | →→¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑] into ax-2 | |
| 1293 | →→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1291, 1292 | |
| 1294 | →¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1215, 1293 | |
| 1295 | →→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑 | Subs [𝜑↗¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑, 𝜒↗¬¬→𝜑𝜑] into ax-2 | |
| 1296 | →→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑 | Modus ponens 1288, 1295 | |
| 1297 | →→→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑 | Subs [𝜑↗→→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1 | |
| 1298 | →¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑 | Modus ponens 1296, 1297 | |
| 1299 | →→¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑 | Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬→𝜑𝜑¬¬→𝜑𝜑] into ax-2 | |
| 1300 | →→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑 | Modus ponens 1298, 1299 | |
| 1301 | →¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑 | Modus ponens 1294, 1300 | |
| 1302 | →¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1 | |
| 1303 | →→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1 | |
| 1304 | →¬→𝜑𝜑→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1302, 1303 | |
| 1305 | →→¬→𝜑𝜑→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑, 𝜒↗→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑] into ax-2 | |
| 1306 | →→¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1304, 1305 | |
| 1307 | →→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑 | Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑, 𝜒↗¬¬→𝜑𝜑] into ax-2 | |
| 1308 | →→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑 | Modus ponens 1301, 1307 | |
| 1309 | →→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑 | Subs [𝜑↗→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1 | |
| 1310 | →¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑 | Modus ponens 1308, 1309 | |
| 1311 | →→¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑 | Subs [𝜑↗¬→𝜑𝜑, 𝜓↗→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑] into ax-2 | |
| 1312 | →→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑 | Modus ponens 1310, 1311 | |
| 1313 | →¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑 | Modus ponens 1302, 1312 | |
| 1314 | →→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-3 | |
| 1315 | →→→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1 | |
| 1316 | →¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1314, 1315 | |
| 1317 | →→¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬→𝜑𝜑, 𝜓↗→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑, 𝜒↗→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑] into ax-2 | |
| 1318 | →→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1316, 1317 | |
| 1319 | →¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1313, 1318 | |
| 1320 | →→¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑, 𝜒↗¬→→𝜑𝜑¬→𝜑𝜑] into ax-2 | |
| 1321 | →→¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1319, 1320 | |
| 1322 | →¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1249, 1321 | |
| 1323 | →¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑] into id | |
| 1324 | →→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1 | |
| 1325 | →¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1323, 1324 | |
| 1326 | →¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑] into notnotr | |
| 1327 | →¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1 | |
| 1328 | →→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1 | |
| 1329 | →¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1327, 1328 | |
| 1330 | →→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬¬¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-2 | |
| 1331 | →→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1329, 1330 | |
| 1332 | →¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1326, 1331 | |
| 1333 | →→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜒↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-2 | |
| 1334 | →→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1325, 1333 | |
| 1335 | →→→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1 | |
| 1336 | →¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1334, 1335 | |
| 1337 | →→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬¬¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-2 | |
| 1338 | →→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1336, 1337 | |
| 1339 | →¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬→𝜑𝜑, 𝜓↗¬¬¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1 | |
| 1340 | →→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1 | |
| 1341 | →¬→𝜑𝜑→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1339, 1340 | |
| 1342 | →→¬→𝜑𝜑→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑, 𝜒↗→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑] into ax-2 | |
| 1343 | →→¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1341, 1342 | |
| 1344 | →→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬¬¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑, 𝜒↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-2 | |
| 1345 | →→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1332, 1344 | |
| 1346 | →→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1 | |
| 1347 | →¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1345, 1346 | |
| 1348 | →→¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬→𝜑𝜑, 𝜓↗→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-2 | |
| 1349 | →→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1347, 1348 | |
| 1350 | →¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1339, 1349 | |
| 1351 | →→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→→𝜑𝜑¬→𝜑𝜑] into ax-3 | |
| 1352 | →→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1 | |
| 1353 | →¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1351, 1352 | |
| 1354 | →→¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬→𝜑𝜑, 𝜓↗→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-2 | |
| 1355 | →→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1353, 1354 | |
| 1356 | →¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1350, 1355 | |
| 1357 | →→¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬→𝜑𝜑, 𝜓↗¬→→𝜑𝜑¬→𝜑𝜑, 𝜒↗¬¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-2 | |
| 1358 | →→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1356, 1357 | |
| 1359 | →¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1322, 1358 | |
| 1360 | →→¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑 | Subs [𝜑↗→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-3 | |
| 1361 | →¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑 | Modus ponens 1359, 1360 | |
| 1362 | →→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1 | |
| 1363 | →¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1248, 1362 | |
| 1364 | →→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→𝜑𝜑, 𝜒↗¬→→𝜑𝜑¬→𝜑𝜑] into ax-2 | |
| 1365 | →→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1363, 1364 | |
| 1366 | →¬¬→→𝜑𝜑¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1361, 1365 | |
| 1367 | →→¬¬→→𝜑𝜑¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑 | Subs [𝜑↗¬→→𝜑𝜑¬→𝜑𝜑] into pm2.18 | |
| 1368 | ¬→→𝜑𝜑¬→𝜑𝜑 | Modus ponens 1366, 1367 | bijust0 |
| 1369 | ¬→→¬→→𝜑𝜓¬→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬→→𝜑𝜓¬→𝜓𝜑] into bijust0 | bijust |
| 1370 | →¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into simprim | |
| 1371 | →¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens df-bi, 1370 | |
| 1372 | →→𝜑𝜓→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜑] into pm3.2im | |
| 1373 | →→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→𝜓𝜑] into ax-1 | |
| 1374 | →→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1371, 1373 | |
| 1375 | →→→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→𝜓𝜑, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗↔𝜑𝜓] into ax-2 | |
| 1376 | →→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜓𝜑↔𝜑𝜓 | Modus ponens 1374, 1375 | |
| 1377 | →→→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜓𝜑↔𝜑𝜓→→𝜑𝜓→→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜓𝜑↔𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 1378 | →→𝜑𝜓→→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜓𝜑↔𝜑𝜓 | Modus ponens 1376, 1377 | |
| 1379 | →→→𝜑𝜓→→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜓𝜑↔𝜑𝜓→→→𝜑𝜓→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜑𝜓→→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 1380 | →→→𝜑𝜓→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜑𝜓→→𝜓𝜑↔𝜑𝜓 | Modus ponens 1378, 1379 | |
| 1381 | →→𝜑𝜓→→𝜓𝜑↔𝜑𝜓 | Modus ponens 1372, 1380 | impbi |
| 1382 | →→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑] into impbi | |
| 1383 | →¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into notnotr | |
| 1384 | →→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1 | |
| 1385 | →→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1 | |
| 1386 | →¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1384, 1385 | |
| 1387 | →→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 1388 | →→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1386, 1387 | |
| 1389 | →¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1383, 1388 | |
| 1390 | →→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2 | |
| 1391 | →→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1382, 1390 | |
| 1392 | →→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1 | |
| 1393 | →¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1391, 1392 | |
| 1394 | →→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2 | |
| 1395 | →→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1393, 1394 | |
| 1396 | →¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1389, 1395 | |
| 1397 | →→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into id | |
| 1398 | →→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1 | |
| 1399 | →→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1 | |
| 1400 | →→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1398, 1399 | |
| 1401 | →→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2 | |
| 1402 | →→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1400, 1401 | |
| 1403 | →→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2 | |
| 1404 | →→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1396, 1403 | |
| 1405 | →→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1 | |
| 1406 | →→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1404, 1405 | |
| 1407 | →→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2 | |
| 1408 | →→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1406, 1407 | |
| 1409 | →→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1398, 1408 | |
| 1410 | →↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into notnot | |
| 1411 | →→↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1 | |
| 1412 | →¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1410, 1411 | |
| 1413 | →→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2 | |
| 1414 | →→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1412, 1413 | |
| 1415 | →→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1 | |
| 1416 | →→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1414, 1415 | |
| 1417 | →→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2 | |
| 1418 | →→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1416, 1417 | |
| 1419 | →→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1409, 1418 | |
| 1420 | →→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-3 | |
| 1421 | →→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1 | |
| 1422 | →→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1420, 1421 | |
| 1423 | →→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 1424 | →→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1422, 1423 | |
| 1425 | →→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1419, 1424 | |
| 1426 | →¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into id | |
| 1427 | →¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1 | |
| 1428 | →→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1 | |
| 1429 | →¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1427, 1428 | |
| 1430 | →→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2 | |
| 1431 | →→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1429, 1430 | |
| 1432 | →→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 1433 | →→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1425, 1432 | |
| 1434 | →→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1 | |
| 1435 | →¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1433, 1434 | |
| 1436 | →→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 1437 | →→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1435, 1436 | |
| 1438 | →¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1427, 1437 | |
| 1439 | →¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1 | |
| 1440 | →¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens df-bi, 1439 | |
| 1441 | →→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into id | |
| 1442 | →→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1 | |
| 1443 | →→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1440, 1442 | |
| 1444 | →¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into notnotr | |
| 1445 | →¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1 | |
| 1446 | →→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1 | |
| 1447 | →¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1445, 1446 | |
| 1448 | →→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2 | |
| 1449 | →→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1447, 1448 | |
| 1450 | →¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1444, 1449 | |
| 1451 | →→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 1452 | →→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1443, 1451 | |
| 1453 | →→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1 | |
| 1454 | →¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1452, 1453 | |
| 1455 | →→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 1456 | →→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1454, 1455 | |
| 1457 | →¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1450, 1456 | |
| 1458 | →→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1 | |
| 1459 | →→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1 | |
| 1460 | →→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1458, 1459 | |
| 1461 | →→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 1462 | →→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1460, 1461 | |
| 1463 | →→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 1464 | →→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1457, 1463 | |
| 1465 | →→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1 | |
| 1466 | →→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1464, 1465 | |
| 1467 | →→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 1468 | →→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1466, 1467 | |
| 1469 | →→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1458, 1468 | |
| 1470 | →→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-3 | |
| 1471 | →→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1 | |
| 1472 | →→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1470, 1471 | |
| 1473 | →→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2 | |
| 1474 | →→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1472, 1473 | |
| 1475 | →→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1469, 1474 | |
| 1476 | →→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2 | |
| 1477 | →→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1475, 1476 | |
| 1478 | →→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1441, 1477 | |
| 1479 | →¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into id | |
| 1480 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1 | |
| 1481 | →¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1479, 1480 | |
| 1482 | →¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into notnotr | |
| 1483 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1 | |
| 1484 | →¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1439, 1483 | |
| 1485 | →→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 1486 | →→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1484, 1485 | |
| 1487 | →¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1482, 1486 | |
| 1488 | →→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 1489 | →→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1481, 1488 | |
| 1490 | →→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1 | |
| 1491 | →¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1489, 1490 | |
| 1492 | →→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 1493 | →→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1491, 1492 | |
| 1494 | →¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1 | |
| 1495 | →→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1 | |
| 1496 | →¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1494, 1495 | |
| 1497 | →→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2 | |
| 1498 | →→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1496, 1497 | |
| 1499 | →→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 1500 | →→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1487, 1499 | |
| 1501 | →→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1 | |
| 1502 | →¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1500, 1501 | |
| 1503 | →→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 1504 | →→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1502, 1503 | |
| 1505 | →¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1494, 1504 | |
| 1506 | →→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-3 | |
| 1507 | →→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1 | |
| 1508 | →¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1506, 1507 | |
| 1509 | →→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 1510 | →→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1508, 1509 | |
| 1511 | →¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1505, 1510 | |
| 1512 | →→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 1513 | →→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1511, 1512 | |
| 1514 | →¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1438, 1513 | |
| 1515 | →→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1 | |
| 1516 | →¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1514, 1515 | |
| 1517 | →¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1 | |
| 1518 | →→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1 | |
| 1519 | →¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1517, 1518 | |
| 1520 | →→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2 | |
| 1521 | →→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1519, 1520 | |
| 1522 | →¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1444, 1521 | |
| 1523 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 1524 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1516, 1523 | |
| 1525 | →→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1 | |
| 1526 | →¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1524, 1525 | |
| 1527 | →→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 1528 | →→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1526, 1527 | |
| 1529 | →¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1522, 1528 | |
| 1530 | →¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1 | |
| 1531 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1 | |
| 1532 | →¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1530, 1531 | |
| 1533 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 1534 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1532, 1533 | |
| 1535 | →→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 1536 | →→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1529, 1535 | |
| 1537 | →→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1 | |
| 1538 | →¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1536, 1537 | |
| 1539 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 1540 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1538, 1539 | |
| 1541 | →¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1530, 1540 | |
| 1542 | →→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-3 | |
| 1543 | →→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1 | |
| 1544 | →¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1542, 1543 | |
| 1545 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2 | |
| 1546 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1544, 1545 | |
| 1547 | →¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1541, 1546 | |
| 1548 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2 | |
| 1549 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1547, 1548 | |
| 1550 | →¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1479, 1549 | |
| 1551 | →¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into id | |
| 1552 | →→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1 | |
| 1553 | →¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1551, 1552 | |
| 1554 | →¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into notnotr | |
| 1555 | →¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1 | |
| 1556 | →→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1 | |
| 1557 | →¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1555, 1556 | |
| 1558 | →→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2 | |
| 1559 | →→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1557, 1558 | |
| 1560 | →¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1554, 1559 | |
| 1561 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2 | |
| 1562 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1553, 1561 | |
| 1563 | →→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1 | |
| 1564 | →¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1562, 1563 | |
| 1565 | →→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2 | |
| 1566 | →→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1564, 1565 | |
| 1567 | →¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1 | |
| 1568 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1 | |
| 1569 | →¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1567, 1568 | |
| 1570 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 1571 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1569, 1570 | |
| 1572 | →→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2 | |
| 1573 | →→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1560, 1572 | |
| 1574 | →→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1 | |
| 1575 | →¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1573, 1574 | |
| 1576 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2 | |
| 1577 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1575, 1576 | |
| 1578 | →¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1567, 1577 | |
| 1579 | →→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-3 | |
| 1580 | →→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1 | |
| 1581 | →¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1579, 1580 | |
| 1582 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2 | |
| 1583 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1581, 1582 | |
| 1584 | →¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1578, 1583 | |
| 1585 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2 | |
| 1586 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1584, 1585 | |
| 1587 | →¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1550, 1586 | |
| 1588 | →→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-3 | |
| 1589 | →¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1587, 1588 | |
| 1590 | →→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1 | |
| 1591 | →¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1478, 1590 | |
| 1592 | →→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2 | |
| 1593 | →→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1591, 1592 | |
| 1594 | →¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1589, 1593 | |
| 1595 | →→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into pm2.18 | |
| 1596 | ¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1594, 1595 | |
| 1597 | →¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1 | |
| 1598 | →¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1596, 1597 | |
| 1599 | →→¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-3 | |
| 1600 | →¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1598, 1599 | |
| 1601 | →→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-3 | |
| 1602 | →¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1600, 1601 | |
| 1603 | ↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 1596, 1602 | dfbi1 |
| 1604 | →¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into simplim | |
| 1605 | →↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens df-bi, 1604 | |
| 1606 | →¬→→𝜑𝜓¬→𝜓𝜑→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→𝜓𝜑] into simplim | |
| 1607 | →→¬→→𝜑𝜓¬→𝜓𝜑→𝜑𝜓→↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑→𝜑𝜓 | Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜑→𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 1608 | →↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑→𝜑𝜓 | Modus ponens 1606, 1607 | |
| 1609 | →→↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑→𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓→𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→𝜑𝜓] into ax-2 | |
| 1610 | →→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓→𝜑𝜓 | Modus ponens 1608, 1609 | |
| 1611 | →↔𝜑𝜓→𝜑𝜓 | Modus ponens 1605, 1610 | biimp |
| 1612 | →¬→→𝜑𝜓¬→𝜓𝜑→𝜓𝜑 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜑] into simprim | |
| 1613 | →↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑] into biimp | |
| 1614 | →→¬→→𝜑𝜓¬→𝜓𝜑→𝜓𝜑→↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑→𝜓𝜑 | Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜑→𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 1615 | →↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑→𝜓𝜑 | Modus ponens 1612, 1614 | |
| 1616 | →→↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓→𝜓𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→𝜓𝜑] into ax-2 | |
| 1617 | →→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓→𝜓𝜑 | Modus ponens 1615, 1616 | |
| 1618 | →↔𝜑𝜓→𝜓𝜑 | Modus ponens 1605, 1617 | biimpr |
| 1619 | →→𝜓𝜑→→𝜑𝜓↔𝜓𝜑 | Subs [𝜑↗𝜓, 𝜓↗𝜑] into impbi | |
| 1620 | →→𝜑𝜓→→𝜓𝜑→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜑] into ax-1 | |
| 1621 | →→→𝜑𝜓→→𝜓𝜑→𝜑𝜓→↔𝜑𝜓→→𝜑𝜓→→𝜓𝜑→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→→𝜓𝜑→𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 1622 | →↔𝜑𝜓→→𝜑𝜓→→𝜓𝜑→𝜑𝜓 | Modus ponens 1620, 1621 | |
| 1623 | →→↔𝜑𝜓→→𝜑𝜓→→𝜓𝜑→𝜑𝜓→→↔𝜑𝜓→𝜑𝜓→↔𝜑𝜓→→𝜓𝜑→𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜓𝜑→𝜑𝜓] into ax-2 | |
| 1624 | →→↔𝜑𝜓→𝜑𝜓→↔𝜑𝜓→→𝜓𝜑→𝜑𝜓 | Modus ponens 1622, 1623 | |
| 1625 | →↔𝜑𝜓→→𝜓𝜑→𝜑𝜓 | Modus ponens biimp, 1624 | |
| 1626 | →→→𝜓𝜑→→𝜑𝜓↔𝜓𝜑→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜓𝜑 | Subs [𝜑↗→𝜓𝜑, 𝜓↗→𝜑𝜓, 𝜒↗↔𝜓𝜑] into ax-2 | |
| 1627 | →→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜓𝜑 | Modus ponens 1619, 1626 | |
| 1628 | →→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜓𝜑→↔𝜑𝜓→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜓𝜑 | Subs [𝜑↗→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 1629 | →↔𝜑𝜓→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜓𝜑 | Modus ponens 1627, 1628 | |
| 1630 | →→↔𝜑𝜓→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜓𝜑→→↔𝜑𝜓→→𝜓𝜑→𝜑𝜓→↔𝜑𝜓→→𝜓𝜑↔𝜓𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜓𝜑→𝜑𝜓, 𝜒↗→→𝜓𝜑↔𝜓𝜑] into ax-2 | |
| 1631 | →→↔𝜑𝜓→→𝜓𝜑→𝜑𝜓→↔𝜑𝜓→→𝜓𝜑↔𝜓𝜑 | Modus ponens 1629, 1630 | |
| 1632 | →↔𝜑𝜓→→𝜓𝜑↔𝜓𝜑 | Modus ponens 1625, 1631 | |
| 1633 | →→𝜓𝜑→𝜓𝜑 | Subs [𝜑↗→𝜓𝜑] into id | |
| 1634 | →→𝜓𝜑→↔𝜑𝜓→𝜓𝜑 | Subs [𝜑↗→𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 1635 | →→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑→→𝜓𝜑→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑 | Subs [𝜑↗→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑, 𝜓↗→𝜓𝜑] into ax-1 | |
| 1636 | →→𝜓𝜑→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑 | Modus ponens 1634, 1635 | |
| 1637 | →→→𝜓𝜑→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑→→→𝜓𝜑→𝜓𝜑→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑 | Subs [𝜑↗→𝜓𝜑, 𝜓↗→𝜓𝜑, 𝜒↗→↔𝜑𝜓→𝜓𝜑] into ax-2 | |
| 1638 | →→→𝜓𝜑→𝜓𝜑→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑 | Modus ponens 1636, 1637 | |
| 1639 | →→↔𝜑𝜓→→𝜓𝜑↔𝜓𝜑→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜓𝜑, 𝜒↗↔𝜓𝜑] into ax-2 | |
| 1640 | →→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑 | Modus ponens 1632, 1639 | |
| 1641 | →→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑→→𝜓𝜑→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑 | Subs [𝜑↗→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑, 𝜓↗→𝜓𝜑] into ax-1 | |
| 1642 | →→𝜓𝜑→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑 | Modus ponens 1640, 1641 | |
| 1643 | →→→𝜓𝜑→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑→→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑→→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑 | Subs [𝜑↗→𝜓𝜑, 𝜓↗→↔𝜑𝜓→𝜓𝜑, 𝜒↗→↔𝜑𝜓↔𝜓𝜑] into ax-2 | |
| 1644 | →→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑→→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑 | Modus ponens 1642, 1643 | |
| 1645 | →→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑 | Modus ponens 1634, 1644 | |
| 1646 | →→→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑→↔𝜑𝜓→→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑 | Subs [𝜑↗→→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 1647 | →↔𝜑𝜓→→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑 | Modus ponens 1645, 1646 | |
| 1648 | →→↔𝜑𝜓→→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜓𝜑, 𝜒↗→↔𝜑𝜓↔𝜓𝜑] into ax-2 | |
| 1649 | →→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑 | Modus ponens 1647, 1648 | |
| 1650 | →↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑 | Modus ponens biimpr, 1649 | |
| 1651 | →↔𝜑𝜓↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓] into id | |
| 1652 | →↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 1653 | →→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓 | Subs [𝜑↗→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 1654 | →↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓 | Modus ponens 1652, 1653 | |
| 1655 | →→↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→↔𝜑𝜓↔𝜑𝜓] into ax-2 | |
| 1656 | →→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓 | Modus ponens 1654, 1655 | |
| 1657 | →→↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗↔𝜓𝜑] into ax-2 | |
| 1658 | →→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑 | Modus ponens 1650, 1657 | |
| 1659 | →→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑→↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑 | Subs [𝜑↗→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 1660 | →↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑 | Modus ponens 1658, 1659 | |
| 1661 | →→↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑→→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→↔𝜑𝜓↔𝜑𝜓, 𝜒↗→↔𝜑𝜓↔𝜓𝜑] into ax-2 | |
| 1662 | →→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑 | Modus ponens 1660, 1661 | |
| 1663 | →↔𝜑𝜓↔𝜓𝜑 | Modus ponens 1651, 1658 | bicom1 |
| 1664 | →↔𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜑] into bicom1 | |
| 1665 | →→↔𝜑𝜓↔𝜓𝜑→→↔𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜓𝜑] into impbi | |
| 1666 | →→↔𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑 | Modus ponens bicom1, 1665 | |
| 1667 | ↔↔𝜑𝜓↔𝜓𝜑 | Modus ponens 1664, 1666 | bicom |
| 1668 | →→𝜑𝜑→→𝜑𝜑↔𝜑𝜑 | Subs [𝜓↗𝜑] into impbi | |
| 1669 | →→𝜑𝜑↔𝜑𝜑 | Modus ponens id, 1668 | |
| 1670 | ↔𝜑𝜑 | Modus ponens id, 1669 | biid |
| 1671 | ↔𝜓𝜓 | Subs [𝜑↗𝜓] into biid | |
| 1672 | →↔𝜓𝜓→𝜑↔𝜓𝜓 | Subs [𝜑↗↔𝜓𝜓, 𝜓↗𝜑] into ax-1 | |
| 1673 | →𝜑↔𝜓𝜓 | Modus ponens 1671, 1672 | biidd |
| 1674 | →→𝜓𝜑→→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗→𝜓𝜑, 𝜓↗→𝜑𝜓] into ax-1 | |
| 1675 | →→→𝜓𝜑→→𝜑𝜓→𝜓𝜑→𝜑→→𝜓𝜑→→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗→→𝜓𝜑→→𝜑𝜓→𝜓𝜑, 𝜓↗𝜑] into ax-1 | |
| 1676 | →𝜑→→𝜓𝜑→→𝜑𝜓→𝜓𝜑 | Modus ponens 1674, 1675 | |
| 1677 | →→𝜑→→𝜓𝜑→→𝜑𝜓→𝜓𝜑→→𝜑→𝜓𝜑→𝜑→→𝜑𝜓→𝜓𝜑 | Subs [𝜓↗→𝜓𝜑, 𝜒↗→→𝜑𝜓→𝜓𝜑] into ax-2 | |
| 1678 | →→𝜑→𝜓𝜑→𝜑→→𝜑𝜓→𝜓𝜑 | Modus ponens 1676, 1677 | |
| 1679 | →𝜑→→𝜑𝜓→𝜓𝜑 | Modus ponens ax-1, 1678 | |
| 1680 | →→→𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜑, 𝜒↗↔𝜑𝜓] into ax-2 | |
| 1681 | →→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓 | Modus ponens impbi, 1680 | |
| 1682 | →→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓→𝜑→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓 | Subs [𝜑↗→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 1683 | →𝜑→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓 | Modus ponens 1681, 1682 | |
| 1684 | →→𝜑→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓→→𝜑→→𝜑𝜓→𝜓𝜑→𝜑→→𝜑𝜓↔𝜑𝜓 | Subs [𝜓↗→→𝜑𝜓→𝜓𝜑, 𝜒↗→→𝜑𝜓↔𝜑𝜓] into ax-2 | |
| 1685 | →→𝜑→→𝜑𝜓→𝜓𝜑→𝜑→→𝜑𝜓↔𝜑𝜓 | Modus ponens 1683, 1684 | |
| 1686 | →𝜑→→𝜑𝜓↔𝜑𝜓 | Modus ponens 1679, 1685 | |
| 1687 | →→→𝜑𝜓→𝜑→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→𝜑→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→𝜑→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 1688 | →→𝜑𝜓→→𝜑𝜓→𝜑→𝜑𝜓 | Modus ponens 533, 1687 | |
| 1689 | →→→𝜑𝜓→→𝜑𝜓→𝜑→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→𝜑→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑→𝜑𝜓] into ax-2 | |
| 1690 | →→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→𝜑→𝜑𝜓 | Modus ponens 1688, 1689 | |
| 1691 | →→𝜑→→𝜑𝜓↔𝜑𝜓→→𝜑→𝜑𝜓→𝜑↔𝜑𝜓 | Subs [𝜓↗→𝜑𝜓, 𝜒↗↔𝜑𝜓] into ax-2 | |
| 1692 | →→𝜑→𝜑𝜓→𝜑↔𝜑𝜓 | Modus ponens 1686, 1691 | |
| 1693 | →→→𝜑→𝜑𝜓→𝜑↔𝜑𝜓→→𝜑𝜓→→𝜑→𝜑𝜓→𝜑↔𝜑𝜓 | Subs [𝜑↗→→𝜑→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 1694 | →→𝜑𝜓→→𝜑→𝜑𝜓→𝜑↔𝜑𝜓 | Modus ponens 1692, 1693 | |
| 1695 | →→→𝜑𝜓→→𝜑→𝜑𝜓→𝜑↔𝜑𝜓→→→𝜑𝜓→𝜑→𝜑𝜓→→𝜑𝜓→𝜑↔𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑→𝜑𝜓, 𝜒↗→𝜑↔𝜑𝜓] into ax-2 | |
| 1696 | →→→𝜑𝜓→𝜑→𝜑𝜓→→𝜑𝜓→𝜑↔𝜑𝜓 | Modus ponens 1694, 1695 | |
| 1697 | →→𝜑𝜓→𝜑↔𝜑𝜓 | Modus ponens 533, 1696 | |
| 1698 | →→→𝜑𝜓→𝜑↔𝜑𝜓→𝜓→→𝜑𝜓→𝜑↔𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→𝜑↔𝜑𝜓] into ax-1 | |
| 1699 | →𝜓→→𝜑𝜓→𝜑↔𝜑𝜓 | Modus ponens 1697, 1698 | |
| 1700 | →→𝜓→→𝜑𝜓→𝜑↔𝜑𝜓→→𝜓→𝜑𝜓→𝜓→𝜑↔𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑↔𝜑𝜓] into ax-2 | |
| 1701 | →→𝜓→𝜑𝜓→𝜓→𝜑↔𝜑𝜓 | Modus ponens 1699, 1700 | |
| 1702 | →𝜓→𝜑↔𝜑𝜓 | Modus ponens 208, 1701 | |
| 1703 | →→𝜑→𝜓𝜑→𝜑→𝜑→𝜓𝜑 | Subs [𝜑↗→𝜑→𝜓𝜑, 𝜓↗𝜑] into ax-1 | |
| 1704 | →𝜑→𝜑→𝜓𝜑 | Modus ponens ax-1, 1703 | |
| 1705 | →→𝜑→𝜑→𝜓𝜑→→𝜑𝜑→𝜑→𝜓𝜑 | Subs [𝜓↗𝜑, 𝜒↗→𝜓𝜑] into ax-2 | |
| 1706 | →→𝜑𝜑→𝜑→𝜓𝜑 | Modus ponens 1704, 1705 | |
| 1707 | →→𝜓→𝜑↔𝜑𝜓→→𝜓𝜑→𝜓↔𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜑, 𝜒↗↔𝜑𝜓] into ax-2 | |
| 1708 | →→𝜓𝜑→𝜓↔𝜑𝜓 | Modus ponens 1702, 1707 | |
| 1709 | →→→𝜓𝜑→𝜓↔𝜑𝜓→𝜑→→𝜓𝜑→𝜓↔𝜑𝜓 | Subs [𝜑↗→→𝜓𝜑→𝜓↔𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 1710 | →𝜑→→𝜓𝜑→𝜓↔𝜑𝜓 | Modus ponens 1708, 1709 | |
| 1711 | →→𝜑→→𝜓𝜑→𝜓↔𝜑𝜓→→𝜑→𝜓𝜑→𝜑→𝜓↔𝜑𝜓 | Subs [𝜓↗→𝜓𝜑, 𝜒↗→𝜓↔𝜑𝜓] into ax-2 | |
| 1712 | →→𝜑→𝜓𝜑→𝜑→𝜓↔𝜑𝜓 | Modus ponens 1710, 1711 | |
| 1713 | →𝜑→𝜓↔𝜑𝜓 | Modus ponens ax-1, 1712 | pm5.1im |
| 1714 | →→𝜓𝜓→→𝜑𝜑→𝜓𝜓 | Subs [𝜑↗→𝜓𝜓, 𝜓↗→𝜑𝜑] into ax-1 | |
| 1715 | →→𝜑𝜑→𝜓𝜓 | Modus ponens 10, 1714 | |
| 1716 | →→𝜑𝜑→→𝜓𝜓→𝜑𝜑 | Subs [𝜑↗→𝜑𝜑, 𝜓↗→𝜓𝜓] into ax-1 | |
| 1717 | →→𝜓𝜓→𝜑𝜑 | Modus ponens id, 1716 | |
| 1718 | →→→𝜑𝜑→𝜓𝜓→→→𝜓𝜓→𝜑𝜑↔→𝜑𝜑→𝜓𝜓 | Subs [𝜑↗→𝜑𝜑, 𝜓↗→𝜓𝜓] into impbi | |
| 1719 | →→→𝜓𝜓→𝜑𝜑↔→𝜑𝜑→𝜓𝜓 | Modus ponens 1715, 1718 | |
| 1720 | ↔→𝜑𝜑→𝜓𝜓 | Modus ponens 1717, 1719 | monothetic |
| 1721 | →↔𝜓𝜒→𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗𝜒] into biimp | |
| 1722 | →→↔𝜓𝜒→𝜓𝜒→𝜑→↔𝜓𝜒→𝜓𝜒 | Subs [𝜑↗→↔𝜓𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 1723 | →𝜑→↔𝜓𝜒→𝜓𝜒 | Modus ponens 1721, 1722 | |
| 1724 | →→𝜑→↔𝜓𝜒→𝜓𝜒→→𝜑↔𝜓𝜒→𝜑→𝜓𝜒 | Subs [𝜓↗↔𝜓𝜒, 𝜒↗→𝜓𝜒] into ax-2 | |
| 1725 | →→𝜑↔𝜓𝜒→𝜑→𝜓𝜒 | Modus ponens 1723, 1724 | |
| 1726 | →→→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1 | |
| 1727 | →→𝜑↔𝜓𝜒→→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens ax-2, 1726 | |
| 1728 | →→→𝜑↔𝜓𝜒→→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→𝜑→𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 1729 | →→→𝜑↔𝜓𝜒→𝜑→𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 1727, 1728 | |
| 1730 | →→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 1725, 1729 | |
| 1731 | →↔𝜓𝜒→𝜒𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜒] into biimpr | |
| 1732 | →→↔𝜓𝜒→𝜒𝜓→𝜑→↔𝜓𝜒→𝜒𝜓 | Subs [𝜑↗→↔𝜓𝜒→𝜒𝜓, 𝜓↗𝜑] into ax-1 | |
| 1733 | →𝜑→↔𝜓𝜒→𝜒𝜓 | Modus ponens 1731, 1732 | |
| 1734 | →→𝜑→↔𝜓𝜒→𝜒𝜓→→𝜑↔𝜓𝜒→𝜑→𝜒𝜓 | Subs [𝜓↗↔𝜓𝜒, 𝜒↗→𝜒𝜓] into ax-2 | |
| 1735 | →→𝜑↔𝜓𝜒→𝜑→𝜒𝜓 | Modus ponens 1733, 1734 | |
| 1736 | →→𝜑→𝜒𝜓→→𝜑𝜒→𝜑𝜓 | Subs [𝜓↗𝜒, 𝜒↗𝜓] into ax-2 | |
| 1737 | →→→𝜑→𝜒𝜓→→𝜑𝜒→𝜑𝜓→→𝜑↔𝜓𝜒→→𝜑→𝜒𝜓→→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜑→𝜒𝜓→→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑↔𝜓𝜒] into ax-1 | |
| 1738 | →→𝜑↔𝜓𝜒→→𝜑→𝜒𝜓→→𝜑𝜒→𝜑𝜓 | Modus ponens 1736, 1737 | |
| 1739 | →→→𝜑↔𝜓𝜒→→𝜑→𝜒𝜓→→𝜑𝜒→𝜑𝜓→→→𝜑↔𝜓𝜒→𝜑→𝜒𝜓→→𝜑↔𝜓𝜒→→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑→𝜒𝜓, 𝜒↗→→𝜑𝜒→𝜑𝜓] into ax-2 | |
| 1740 | →→→𝜑↔𝜓𝜒→𝜑→𝜒𝜓→→𝜑↔𝜓𝜒→→𝜑𝜒→𝜑𝜓 | Modus ponens 1738, 1739 | |
| 1741 | →→𝜑↔𝜓𝜒→→𝜑𝜒→𝜑𝜓 | Modus ponens 1735, 1740 | |
| 1742 | →→→𝜑𝜓→𝜑𝜒→→→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒] into impbi | |
| 1743 | →→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜒→𝜑𝜓, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 1744 | →→→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→𝜑↔𝜓𝜒→→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑↔𝜓𝜒] into ax-1 | |
| 1745 | →→𝜑↔𝜓𝜒→→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓 | Modus ponens 1743, 1744 | |
| 1746 | →→→𝜑↔𝜓𝜒→→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→→𝜑↔𝜓𝜒→→𝜑𝜒→𝜑𝜓→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→→𝜑𝜒→𝜑𝜓, 𝜒↗→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓] into ax-2 | |
| 1747 | →→→𝜑↔𝜓𝜒→→𝜑𝜒→𝜑𝜓→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓 | Modus ponens 1745, 1746 | |
| 1748 | →→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓 | Modus ponens 1741, 1747 | |
| 1749 | →→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜒→𝜑𝜓, 𝜒↗↔→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 1750 | →→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒 | Modus ponens 1742, 1749 | |
| 1751 | →→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1 | |
| 1752 | →→𝜑↔𝜓𝜒→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒 | Modus ponens 1750, 1751 | |
| 1753 | →→→𝜑↔𝜓𝜒→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓, 𝜒↗→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 1754 | →→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒 | Modus ponens 1752, 1753 | |
| 1755 | →→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒 | Modus ponens 1748, 1754 | |
| 1756 | →→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1 | |
| 1757 | →→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 1758 | →→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 1756, 1757 | |
| 1759 | →→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒, 𝜒↗→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 1760 | →→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 1758, 1759 | |
| 1761 | →→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒, 𝜒↗↔→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 1762 | →→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Modus ponens 1755, 1761 | |
| 1763 | →→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 1764 | →→→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Modus ponens 1762, 1763 | |
| 1765 | →→→→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜒↗→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 1766 | →→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Modus ponens 1764, 1765 | |
| 1767 | →→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Modus ponens 1756, 1766 | |
| 1768 | →→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1 | |
| 1769 | →→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Modus ponens 1767, 1768 | |
| 1770 | →→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒, 𝜒↗→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 1771 | →→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Modus ponens 1769, 1770 | |
| 1772 | →→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Modus ponens 1730, 1771 | |
| 1773 | →→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒] into id | |
| 1774 | →→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1 | |
| 1775 | →→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒 | Subs [𝜑↗→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1 | |
| 1776 | →→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒 | Modus ponens 1774, 1775 | |
| 1777 | →→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒, 𝜒↗→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒] into ax-2 | |
| 1778 | →→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒 | Modus ponens 1776, 1777 | |
| 1779 | →→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒, 𝜒↗↔→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 1780 | →→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Modus ponens 1772, 1779 | |
| 1781 | →→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1 | |
| 1782 | →→𝜑↔𝜓𝜒→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Modus ponens 1780, 1781 | |
| 1783 | →→→𝜑↔𝜓𝜒→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒, 𝜒↗→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 1784 | →→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Modus ponens 1782, 1783 | |
| 1785 | →→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Modus ponens 1773, 1780 | |
| 1786 | →↔→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒] into biimp | |
| 1787 | →→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 1788 | →→→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→𝜓→→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓] into ax-1 | |
| 1789 | →𝜓→→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓 | Modus ponens 1787, 1788 | |
| 1790 | →→𝜓→→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→→𝜓→𝜑𝜓→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓] into ax-2 | |
| 1791 | →→𝜓→𝜑𝜓→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓 | Modus ponens 1789, 1790 | |
| 1792 | →𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓 | Modus ponens 208, 1791 | |
| 1793 | →→↔→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒 | Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜒] into ax-2 | |
| 1794 | →→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒 | Modus ponens 1786, 1793 | |
| 1795 | →→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒 | Subs [𝜑↗→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒] into ax-1 | |
| 1796 | →𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒 | Modus ponens 1794, 1795 | |
| 1797 | →→𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒 | Subs [𝜑↗𝜓, 𝜓↗→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓, 𝜒↗→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒] into ax-2 | |
| 1798 | →→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒 | Modus ponens 1796, 1797 | |
| 1799 | →𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒 | Modus ponens 1792, 1798 | |
| 1800 | →↔→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒] into id | |
| 1801 | →↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 1802 | →→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 1803 | →↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒 | Modus ponens 1801, 1802 | |
| 1804 | →→↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜓↔→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 1805 | →→↔→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒 | Modus ponens 1803, 1804 | |
| 1806 | →→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→→𝜓↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒 | Subs [𝜑↗𝜓, 𝜓↗↔→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜑𝜒] into ax-2 | |
| 1807 | →→𝜓↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒 | Modus ponens 1799, 1806 | |
| 1808 | →→→𝜓↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜓↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜓↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 1809 | →↔→𝜑𝜓→𝜑𝜒→→𝜓↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒 | Modus ponens 1807, 1808 | |
| 1810 | →→↔→𝜑𝜓→𝜑𝜒→→𝜓↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒 | Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜓↔→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜓→𝜑𝜒] into ax-2 | |
| 1811 | →→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒 | Modus ponens 1809, 1810 | |
| 1812 | →↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒 | Modus ponens 1801, 1811 | |
| 1813 | →→𝜑→→𝜑𝜒𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜒𝜒 | Subs [𝜑↗→𝜑→→𝜑𝜒𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 1814 | →↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜒𝜒 | Modus ponens 264, 1813 | |
| 1815 | →→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 1816 | →↔→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒 | Modus ponens 267, 1815 | |
| 1817 | →→↔→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒 | Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜓→𝜑𝜒, 𝜒↗→𝜑→𝜓→𝜑𝜒] into ax-2 | |
| 1818 | →→↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒 | Modus ponens 1816, 1817 | |
| 1819 | →↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒 | Modus ponens 1812, 1818 | |
| 1820 | →→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 1821 | →↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒 | Modus ponens 277, 1820 | |
| 1822 | →→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜒𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→→𝜑𝜒𝜒, 𝜒↗→𝜑→→𝜓→𝜑𝜒→𝜓𝜒] into ax-2 | |
| 1823 | →→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜒𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒 | Modus ponens 1821, 1822 | |
| 1824 | →↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒 | Modus ponens 1814, 1823 | |
| 1825 | →→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒 | Subs [𝜑↗→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 1826 | →↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒 | Modus ponens 283, 1825 | |
| 1827 | →→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒 | Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→→𝜓→𝜑𝜒→𝜓𝜒, 𝜒↗→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒] into ax-2 | |
| 1828 | →→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒 | Modus ponens 1826, 1827 | |
| 1829 | →↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒 | Modus ponens 1824, 1828 | |
| 1830 | →→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒 | Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→𝜓→𝜑𝜒, 𝜒↗→𝜑→𝜓𝜒] into ax-2 | |
| 1831 | →→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒 | Modus ponens 1829, 1830 | |
| 1832 | →↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒 | Modus ponens 1819, 1831 | |
| 1833 | →↔→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒] into biimpr | |
| 1834 | →𝜒→𝜑𝜒 | Subs [𝜑↗𝜒, 𝜓↗𝜑] into ax-1 | |
| 1835 | →→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒 | Subs [𝜑↗→𝜑𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 1836 | →→→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→𝜒→→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒, 𝜓↗𝜒] into ax-1 | |
| 1837 | →𝜒→→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒 | Modus ponens 1835, 1836 | |
| 1838 | →→𝜒→→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→→𝜒→𝜑𝜒→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒] into ax-2 | |
| 1839 | →→𝜒→𝜑𝜒→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒 | Modus ponens 1837, 1838 | |
| 1840 | →𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒 | Modus ponens 1834, 1839 | |
| 1841 | →→↔→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑𝜓] into ax-2 | |
| 1842 | →→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓 | Modus ponens 1833, 1841 | |
| 1843 | →→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓, 𝜓↗𝜒] into ax-1 | |
| 1844 | →𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓 | Modus ponens 1842, 1843 | |
| 1845 | →→𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗𝜒, 𝜓↗→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒, 𝜒↗→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓] into ax-2 | |
| 1846 | →→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓 | Modus ponens 1844, 1845 | |
| 1847 | →𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓 | Modus ponens 1840, 1846 | |
| 1848 | →↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗𝜒] into ax-1 | |
| 1849 | →→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 1850 | →↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒 | Modus ponens 1848, 1849 | |
| 1851 | →→↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜒↔→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 1852 | →→↔→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒 | Modus ponens 1850, 1851 | |
| 1853 | →→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→→𝜒↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓 | Subs [𝜑↗𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜑𝜓] into ax-2 | |
| 1854 | →→𝜒↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓 | Modus ponens 1847, 1853 | |
| 1855 | →→→𝜒↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→→𝜒↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜒↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 1856 | →↔→𝜑𝜓→𝜑𝜒→→𝜒↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓 | Modus ponens 1854, 1855 | |
| 1857 | →→↔→𝜑𝜓→𝜑𝜒→→𝜒↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜒↔→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜒→𝜑𝜓] into ax-2 | |
| 1858 | →→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓 | Modus ponens 1856, 1857 | |
| 1859 | →↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓 | Modus ponens 1848, 1858 | |
| 1860 | →→𝜑→→𝜑𝜓𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜓𝜓 | Subs [𝜑↗→𝜑→→𝜑𝜓𝜓, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 1861 | →↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜓𝜓 | Modus ponens pm2.27, 1860 | |
| 1862 | →→𝜒→𝜑𝜓→𝜑→𝜒→𝜑𝜓 | Subs [𝜑↗→𝜒→𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 1863 | →→→𝜒→𝜑𝜓→𝜑→𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→→𝜒→𝜑𝜓→𝜑→𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜒→𝜑𝜓→𝜑→𝜒→𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 1864 | →↔→𝜑𝜓→𝜑𝜒→→𝜒→𝜑𝜓→𝜑→𝜒→𝜑𝜓 | Modus ponens 1862, 1863 | |
| 1865 | →→↔→𝜑𝜓→𝜑𝜒→→𝜒→𝜑𝜓→𝜑→𝜒→𝜑𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒→𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜒→𝜑𝜓, 𝜒↗→𝜑→𝜒→𝜑𝜓] into ax-2 | |
| 1866 | →→↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒→𝜑𝜓 | Modus ponens 1864, 1865 | |
| 1867 | →↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒→𝜑𝜓 | Modus ponens 1859, 1866 | |
| 1868 | →→→𝜑𝜓𝜓→→𝜒→𝜑𝜓→𝜒𝜓 | Subs [𝜑↗→𝜑𝜓] into imim2 | |
| 1869 | →→→→𝜑𝜓𝜓→→𝜒→𝜑𝜓→𝜒𝜓→𝜑→→→𝜑𝜓𝜓→→𝜒→𝜑𝜓→𝜒𝜓 | Subs [𝜑↗→→→𝜑𝜓𝜓→→𝜒→𝜑𝜓→𝜒𝜓, 𝜓↗𝜑] into ax-1 | |
| 1870 | →𝜑→→→𝜑𝜓𝜓→→𝜒→𝜑𝜓→𝜒𝜓 | Modus ponens 1868, 1869 | |
| 1871 | →→𝜑→→→𝜑𝜓𝜓→→𝜒→𝜑𝜓→𝜒𝜓→→𝜑→→𝜑𝜓𝜓→𝜑→→𝜒→𝜑𝜓→𝜒𝜓 | Subs [𝜓↗→→𝜑𝜓𝜓, 𝜒↗→→𝜒→𝜑𝜓→𝜒𝜓] into ax-2 | |
| 1872 | →→𝜑→→𝜑𝜓𝜓→𝜑→→𝜒→𝜑𝜓→𝜒𝜓 | Modus ponens 1870, 1871 | |
| 1873 | →→→𝜑→→𝜑𝜓𝜓→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜓𝜓→𝜑→→𝜒→𝜑𝜓→𝜒𝜓 | Subs [𝜑↗→→𝜑→→𝜑𝜓𝜓→𝜑→→𝜒→𝜑𝜓→𝜒𝜓, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 1874 | →↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜓𝜓→𝜑→→𝜒→𝜑𝜓→𝜒𝜓 | Modus ponens 1872, 1873 | |
| 1875 | →→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜓𝜓→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜓𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒→𝜑𝜓→𝜒𝜓 | Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→→𝜑𝜓𝜓, 𝜒↗→𝜑→→𝜒→𝜑𝜓→𝜒𝜓] into ax-2 | |
| 1876 | →→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜓𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒→𝜑𝜓→𝜒𝜓 | Modus ponens 1874, 1875 | |
| 1877 | →↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒→𝜑𝜓→𝜒𝜓 | Modus ponens 1861, 1876 | |
| 1878 | →→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓 | Subs [𝜓↗→𝜒→𝜑𝜓, 𝜒↗→𝜒𝜓] into ax-2 | |
| 1879 | →→→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓 | Subs [𝜑↗→→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 1880 | →↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓 | Modus ponens 1878, 1879 | |
| 1881 | →→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓 | Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→→𝜒→𝜑𝜓→𝜒𝜓, 𝜒↗→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓] into ax-2 | |
| 1882 | →→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓 | Modus ponens 1880, 1881 | |
| 1883 | →↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓 | Modus ponens 1877, 1882 | |
| 1884 | →→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒𝜓 | Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→𝜒→𝜑𝜓, 𝜒↗→𝜑→𝜒𝜓] into ax-2 | |
| 1885 | →→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒𝜓 | Modus ponens 1883, 1884 | |
| 1886 | →↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒𝜓 | Modus ponens 1867, 1885 | |
| 1887 | →→𝜓𝜒→→𝜒𝜓↔𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗𝜒] into impbi | |
| 1888 | →→→𝜓𝜒→→𝜒𝜓↔𝜓𝜒→𝜑→→𝜓𝜒→→𝜒𝜓↔𝜓𝜒 | Subs [𝜑↗→→𝜓𝜒→→𝜒𝜓↔𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 1889 | →𝜑→→𝜓𝜒→→𝜒𝜓↔𝜓𝜒 | Modus ponens 1887, 1888 | |
| 1890 | →→𝜑→→𝜓𝜒→→𝜒𝜓↔𝜓𝜒→→𝜑→𝜓𝜒→𝜑→→𝜒𝜓↔𝜓𝜒 | Subs [𝜓↗→𝜓𝜒, 𝜒↗→→𝜒𝜓↔𝜓𝜒] into ax-2 | |
| 1891 | →→𝜑→𝜓𝜒→𝜑→→𝜒𝜓↔𝜓𝜒 | Modus ponens 1889, 1890 | |
| 1892 | →→→𝜑→𝜓𝜒→𝜑→→𝜒𝜓↔𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜓𝜒→𝜑→→𝜒𝜓↔𝜓𝜒 | Subs [𝜑↗→→𝜑→𝜓𝜒→𝜑→→𝜒𝜓↔𝜓𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 1893 | →↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜓𝜒→𝜑→→𝜒𝜓↔𝜓𝜒 | Modus ponens 1891, 1892 | |
| 1894 | →→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜓𝜒→𝜑→→𝜒𝜓↔𝜓𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒𝜓↔𝜓𝜒 | Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→𝜑→→𝜒𝜓↔𝜓𝜒] into ax-2 | |
| 1895 | →→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒𝜓↔𝜓𝜒 | Modus ponens 1893, 1894 | |
| 1896 | →↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒𝜓↔𝜓𝜒 | Modus ponens 1832, 1895 | |
| 1897 | →→𝜑→→𝜒𝜓↔𝜓𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒 | Subs [𝜓↗→𝜒𝜓, 𝜒↗↔𝜓𝜒] into ax-2 | |
| 1898 | →→→𝜑→→𝜒𝜓↔𝜓𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜒𝜓↔𝜓𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒 | Subs [𝜑↗→→𝜑→→𝜒𝜓↔𝜓𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 1899 | →↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜒𝜓↔𝜓𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒 | Modus ponens 1897, 1898 | |
| 1900 | →→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜒𝜓↔𝜓𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒𝜓↔𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒 | Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→→𝜒𝜓↔𝜓𝜒, 𝜒↗→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒] into ax-2 | |
| 1901 | →→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒𝜓↔𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒 | Modus ponens 1899, 1900 | |
| 1902 | →↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒 | Modus ponens 1896, 1901 | |
| 1903 | →→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒 | Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→𝜒𝜓, 𝜒↗→𝜑↔𝜓𝜒] into ax-2 | |
| 1904 | →→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒 | Modus ponens 1902, 1903 | |
| 1905 | →↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒 | Modus ponens 1886, 1904 | |
| 1906 | →→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into impbi | |
| 1907 | →→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Modus ponens 1785, 1906 | |
| 1908 | ↔→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Modus ponens 1905, 1907 | pm5.74 |
| 1909 | →→𝜑¬¬𝜑→→¬¬𝜑𝜑↔𝜑¬¬𝜑 | Subs [𝜓↗¬¬𝜑] into impbi | |
| 1910 | →→¬¬𝜑𝜑↔𝜑¬¬𝜑 | Modus ponens notnot, 1909 | |
| 1911 | ↔𝜑¬¬𝜑 | Modus ponens notnotr, 1910 | notnotb |
| 1912 | →→→𝜑𝜓→¬𝜓¬𝜑→→→¬𝜓¬𝜑→𝜑𝜓↔→𝜑𝜓→¬𝜓¬𝜑 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬𝜓¬𝜑] into impbi | |
| 1913 | →→→¬𝜓¬𝜑→𝜑𝜓↔→𝜑𝜓→¬𝜓¬𝜑 | Modus ponens con3, 1912 | |
| 1914 | ↔→𝜑𝜓→¬𝜓¬𝜑 | Modus ponens 316, 1913 | con34b |
| 1915 | ↔𝜓¬¬𝜓 | Subs [𝜑↗𝜓] into notnotb | |
| 1916 | →↔𝜑¬¬𝜑↔¬¬𝜑𝜑 | Subs [𝜓↗¬¬𝜑] into bicom1 | |
| 1917 | ↔¬¬𝜑𝜑 | Modus ponens notnotb, 1916 | |
| 1918 | →↔¬¬𝜑𝜑→↔𝜑𝜓↔¬¬𝜑𝜑 | Subs [𝜑↗↔¬¬𝜑𝜑, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 1919 | →↔𝜑𝜓↔¬¬𝜑𝜑 | Modus ponens 1917, 1918 | |
| 1920 | ↔→↔𝜑𝜓↔¬¬𝜑𝜑↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬¬𝜑, 𝜒↗𝜑] into pm5.74 | |
| 1921 | →↔→↔𝜑𝜓↔¬¬𝜑𝜑↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑→→↔𝜑𝜓↔¬¬𝜑𝜑↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑 | Subs [𝜑↗→↔𝜑𝜓↔¬¬𝜑𝜑, 𝜓↗↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑] into biimp | |
| 1922 | →→↔𝜑𝜓↔¬¬𝜑𝜑↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑 | Modus ponens 1920, 1921 | |
| 1923 | ↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑 | Modus ponens 1919, 1922 | |
| 1924 | ↔→↔𝜑𝜓↔𝜑𝜓↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into pm5.74 | |
| 1925 | →↔→↔𝜑𝜓↔𝜑𝜓↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔𝜑𝜓↔𝜑𝜓↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜓, 𝜓↗↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓] into biimp | |
| 1926 | →→↔𝜑𝜓↔𝜑𝜓↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Modus ponens 1924, 1925 | |
| 1927 | ↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Modus ponens 1651, 1926 | |
| 1928 | →↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Subs [𝜑↗→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓𝜓] into biimp | |
| 1929 | →→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Modus ponens 1927, 1928 | |
| 1930 | →↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑 | Subs [𝜑↗→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓𝜑] into biimp | |
| 1931 | →→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑 | Modus ponens 1923, 1930 | |
| 1932 | →→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Subs [𝜑↗→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓¬¬𝜑] into ax-1 | |
| 1933 | →→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Modus ponens 1929, 1932 | |
| 1934 | →→→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓 | Subs [𝜑↗→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓𝜑, 𝜒↗→↔𝜑𝜓𝜓] into ax-2 | |
| 1935 | →→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓 | Modus ponens 1933, 1934 | |
| 1936 | →→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓 | Modus ponens 1931, 1935 | |
| 1937 | →↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑 | Subs [𝜑↗→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓𝜓] into bicom1 | |
| 1938 | ↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑 | Modus ponens 1927, 1937 | |
| 1939 | →↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑 | Subs [𝜑↗→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓𝜑] into biimp | |
| 1940 | →→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑 | Modus ponens 1938, 1939 | |
| 1941 | →↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑 | Subs [𝜑↗→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓𝜑] into bicom1 | |
| 1942 | ↔→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑 | Modus ponens 1923, 1941 | |
| 1943 | →↔→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑 | Subs [𝜑↗→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓¬¬𝜑] into biimp | |
| 1944 | →→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑 | Modus ponens 1942, 1943 | |
| 1945 | →→→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜓→→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑 | Subs [𝜑↗→→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓𝜓] into ax-1 | |
| 1946 | →→↔𝜑𝜓𝜓→→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑 | Modus ponens 1944, 1945 | |
| 1947 | →→→↔𝜑𝜓𝜓→→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑→→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑 | Subs [𝜑↗→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓𝜑, 𝜒↗→↔𝜑𝜓¬¬𝜑] into ax-2 | |
| 1948 | →→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑 | Modus ponens 1946, 1947 | |
| 1949 | →→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑 | Modus ponens 1940, 1948 | |
| 1950 | →→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓 | Subs [𝜑↗→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓𝜓] into impbi | |
| 1951 | →→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓 | Modus ponens 1936, 1950 | |
| 1952 | ↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓 | Modus ponens 1949, 1951 | |
| 1953 | ↔→↔𝜑𝜓↔¬¬𝜑𝜓↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬¬𝜑, 𝜒↗𝜓] into pm5.74 | |
| 1954 | →↔→↔𝜑𝜓↔¬¬𝜑𝜓↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓↔↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→↔𝜑𝜓↔¬¬𝜑𝜓 | Subs [𝜑↗→↔𝜑𝜓↔¬¬𝜑𝜓, 𝜓↗↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓] into bicom1 | |
| 1955 | ↔↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→↔𝜑𝜓↔¬¬𝜑𝜓 | Modus ponens 1953, 1954 | |
| 1956 | →↔↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→↔𝜑𝜓↔¬¬𝜑𝜓→↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→↔𝜑𝜓↔¬¬𝜑𝜓 | Subs [𝜑↗↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓↔¬¬𝜑𝜓] into biimp | |
| 1957 | →↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→↔𝜑𝜓↔¬¬𝜑𝜓 | Modus ponens 1955, 1956 | |
| 1958 | →↔𝜑𝜓↔¬¬𝜑𝜓 | Modus ponens 1952, 1957 | |
| 1959 | →↔𝜓¬¬𝜓→↔𝜑𝜓↔𝜓¬¬𝜓 | Subs [𝜑↗↔𝜓¬¬𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 1960 | →↔𝜑𝜓↔𝜓¬¬𝜓 | Modus ponens 1915, 1959 | |
| 1961 | →↔→↔𝜑𝜓↔¬¬𝜑𝜓↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→→↔𝜑𝜓↔¬¬𝜑𝜓↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓 | Subs [𝜑↗→↔𝜑𝜓↔¬¬𝜑𝜓, 𝜓↗↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓] into biimp | |
| 1962 | →→↔𝜑𝜓↔¬¬𝜑𝜓↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓 | Modus ponens 1953, 1961 | |
| 1963 | ↔→↔𝜑𝜓↔𝜓¬¬𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜒↗¬¬𝜓] into pm5.74 | |
| 1964 | →↔→↔𝜑𝜓↔𝜓¬¬𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓→→↔𝜑𝜓↔𝜓¬¬𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓 | Subs [𝜑↗→↔𝜑𝜓↔𝜓¬¬𝜓, 𝜓↗↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓] into biimp | |
| 1965 | →→↔𝜑𝜓↔𝜓¬¬𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓 | Modus ponens 1963, 1964 | |
| 1966 | ↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓 | Modus ponens 1960, 1965 | |
| 1967 | →↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓 | Subs [𝜑↗→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓¬¬𝜓] into biimp | |
| 1968 | →→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓 | Modus ponens 1966, 1967 | |
| 1969 | →↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓 | Subs [𝜑↗→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓𝜓] into biimp | |
| 1970 | →→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓→→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓 | Subs [𝜑↗→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓, 𝜓↗→↔𝜑𝜓¬¬𝜑] into ax-1 | |
| 1971 | →→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓 | Modus ponens 1968, 1970 | |
| 1972 | →→→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓→→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓 | Subs [𝜑↗→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓𝜓, 𝜒↗→↔𝜑𝜓¬¬𝜓] into ax-2 | |
| 1973 | →→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓 | Modus ponens 1971, 1972 | |
| 1974 | →→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓 | Modus ponens 1936, 1973 | |
| 1975 | →↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓↔→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓𝜓 | Subs [𝜑↗→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓¬¬𝜓] into bicom1 | |
| 1976 | ↔→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓𝜓 | Modus ponens 1966, 1975 | |
| 1977 | →↔→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓𝜓→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓𝜓 | Subs [𝜑↗→↔𝜑𝜓¬¬𝜓, 𝜓↗→↔𝜑𝜓𝜓] into biimp | |
| 1978 | →→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓𝜓 | Modus ponens 1976, 1977 | |
| 1979 | →↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑 | Subs [𝜑↗→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓𝜓] into bicom1 | |
| 1980 | ↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑 | Modus ponens 1952, 1979 | |
| 1981 | →↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑 | Subs [𝜑↗→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓¬¬𝜑] into biimp | |
| 1982 | →→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓¬¬𝜓→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑 | Subs [𝜑↗→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓¬¬𝜓] into ax-1 | |
| 1983 | →→↔𝜑𝜓¬¬𝜓→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑 | Modus ponens 1949, 1982 | |
| 1984 | →→→↔𝜑𝜓¬¬𝜓→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑→→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓𝜓→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑 | Subs [𝜑↗→↔𝜑𝜓¬¬𝜓, 𝜓↗→↔𝜑𝜓𝜓, 𝜒↗→↔𝜑𝜓¬¬𝜑] into ax-2 | |
| 1985 | →→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓𝜓→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑 | Modus ponens 1983, 1984 | |
| 1986 | →→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑 | Modus ponens 1978, 1985 | |
| 1987 | →→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓→→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓 | Subs [𝜑↗→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓¬¬𝜓] into impbi | |
| 1988 | →→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓 | Modus ponens 1974, 1987 | |
| 1989 | ↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓 | Modus ponens 1986, 1988 | |
| 1990 | ↔→↔𝜑𝜓↔¬¬𝜑¬¬𝜓↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬¬𝜑, 𝜒↗¬¬𝜓] into pm5.74 | |
| 1991 | →↔→↔𝜑𝜓↔¬¬𝜑¬¬𝜓↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓↔↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓↔¬¬𝜑¬¬𝜓 | Subs [𝜑↗→↔𝜑𝜓↔¬¬𝜑¬¬𝜓, 𝜓↗↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓] into bicom1 | |
| 1992 | ↔↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓↔¬¬𝜑¬¬𝜓 | Modus ponens 1990, 1991 | |
| 1993 | →↔↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓↔¬¬𝜑¬¬𝜓→↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓↔¬¬𝜑¬¬𝜓 | Subs [𝜑↗↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓, 𝜓↗→↔𝜑𝜓↔¬¬𝜑¬¬𝜓] into biimp | |
| 1994 | →↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓↔¬¬𝜑¬¬𝜓 | Modus ponens 1992, 1993 | |
| 1995 | →↔𝜑𝜓↔¬¬𝜑¬¬𝜓 | Modus ponens 1989, 1994 | |
| 1996 | →¬¬𝜓¬¬𝜓 | Subs [𝜑↗¬¬𝜓] into id | |
| 1997 | ↔↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑 | Subs [𝜑↗¬¬𝜑, 𝜓↗¬¬𝜓] into bicom | |
| 1998 | →↔↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑→↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑 | Subs [𝜑↗↔¬¬𝜑¬¬𝜓, 𝜓↗↔¬¬𝜓¬¬𝜑] into biimp | |
| 1999 | →↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑 | Modus ponens 1997, 1998 | |
| 2000 | →→↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑→↔𝜑𝜓→↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑 | Subs [𝜑↗→↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2001 | →↔𝜑𝜓→↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑 | Modus ponens 1999, 2000 | |
| 2002 | →→↔𝜑𝜓→↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑→→↔𝜑𝜓↔¬¬𝜑¬¬𝜓→↔𝜑𝜓↔¬¬𝜓¬¬𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔¬¬𝜑¬¬𝜓, 𝜒↗↔¬¬𝜓¬¬𝜑] into ax-2 | |
| 2003 | →→↔𝜑𝜓↔¬¬𝜑¬¬𝜓→↔𝜑𝜓↔¬¬𝜓¬¬𝜑 | Modus ponens 2001, 2002 | |
| 2004 | →↔𝜑𝜓↔¬¬𝜓¬¬𝜑 | Modus ponens 1995, 2003 | |
| 2005 | →↔¬¬𝜓¬¬𝜑→¬¬𝜓¬¬𝜑 | Subs [𝜑↗¬¬𝜓, 𝜓↗¬¬𝜑] into biimp | |
| 2006 | →→↔¬¬𝜓¬¬𝜑→¬¬𝜓¬¬𝜑→↔𝜑𝜓→↔¬¬𝜓¬¬𝜑→¬¬𝜓¬¬𝜑 | Subs [𝜑↗→↔¬¬𝜓¬¬𝜑→¬¬𝜓¬¬𝜑, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2007 | →↔𝜑𝜓→↔¬¬𝜓¬¬𝜑→¬¬𝜓¬¬𝜑 | Modus ponens 2005, 2006 | |
| 2008 | →→↔𝜑𝜓→↔¬¬𝜓¬¬𝜑→¬¬𝜓¬¬𝜑→→↔𝜑𝜓↔¬¬𝜓¬¬𝜑→↔𝜑𝜓→¬¬𝜓¬¬𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔¬¬𝜓¬¬𝜑, 𝜒↗→¬¬𝜓¬¬𝜑] into ax-2 | |
| 2009 | →→↔𝜑𝜓↔¬¬𝜓¬¬𝜑→↔𝜑𝜓→¬¬𝜓¬¬𝜑 | Modus ponens 2007, 2008 | |
| 2010 | →↔𝜑𝜓→¬¬𝜓¬¬𝜑 | Modus ponens 2004, 2009 | |
| 2011 | →¬¬𝜓→↔𝜑𝜓¬¬𝜓 | Subs [𝜑↗¬¬𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2012 | →→¬¬𝜓→↔𝜑𝜓¬¬𝜓→¬¬𝜓→¬¬𝜓→↔𝜑𝜓¬¬𝜓 | Subs [𝜑↗→¬¬𝜓→↔𝜑𝜓¬¬𝜓, 𝜓↗¬¬𝜓] into ax-1 | |
| 2013 | →¬¬𝜓→¬¬𝜓→↔𝜑𝜓¬¬𝜓 | Modus ponens 2011, 2012 | |
| 2014 | →→¬¬𝜓→¬¬𝜓→↔𝜑𝜓¬¬𝜓→→¬¬𝜓¬¬𝜓→¬¬𝜓→↔𝜑𝜓¬¬𝜓 | Subs [𝜑↗¬¬𝜓, 𝜓↗¬¬𝜓, 𝜒↗→↔𝜑𝜓¬¬𝜓] into ax-2 | |
| 2015 | →→¬¬𝜓¬¬𝜓→¬¬𝜓→↔𝜑𝜓¬¬𝜓 | Modus ponens 2013, 2014 | |
| 2016 | →→↔𝜑𝜓→¬¬𝜓¬¬𝜑→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬¬𝜓, 𝜒↗¬¬𝜑] into ax-2 | |
| 2017 | →→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑→¬¬𝜓→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑 | Subs [𝜑↗→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑, 𝜓↗¬¬𝜓] into ax-1 | |
| 2018 | →¬¬𝜓→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑 | Modus ponens 1986, 2017 | |
| 2019 | →→¬¬𝜓→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑→→¬¬𝜓→↔𝜑𝜓¬¬𝜓→¬¬𝜓→↔𝜑𝜓¬¬𝜑 | Subs [𝜑↗¬¬𝜓, 𝜓↗→↔𝜑𝜓¬¬𝜓, 𝜒↗→↔𝜑𝜓¬¬𝜑] into ax-2 | |
| 2020 | →→¬¬𝜓→↔𝜑𝜓¬¬𝜓→¬¬𝜓→↔𝜑𝜓¬¬𝜑 | Modus ponens 2018, 2019 | |
| 2021 | →¬¬𝜓→↔𝜑𝜓¬¬𝜑 | Modus ponens 2011, 2020 | |
| 2022 | →↔𝜑𝜓→¬¬𝜓↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬¬𝜓] into ax-1 | |
| 2023 | →→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓 | Subs [𝜑↗→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2024 | →↔𝜑𝜓→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓 | Modus ponens 2022, 2023 | |
| 2025 | →→↔𝜑𝜓→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→¬¬𝜓↔𝜑𝜓] into ax-2 | |
| 2026 | →→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓 | Modus ponens 2024, 2025 | |
| 2027 | →→¬¬𝜓→↔𝜑𝜓¬¬𝜑→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬𝜑 | Subs [𝜑↗¬¬𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗¬¬𝜑] into ax-2 | |
| 2028 | →→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬𝜑 | Modus ponens 2021, 2027 | |
| 2029 | →→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬𝜑→↔𝜑𝜓→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬𝜑 | Subs [𝜑↗→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬𝜑, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2030 | →↔𝜑𝜓→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬𝜑 | Modus ponens 2028, 2029 | |
| 2031 | →→↔𝜑𝜓→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬𝜑→→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬𝜓¬¬𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬𝜓↔𝜑𝜓, 𝜒↗→¬¬𝜓¬¬𝜑] into ax-2 | |
| 2032 | →→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬𝜓¬¬𝜑 | Modus ponens 2030, 2031 | |
| 2033 | →→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜑] into ax-3 | |
| 2034 | →→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓→↔𝜑𝜓→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓 | Subs [𝜑↗→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2035 | →↔𝜑𝜓→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓 | Modus ponens 2033, 2034 | |
| 2036 | →→↔𝜑𝜓→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓→→↔𝜑𝜓→¬¬𝜓¬¬𝜑→↔𝜑𝜓→¬𝜑¬𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬𝜓¬¬𝜑, 𝜒↗→¬𝜑¬𝜓] into ax-2 | |
| 2037 | →→↔𝜑𝜓→¬¬𝜓¬¬𝜑→↔𝜑𝜓→¬𝜑¬𝜓 | Modus ponens 2035, 2036 | |
| 2038 | →↔𝜑𝜓→¬𝜑¬𝜓 | Modus ponens 2010, 2037 | |
| 2039 | →↔¬¬𝜑¬¬𝜓→¬¬𝜑¬¬𝜓 | Subs [𝜑↗¬¬𝜑, 𝜓↗¬¬𝜓] into biimp | |
| 2040 | →→↔¬¬𝜑¬¬𝜓→¬¬𝜑¬¬𝜓→↔𝜑𝜓→↔¬¬𝜑¬¬𝜓→¬¬𝜑¬¬𝜓 | Subs [𝜑↗→↔¬¬𝜑¬¬𝜓→¬¬𝜑¬¬𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2041 | →↔𝜑𝜓→↔¬¬𝜑¬¬𝜓→¬¬𝜑¬¬𝜓 | Modus ponens 2039, 2040 | |
| 2042 | →→↔𝜑𝜓→↔¬¬𝜑¬¬𝜓→¬¬𝜑¬¬𝜓→→↔𝜑𝜓↔¬¬𝜑¬¬𝜓→↔𝜑𝜓→¬¬𝜑¬¬𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔¬¬𝜑¬¬𝜓, 𝜒↗→¬¬𝜑¬¬𝜓] into ax-2 | |
| 2043 | →→↔𝜑𝜓↔¬¬𝜑¬¬𝜓→↔𝜑𝜓→¬¬𝜑¬¬𝜓 | Modus ponens 2041, 2042 | |
| 2044 | →↔𝜑𝜓→¬¬𝜑¬¬𝜓 | Modus ponens 1995, 2043 | |
| 2045 | →→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑→↔𝜑𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑 | Subs [𝜑↗→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2046 | →↔𝜑𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑 | Modus ponens 494, 2045 | |
| 2047 | →→↔𝜑𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑→→↔𝜑𝜓→¬¬𝜑¬¬𝜓→↔𝜑𝜓→¬𝜓¬𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬𝜑¬¬𝜓, 𝜒↗→¬𝜓¬𝜑] into ax-2 | |
| 2048 | →→↔𝜑𝜓→¬¬𝜑¬¬𝜓→↔𝜑𝜓→¬𝜓¬𝜑 | Modus ponens 2046, 2047 | |
| 2049 | →↔𝜑𝜓→¬𝜓¬𝜑 | Modus ponens 2044, 2048 | |
| 2050 | →→¬𝜑¬𝜓→→¬𝜓¬𝜑↔¬𝜑¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓] into impbi | |
| 2051 | →→¬𝜓¬𝜑→→¬𝜑¬𝜓→¬𝜓¬𝜑 | Subs [𝜑↗→¬𝜓¬𝜑, 𝜓↗→¬𝜑¬𝜓] into ax-1 | |
| 2052 | →→→¬𝜓¬𝜑→→¬𝜑¬𝜓→¬𝜓¬𝜑→↔𝜑𝜓→→¬𝜓¬𝜑→→¬𝜑¬𝜓→¬𝜓¬𝜑 | Subs [𝜑↗→→¬𝜓¬𝜑→→¬𝜑¬𝜓→¬𝜓¬𝜑, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2053 | →↔𝜑𝜓→→¬𝜓¬𝜑→→¬𝜑¬𝜓→¬𝜓¬𝜑 | Modus ponens 2051, 2052 | |
| 2054 | →→↔𝜑𝜓→→¬𝜓¬𝜑→→¬𝜑¬𝜓→¬𝜓¬𝜑→→↔𝜑𝜓→¬𝜓¬𝜑→↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜓¬𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬𝜓¬𝜑, 𝜒↗→→¬𝜑¬𝜓→¬𝜓¬𝜑] into ax-2 | |
| 2055 | →→↔𝜑𝜓→¬𝜓¬𝜑→↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜓¬𝜑 | Modus ponens 2053, 2054 | |
| 2056 | →↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜓¬𝜑 | Modus ponens 2049, 2055 | |
| 2057 | →→→¬𝜑¬𝜓→→¬𝜓¬𝜑↔¬𝜑¬𝜓→→→¬𝜑¬𝜓→¬𝜓¬𝜑→→¬𝜑¬𝜓↔¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜓¬𝜑, 𝜒↗↔¬𝜑¬𝜓] into ax-2 | |
| 2058 | →→→¬𝜑¬𝜓→¬𝜓¬𝜑→→¬𝜑¬𝜓↔¬𝜑¬𝜓 | Modus ponens 2050, 2057 | |
| 2059 | →→→→¬𝜑¬𝜓→¬𝜓¬𝜑→→¬𝜑¬𝜓↔¬𝜑¬𝜓→↔𝜑𝜓→→→¬𝜑¬𝜓→¬𝜓¬𝜑→→¬𝜑¬𝜓↔¬𝜑¬𝜓 | Subs [𝜑↗→→→¬𝜑¬𝜓→¬𝜓¬𝜑→→¬𝜑¬𝜓↔¬𝜑¬𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2060 | →↔𝜑𝜓→→→¬𝜑¬𝜓→¬𝜓¬𝜑→→¬𝜑¬𝜓↔¬𝜑¬𝜓 | Modus ponens 2058, 2059 | |
| 2061 | →→↔𝜑𝜓→→→¬𝜑¬𝜓→¬𝜓¬𝜑→→¬𝜑¬𝜓↔¬𝜑¬𝜓→→↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜓¬𝜑→↔𝜑𝜓→→¬𝜑¬𝜓↔¬𝜑¬𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→¬𝜑¬𝜓→¬𝜓¬𝜑, 𝜒↗→→¬𝜑¬𝜓↔¬𝜑¬𝜓] into ax-2 | |
| 2062 | →→↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜓¬𝜑→↔𝜑𝜓→→¬𝜑¬𝜓↔¬𝜑¬𝜓 | Modus ponens 2060, 2061 | |
| 2063 | →↔𝜑𝜓→→¬𝜑¬𝜓↔¬𝜑¬𝜓 | Modus ponens 2056, 2062 | |
| 2064 | →→¬𝜑¬𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑¬𝜓] into id | |
| 2065 | →→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2066 | →→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓→→¬𝜑¬𝜓→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓] into ax-1 | |
| 2067 | →→¬𝜑¬𝜓→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓 | Modus ponens 2065, 2066 | |
| 2068 | →→→¬𝜑¬𝜓→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓→→→¬𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓, 𝜒↗→↔𝜑𝜓→¬𝜑¬𝜓] into ax-2 | |
| 2069 | →→→¬𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓 | Modus ponens 2067, 2068 | |
| 2070 | →→↔𝜑𝜓→→¬𝜑¬𝜓↔¬𝜑¬𝜓→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬𝜑¬𝜓, 𝜒↗↔¬𝜑¬𝜓] into ax-2 | |
| 2071 | →→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓 | Modus ponens 2063, 2070 | |
| 2072 | →→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓→→¬𝜑¬𝜓→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓 | Subs [𝜑↗→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓] into ax-1 | |
| 2073 | →→¬𝜑¬𝜓→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓 | Modus ponens 2071, 2072 | |
| 2074 | →→→¬𝜑¬𝜓→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓→→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓→→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→↔𝜑𝜓→¬𝜑¬𝜓, 𝜒↗→↔𝜑𝜓↔¬𝜑¬𝜓] into ax-2 | |
| 2075 | →→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓→→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓 | Modus ponens 2073, 2074 | |
| 2076 | →→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓 | Modus ponens 2065, 2075 | |
| 2077 | →→→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓→↔𝜑𝜓→→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓 | Subs [𝜑↗→→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2078 | →↔𝜑𝜓→→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓 | Modus ponens 2076, 2077 | |
| 2079 | →→↔𝜑𝜓→→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬𝜑¬𝜓, 𝜒↗→↔𝜑𝜓↔¬𝜑¬𝜓] into ax-2 | |
| 2080 | →→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓 | Modus ponens 2078, 2079 | |
| 2081 | →↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓 | Modus ponens 2038, 2080 | |
| 2082 | →→↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗↔¬𝜑¬𝜓] into ax-2 | |
| 2083 | →→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓 | Modus ponens 2081, 2082 | |
| 2084 | →→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓→↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓 | Subs [𝜑↗→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2085 | →↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓 | Modus ponens 2083, 2084 | |
| 2086 | →→↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓→→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→↔𝜑𝜓↔𝜑𝜓, 𝜒↗→↔𝜑𝜓↔¬𝜑¬𝜓] into ax-2 | |
| 2087 | →→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓 | Modus ponens 2085, 2086 | |
| 2088 | →↔𝜑𝜓↔¬𝜑¬𝜓 | Modus ponens 1651, 2083 | |
| 2089 | →↔¬𝜑¬𝜓↔¬𝜑¬𝜓 | Subs [𝜑↗↔¬𝜑¬𝜓] into id | |
| 2090 | ↔↔¬𝜑¬𝜓↔¬𝜓¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓] into bicom | |
| 2091 | →↔↔¬𝜑¬𝜓↔¬𝜓¬𝜑→↔¬𝜑¬𝜓↔¬𝜓¬𝜑 | Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗↔¬𝜓¬𝜑] into biimp | |
| 2092 | →↔¬𝜑¬𝜓↔¬𝜓¬𝜑 | Modus ponens 2090, 2091 | |
| 2093 | →→↔¬𝜑¬𝜓↔¬𝜓¬𝜑→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜓¬𝜑 | Subs [𝜑↗→↔¬𝜑¬𝜓↔¬𝜓¬𝜑, 𝜓↗↔¬𝜑¬𝜓] into ax-1 | |
| 2094 | →↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜓¬𝜑 | Modus ponens 2092, 2093 | |
| 2095 | →→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜓¬𝜑→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜓¬𝜑 | Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓, 𝜒↗↔¬𝜓¬𝜑] into ax-2 | |
| 2096 | →→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜓¬𝜑 | Modus ponens 2094, 2095 | |
| 2097 | →↔¬𝜓¬𝜑→¬𝜓¬𝜑 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜑] into biimp | |
| 2098 | →→↔¬𝜓¬𝜑→¬𝜓¬𝜑→↔¬𝜑¬𝜓→↔¬𝜓¬𝜑→¬𝜓¬𝜑 | Subs [𝜑↗→↔¬𝜓¬𝜑→¬𝜓¬𝜑, 𝜓↗↔¬𝜑¬𝜓] into ax-1 | |
| 2099 | →↔¬𝜑¬𝜓→↔¬𝜓¬𝜑→¬𝜓¬𝜑 | Modus ponens 2097, 2098 | |
| 2100 | →→↔¬𝜑¬𝜓→↔¬𝜓¬𝜑→¬𝜓¬𝜑→→↔¬𝜑¬𝜓↔¬𝜓¬𝜑→↔¬𝜑¬𝜓→¬𝜓¬𝜑 | Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗↔¬𝜓¬𝜑, 𝜒↗→¬𝜓¬𝜑] into ax-2 | |
| 2101 | →→↔¬𝜑¬𝜓↔¬𝜓¬𝜑→↔¬𝜑¬𝜓→¬𝜓¬𝜑 | Modus ponens 2099, 2100 | |
| 2102 | →↔¬𝜑¬𝜓→¬𝜓¬𝜑 | Modus ponens 2092, 2101 | |
| 2103 | →¬𝜓→↔¬𝜑¬𝜓¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1 | |
| 2104 | →→¬𝜓→↔¬𝜑¬𝜓¬𝜓→¬𝜓→¬𝜓→↔¬𝜑¬𝜓¬𝜓 | Subs [𝜑↗→¬𝜓→↔¬𝜑¬𝜓¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 2105 | →¬𝜓→¬𝜓→↔¬𝜑¬𝜓¬𝜓 | Modus ponens 2103, 2104 | |
| 2106 | →→¬𝜓→¬𝜓→↔¬𝜑¬𝜓¬𝜓→→¬𝜓¬𝜓→¬𝜓→↔¬𝜑¬𝜓¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→↔¬𝜑¬𝜓¬𝜓] into ax-2 | |
| 2107 | →→¬𝜓¬𝜓→¬𝜓→↔¬𝜑¬𝜓¬𝜓 | Modus ponens 2105, 2106 | |
| 2108 | →→↔¬𝜑¬𝜓→¬𝜓¬𝜑→→↔¬𝜑¬𝜓¬𝜓→↔¬𝜑¬𝜓¬𝜑 | Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗¬𝜓, 𝜒↗¬𝜑] into ax-2 | |
| 2109 | →→↔¬𝜑¬𝜓¬𝜓→↔¬𝜑¬𝜓¬𝜑 | Modus ponens 2102, 2108 | |
| 2110 | →→→↔¬𝜑¬𝜓¬𝜓→↔¬𝜑¬𝜓¬𝜑→¬𝜓→→↔¬𝜑¬𝜓¬𝜓→↔¬𝜑¬𝜓¬𝜑 | Subs [𝜑↗→→↔¬𝜑¬𝜓¬𝜓→↔¬𝜑¬𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1 | |
| 2111 | →¬𝜓→→↔¬𝜑¬𝜓¬𝜓→↔¬𝜑¬𝜓¬𝜑 | Modus ponens 2109, 2110 | |
| 2112 | →→¬𝜓→→↔¬𝜑¬𝜓¬𝜓→↔¬𝜑¬𝜓¬𝜑→→¬𝜓→↔¬𝜑¬𝜓¬𝜓→¬𝜓→↔¬𝜑¬𝜓¬𝜑 | Subs [𝜑↗¬𝜓, 𝜓↗→↔¬𝜑¬𝜓¬𝜓, 𝜒↗→↔¬𝜑¬𝜓¬𝜑] into ax-2 | |
| 2113 | →→¬𝜓→↔¬𝜑¬𝜓¬𝜓→¬𝜓→↔¬𝜑¬𝜓¬𝜑 | Modus ponens 2111, 2112 | |
| 2114 | →¬𝜓→↔¬𝜑¬𝜓¬𝜑 | Modus ponens 2103, 2113 | |
| 2115 | →↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓 | Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 2116 | →→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓 | Subs [𝜑↗→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1 | |
| 2117 | →↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓 | Modus ponens 2115, 2116 | |
| 2118 | →→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓 | Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓, 𝜒↗→¬𝜓↔¬𝜑¬𝜓] into ax-2 | |
| 2119 | →→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓 | Modus ponens 2117, 2118 | |
| 2120 | →→¬𝜓→↔¬𝜑¬𝜓¬𝜑→→¬𝜓↔¬𝜑¬𝜓→¬𝜓¬𝜑 | Subs [𝜑↗¬𝜓, 𝜓↗↔¬𝜑¬𝜓, 𝜒↗¬𝜑] into ax-2 | |
| 2121 | →→¬𝜓↔¬𝜑¬𝜓→¬𝜓¬𝜑 | Modus ponens 2114, 2120 | |
| 2122 | →→→¬𝜓↔¬𝜑¬𝜓→¬𝜓¬𝜑→↔¬𝜑¬𝜓→→¬𝜓↔¬𝜑¬𝜓→¬𝜓¬𝜑 | Subs [𝜑↗→→¬𝜓↔¬𝜑¬𝜓→¬𝜓¬𝜑, 𝜓↗↔¬𝜑¬𝜓] into ax-1 | |
| 2123 | →↔¬𝜑¬𝜓→→¬𝜓↔¬𝜑¬𝜓→¬𝜓¬𝜑 | Modus ponens 2121, 2122 | |
| 2124 | →→↔¬𝜑¬𝜓→→¬𝜓↔¬𝜑¬𝜓→¬𝜓¬𝜑→→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜓¬𝜑 | Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗→¬𝜓↔¬𝜑¬𝜓, 𝜒↗→¬𝜓¬𝜑] into ax-2 | |
| 2125 | →→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜓¬𝜑 | Modus ponens 2123, 2124 | |
| 2126 | →→→¬𝜓¬𝜑→𝜑𝜓→↔¬𝜑¬𝜓→→¬𝜓¬𝜑→𝜑𝜓 | Subs [𝜑↗→→¬𝜓¬𝜑→𝜑𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1 | |
| 2127 | →↔¬𝜑¬𝜓→→¬𝜓¬𝜑→𝜑𝜓 | Modus ponens 316, 2126 | |
| 2128 | →→↔¬𝜑¬𝜓→→¬𝜓¬𝜑→𝜑𝜓→→↔¬𝜑¬𝜓→¬𝜓¬𝜑→↔¬𝜑¬𝜓→𝜑𝜓 | Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗→¬𝜓¬𝜑, 𝜒↗→𝜑𝜓] into ax-2 | |
| 2129 | →→↔¬𝜑¬𝜓→¬𝜓¬𝜑→↔¬𝜑¬𝜓→𝜑𝜓 | Modus ponens 2127, 2128 | |
| 2130 | →↔¬𝜑¬𝜓→𝜑𝜓 | Modus ponens 2102, 2129 | |
| 2131 | →↔¬𝜑¬𝜓→¬𝜑¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓] into biimp | |
| 2132 | →→↔¬𝜑¬𝜓→¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→↔¬𝜑¬𝜓→¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1 | |
| 2133 | →↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜑¬𝜓 | Modus ponens 2131, 2132 | |
| 2134 | →→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜑¬𝜓→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜑¬𝜓 | Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓, 𝜒↗→¬𝜑¬𝜓] into ax-2 | |
| 2135 | →→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜑¬𝜓 | Modus ponens 2133, 2134 | |
| 2136 | →→→¬𝜑¬𝜓→𝜓𝜑→↔¬𝜑¬𝜓→→¬𝜑¬𝜓→𝜓𝜑 | Subs [𝜑↗→→¬𝜑¬𝜓→𝜓𝜑, 𝜓↗↔¬𝜑¬𝜓] into ax-1 | |
| 2137 | →↔¬𝜑¬𝜓→→¬𝜑¬𝜓→𝜓𝜑 | Modus ponens ax-3, 2136 | |
| 2138 | →→↔¬𝜑¬𝜓→→¬𝜑¬𝜓→𝜓𝜑→→↔¬𝜑¬𝜓→¬𝜑¬𝜓→↔¬𝜑¬𝜓→𝜓𝜑 | Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓, 𝜒↗→𝜓𝜑] into ax-2 | |
| 2139 | →→↔¬𝜑¬𝜓→¬𝜑¬𝜓→↔¬𝜑¬𝜓→𝜓𝜑 | Modus ponens 2137, 2138 | |
| 2140 | →↔¬𝜑¬𝜓→𝜓𝜑 | Modus ponens 2131, 2139 | |
| 2141 | →→→𝜓𝜑→→𝜑𝜓→𝜓𝜑→↔¬𝜑¬𝜓→→𝜓𝜑→→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗→→𝜓𝜑→→𝜑𝜓→𝜓𝜑, 𝜓↗↔¬𝜑¬𝜓] into ax-1 | |
| 2142 | →↔¬𝜑¬𝜓→→𝜓𝜑→→𝜑𝜓→𝜓𝜑 | Modus ponens 1674, 2141 | |
| 2143 | →→↔¬𝜑¬𝜓→→𝜓𝜑→→𝜑𝜓→𝜓𝜑→→↔¬𝜑¬𝜓→𝜓𝜑→↔¬𝜑¬𝜓→→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗→𝜓𝜑, 𝜒↗→→𝜑𝜓→𝜓𝜑] into ax-2 | |
| 2144 | →→↔¬𝜑¬𝜓→𝜓𝜑→↔¬𝜑¬𝜓→→𝜑𝜓→𝜓𝜑 | Modus ponens 2142, 2143 | |
| 2145 | →↔¬𝜑¬𝜓→→𝜑𝜓→𝜓𝜑 | Modus ponens 2140, 2144 | |
| 2146 | →→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓→↔¬𝜑¬𝜓→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓 | Subs [𝜑↗→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1 | |
| 2147 | →↔¬𝜑¬𝜓→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓 | Modus ponens 1681, 2146 | |
| 2148 | →→↔¬𝜑¬𝜓→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓→→↔¬𝜑¬𝜓→→𝜑𝜓→𝜓𝜑→↔¬𝜑¬𝜓→→𝜑𝜓↔𝜑𝜓 | Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗→→𝜑𝜓→𝜓𝜑, 𝜒↗→→𝜑𝜓↔𝜑𝜓] into ax-2 | |
| 2149 | →→↔¬𝜑¬𝜓→→𝜑𝜓→𝜓𝜑→↔¬𝜑¬𝜓→→𝜑𝜓↔𝜑𝜓 | Modus ponens 2147, 2148 | |
| 2150 | →↔¬𝜑¬𝜓→→𝜑𝜓↔𝜑𝜓 | Modus ponens 2145, 2149 | |
| 2151 | →→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1 | |
| 2152 | →→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 2153 | →→𝜑𝜓→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓 | Modus ponens 2151, 2152 | |
| 2154 | →→→𝜑𝜓→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→↔¬𝜑¬𝜓→𝜑𝜓] into ax-2 | |
| 2155 | →→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓 | Modus ponens 2153, 2154 | |
| 2156 | →→↔¬𝜑¬𝜓→→𝜑𝜓↔𝜑𝜓→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓 | Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗↔𝜑𝜓] into ax-2 | |
| 2157 | →→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓 | Modus ponens 2150, 2156 | |
| 2158 | →→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓→→𝜑𝜓→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓 | Subs [𝜑↗→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 2159 | →→𝜑𝜓→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓 | Modus ponens 2157, 2158 | |
| 2160 | →→→𝜑𝜓→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓→→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓→→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→↔¬𝜑¬𝜓→𝜑𝜓, 𝜒↗→↔¬𝜑¬𝜓↔𝜑𝜓] into ax-2 | |
| 2161 | →→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓→→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓 | Modus ponens 2159, 2160 | |
| 2162 | →→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓 | Modus ponens 2151, 2161 | |
| 2163 | →→→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓→↔¬𝜑¬𝜓→→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1 | |
| 2164 | →↔¬𝜑¬𝜓→→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓 | Modus ponens 2162, 2163 | |
| 2165 | →→↔¬𝜑¬𝜓→→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓 | Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→↔¬𝜑¬𝜓↔𝜑𝜓] into ax-2 | |
| 2166 | →→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓 | Modus ponens 2164, 2165 | |
| 2167 | →↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓 | Modus ponens 2130, 2166 | |
| 2168 | →↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓 | Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1 | |
| 2169 | →→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓 | Subs [𝜑↗→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1 | |
| 2170 | →↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓 | Modus ponens 2168, 2169 | |
| 2171 | →→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓 | Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓, 𝜒↗→↔¬𝜑¬𝜓↔¬𝜑¬𝜓] into ax-2 | |
| 2172 | →→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓 | Modus ponens 2170, 2171 | |
| 2173 | →→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓 | Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓, 𝜒↗↔𝜑𝜓] into ax-2 | |
| 2174 | →→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓 | Modus ponens 2167, 2173 | |
| 2175 | →→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓→↔¬𝜑¬𝜓→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓 | Subs [𝜑↗→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1 | |
| 2176 | →↔¬𝜑¬𝜓→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓 | Modus ponens 2174, 2175 | |
| 2177 | →→↔¬𝜑¬𝜓→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓→→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓 | Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗→↔¬𝜑¬𝜓↔¬𝜑¬𝜓, 𝜒↗→↔¬𝜑¬𝜓↔𝜑𝜓] into ax-2 | |
| 2178 | →→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓 | Modus ponens 2176, 2177 | |
| 2179 | →↔¬𝜑¬𝜓↔𝜑𝜓 | Modus ponens 2089, 2174 | |
| 2180 | →→↔𝜑𝜓↔¬𝜑¬𝜓→→↔¬𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓↔¬𝜑¬𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔¬𝜑¬𝜓] into impbi | |
| 2181 | →→↔¬𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓↔¬𝜑¬𝜓 | Modus ponens 2088, 2180 | |
| 2182 | ↔↔𝜑𝜓↔¬𝜑¬𝜓 | Modus ponens 2179, 2181 | notbi |
| 2183 | →¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬↔𝜒𝜃] into simplim | |
| 2184 | →¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜒𝜃 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒𝜃] into simprim | |
| 2185 | →↔↔𝜑𝜓↔𝜓𝜑→↔𝜑𝜓↔𝜓𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜓𝜑] into biimp | |
| 2186 | →→↔𝜑𝜓↔𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜑𝜓↔𝜓𝜑 | Subs [𝜑↗→↔𝜑𝜓↔𝜓𝜑, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2187 | →¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜑𝜓↔𝜓𝜑 | Modus ponens bicom1, 2186 | |
| 2188 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜑𝜓↔𝜓𝜑→→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜓𝜑 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗↔𝜑𝜓, 𝜒↗↔𝜓𝜑] into ax-2 | |
| 2189 | →→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜓𝜑 | Modus ponens 2187, 2188 | |
| 2190 | →¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜓𝜑 | Modus ponens 2183, 2189 | |
| 2191 | →↔𝜓𝜑→𝜓𝜑 | Subs [𝜑↗𝜓, 𝜓↗𝜑] into biimp | |
| 2192 | →→↔𝜓𝜑→𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜓𝜑→𝜓𝜑 | Subs [𝜑↗→↔𝜓𝜑→𝜓𝜑, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2193 | →¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜓𝜑→𝜓𝜑 | Modus ponens 2191, 2192 | |
| 2194 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜓𝜑→𝜓𝜑→→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗↔𝜓𝜑, 𝜒↗→𝜓𝜑] into ax-2 | |
| 2195 | →→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑 | Modus ponens 2193, 2194 | |
| 2196 | →¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑 | Modus ponens 2190, 2195 | |
| 2197 | →𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2198 | →→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→𝜓→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓 | Subs [𝜑↗→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓] into ax-1 | |
| 2199 | →𝜓→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓 | Modus ponens 2197, 2198 | |
| 2200 | →→𝜓→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→→𝜓𝜓→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓 | Subs [𝜑↗𝜓, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓] into ax-2 | |
| 2201 | →→𝜓𝜓→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓 | Modus ponens 2199, 2200 | |
| 2202 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑→→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗𝜑] into ax-2 | |
| 2203 | →→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑 | Modus ponens 2196, 2202 | |
| 2204 | →→→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑→𝜓→→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑 | Subs [𝜑↗→→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑] into ax-1 | |
| 2205 | →𝜓→→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑 | Modus ponens 2203, 2204 | |
| 2206 | →→𝜓→→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑→→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑 | Subs [𝜑↗𝜓, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑] into ax-2 | |
| 2207 | →→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑 | Modus ponens 2205, 2206 | |
| 2208 | →𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑 | Modus ponens 2197, 2207 | |
| 2209 | →¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃] into id | |
| 2210 | →¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2211 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃 | Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2212 | →¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃 | Modus ponens 2210, 2211 | |
| 2213 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-2 | |
| 2214 | →→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃 | Modus ponens 2212, 2213 | |
| 2215 | →→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑→→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑 | Subs [𝜑↗𝜓, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗𝜑] into ax-2 | |
| 2216 | →→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑 | Modus ponens 2208, 2215 | |
| 2217 | →→→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑 | Subs [𝜑↗→→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2218 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑 | Modus ponens 2216, 2217 | |
| 2219 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗→𝜓𝜑] into ax-2 | |
| 2220 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑 | Modus ponens 2218, 2219 | |
| 2221 | →¬→↔𝜑𝜓¬↔𝜒𝜃→𝜒𝜒 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗𝜒] into idd | |
| 2222 | →→𝜒𝜒→𝜑→𝜒𝜒 | Subs [𝜑↗→𝜒𝜒, 𝜓↗𝜑] into ax-1 | |
| 2223 | →→→𝜒𝜒→𝜑→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜒𝜒→𝜑→𝜒𝜒 | Subs [𝜑↗→→𝜒𝜒→𝜑→𝜒𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2224 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜒𝜒→𝜑→𝜒𝜒 | Modus ponens 2222, 2223 | |
| 2225 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜒𝜒→𝜑→𝜒𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑→𝜒𝜒 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜒𝜒, 𝜒↗→𝜑→𝜒𝜒] into ax-2 | |
| 2226 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑→𝜒𝜒 | Modus ponens 2224, 2225 | |
| 2227 | →¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑→𝜒𝜒 | Modus ponens 2221, 2226 | |
| 2228 | →→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒 | Subs [𝜓↗𝜒] into ax-2 | |
| 2229 | →→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒 | Subs [𝜑↗→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2230 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒 | Modus ponens 2228, 2229 | |
| 2231 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜑𝜒 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜑→𝜒𝜒, 𝜒↗→→𝜑𝜒→𝜑𝜒] into ax-2 | |
| 2232 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜑𝜒 | Modus ponens 2230, 2231 | |
| 2233 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜑𝜒 | Modus ponens 2227, 2232 | |
| 2234 | →→𝜓𝜑→→𝜑𝜒→𝜓𝜑 | Subs [𝜑↗→𝜓𝜑, 𝜓↗→𝜑𝜒] into ax-1 | |
| 2235 | →→→𝜓𝜑→→𝜑𝜒→𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜑 | Subs [𝜑↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜑, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2236 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜑 | Modus ponens 2234, 2235 | |
| 2237 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜑→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜑 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜓𝜑, 𝜒↗→→𝜑𝜒→𝜓𝜑] into ax-2 | |
| 2238 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜑 | Modus ponens 2236, 2237 | |
| 2239 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜑 | Modus ponens 2196, 2238 | |
| 2240 | →→𝜑𝜒→→𝜓𝜑→𝜓𝜒 | Subs [𝜓↗𝜒, 𝜒↗𝜓] into imim2 | |
| 2241 | →→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒 | Subs [𝜑↗→→𝜑𝜒→→𝜓𝜑→𝜓𝜒, 𝜓↗→𝜑𝜒] into ax-1 | |
| 2242 | →→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒 | Modus ponens 2240, 2241 | |
| 2243 | →→→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒 | Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→→𝜓𝜑→𝜓𝜒] into ax-2 | |
| 2244 | →→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒 | Modus ponens 2242, 2243 | |
| 2245 | →→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2246 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒 | Modus ponens 2244, 2245 | |
| 2247 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→→𝜓𝜑→𝜓𝜒 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜑𝜒→𝜑𝜒, 𝜒↗→→𝜑𝜒→→𝜓𝜑→𝜓𝜒] into ax-2 | |
| 2248 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→→𝜓𝜑→𝜓𝜒 | Modus ponens 2246, 2247 | |
| 2249 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→→𝜓𝜑→𝜓𝜒 | Modus ponens 2233, 2248 | |
| 2250 | →→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜓𝜑, 𝜒↗→𝜓𝜒] into ax-2 | |
| 2251 | →→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2252 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒 | Modus ponens 2250, 2251 | |
| 2253 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜑𝜒→→𝜓𝜑→𝜓𝜒, 𝜒↗→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒] into ax-2 | |
| 2254 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒 | Modus ponens 2252, 2253 | |
| 2255 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒 | Modus ponens 2249, 2254 | |
| 2256 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜑𝜒→𝜓𝜑, 𝜒↗→→𝜑𝜒→𝜓𝜒] into ax-2 | |
| 2257 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒 | Modus ponens 2255, 2256 | |
| 2258 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒 | Modus ponens 2239, 2257 | |
| 2259 | →→↔𝜑𝜓→𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→↔𝜑𝜓→𝜑𝜓, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2260 | →¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜑𝜓→𝜑𝜓 | Modus ponens biimp, 2259 | |
| 2261 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜑𝜓→𝜑𝜓→→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜓 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗↔𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2 | |
| 2262 | →→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜓 | Modus ponens 2260, 2261 | |
| 2263 | →¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜓 | Modus ponens 2183, 2262 | |
| 2264 | →→→𝜒𝜒→𝜓→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜒𝜒→𝜓→𝜒𝜒 | Subs [𝜑↗→→𝜒𝜒→𝜓→𝜒𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2265 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜒𝜒→𝜓→𝜒𝜒 | Modus ponens 51, 2264 | |
| 2266 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜒𝜒→𝜓→𝜒𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓→𝜒𝜒 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜒𝜒, 𝜒↗→𝜓→𝜒𝜒] into ax-2 | |
| 2267 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓→𝜒𝜒 | Modus ponens 2265, 2266 | |
| 2268 | →¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓→𝜒𝜒 | Modus ponens 2221, 2267 | |
| 2269 | →→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒 | Subs [𝜑↗→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2270 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒 | Modus ponens 57, 2269 | |
| 2271 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜓𝜒 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜓→𝜒𝜒, 𝜒↗→→𝜓𝜒→𝜓𝜒] into ax-2 | |
| 2272 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜓𝜒 | Modus ponens 2270, 2271 | |
| 2273 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜓𝜒 | Modus ponens 2268, 2272 | |
| 2274 | →→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→→𝜓𝜒→𝜑𝜓, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2275 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜓 | Modus ponens 63, 2274 | |
| 2276 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜓 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜓] into ax-2 | |
| 2277 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜓 | Modus ponens 2275, 2276 | |
| 2278 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜓 | Modus ponens 2263, 2277 | |
| 2279 | →→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2280 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 72, 2279 | |
| 2281 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜓𝜒→𝜓𝜒, 𝜒↗→→𝜓𝜒→→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 2282 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 2280, 2281 | |
| 2283 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 2273, 2282 | |
| 2284 | →→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2285 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Modus ponens 78, 2284 | |
| 2286 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜒↗→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒] into ax-2 | |
| 2287 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Modus ponens 2285, 2286 | |
| 2288 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Modus ponens 2283, 2287 | |
| 2289 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜓𝜒→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜒] into ax-2 | |
| 2290 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜒 | Modus ponens 2288, 2289 | |
| 2291 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜒 | Modus ponens 2278, 2290 | |
| 2292 | →→→𝜑𝜒→𝜓𝜒→→→𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜓𝜒] into impbi | |
| 2293 | →→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→→𝜓𝜒→𝜑𝜒, 𝜓↗→→𝜑𝜒→𝜓𝜒] into ax-1 | |
| 2294 | →→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2295 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒 | Modus ponens 2293, 2294 | |
| 2296 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜓𝜒→𝜑𝜒, 𝜒↗→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒] into ax-2 | |
| 2297 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒 | Modus ponens 2295, 2296 | |
| 2298 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒 | Modus ponens 2291, 2297 | |
| 2299 | →→→→𝜑𝜒→𝜓𝜒→→→𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜓𝜒→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→→𝜑𝜒→𝜓𝜒, 𝜓↗→→𝜓𝜒→𝜑𝜒, 𝜒↗↔→𝜑𝜒→𝜓𝜒] into ax-2 | |
| 2300 | →→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2292, 2299 | |
| 2301 | →→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2302 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2300, 2301 | |
| 2303 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒, 𝜒↗→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒] into ax-2 | |
| 2304 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2302, 2303 | |
| 2305 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2298, 2304 | |
| 2306 | →→→𝜑𝜒→𝜓𝜒→→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→→𝜑𝜒→𝜓𝜒] into id | |
| 2307 | →→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→→𝜑𝜒→𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2308 | →→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒, 𝜓↗→→𝜑𝜒→𝜓𝜒] into ax-1 | |
| 2309 | →→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒 | Modus ponens 2307, 2308 | |
| 2310 | →→→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→→→→𝜑𝜒→𝜓𝜒→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→→𝜑𝜒→𝜓𝜒, 𝜓↗→→𝜑𝜒→𝜓𝜒, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒] into ax-2 | |
| 2311 | →→→→𝜑𝜒→𝜓𝜒→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒 | Modus ponens 2309, 2310 | |
| 2312 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜑𝜒→𝜓𝜒, 𝜒↗↔→𝜑𝜒→𝜓𝜒] into ax-2 | |
| 2313 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2305, 2312 | |
| 2314 | →→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒, 𝜓↗→→𝜑𝜒→𝜓𝜒] into ax-1 | |
| 2315 | →→→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2313, 2314 | |
| 2316 | →→→→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒→→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→→𝜑𝜒→𝜓𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒] into ax-2 | |
| 2317 | →→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2315, 2316 | |
| 2318 | →→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2307, 2317 | |
| 2319 | →→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2320 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2318, 2319 | |
| 2321 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜑𝜒→𝜓𝜒, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒] into ax-2 | |
| 2322 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2320, 2321 | |
| 2323 | →¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2258, 2322 | |
| 2324 | →¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2325 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃 | Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2326 | →¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃 | Modus ponens 2324, 2325 | |
| 2327 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-2 | |
| 2328 | →→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃 | Modus ponens 2326, 2327 | |
| 2329 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗↔→𝜑𝜒→𝜓𝜒] into ax-2 | |
| 2330 | →→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2323, 2329 | |
| 2331 | →→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2332 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2330, 2331 | |
| 2333 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒] into ax-2 | |
| 2334 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2332, 2333 | |
| 2335 | →¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2209, 2330 | |
| 2336 | →↔𝜒𝜃→𝜓↔𝜒𝜃 | Subs [𝜑↗↔𝜒𝜃] into ax-1 | |
| 2337 | →→↔𝜒𝜃→𝜓↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃→𝜓↔𝜒𝜃 | Subs [𝜑↗→↔𝜒𝜃→𝜓↔𝜒𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2338 | →¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃→𝜓↔𝜒𝜃 | Modus ponens 2336, 2337 | |
| 2339 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃→𝜓↔𝜒𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓↔𝜒𝜃 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗↔𝜒𝜃, 𝜒↗→𝜓↔𝜒𝜃] into ax-2 | |
| 2340 | →→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓↔𝜒𝜃 | Modus ponens 2338, 2339 | |
| 2341 | →¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓↔𝜒𝜃 | Modus ponens 2184, 2340 | |
| 2342 | ↔→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃 | Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗𝜃] into pm5.74 | |
| 2343 | →↔→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃→→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃 | Subs [𝜑↗→𝜓↔𝜒𝜃, 𝜓↗↔→𝜓𝜒→𝜓𝜃] into biimp | |
| 2344 | →→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃 | Modus ponens 2342, 2343 | |
| 2345 | →→→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃 | Subs [𝜑↗→→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1 | |
| 2346 | →¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃 | Modus ponens 2344, 2345 | |
| 2347 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜓↔𝜒𝜃, 𝜒↗↔→𝜓𝜒→𝜓𝜃] into ax-2 | |
| 2348 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃 | Modus ponens 2346, 2347 | |
| 2349 | →¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃 | Modus ponens 2341, 2348 | |
| 2350 | ↔→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜑𝜒, 𝜒↗→𝜓𝜒] into pm5.74 | |
| 2351 | →↔→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒 | Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒, 𝜓↗↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒] into biimp | |
| 2352 | →→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒 | Modus ponens 2350, 2351 | |
| 2353 | ↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒 | Modus ponens 2335, 2352 | |
| 2354 | ↔→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜓𝜒, 𝜒↗→𝜓𝜃] into pm5.74 | |
| 2355 | →↔→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃 | Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃, 𝜓↗↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃] into biimp | |
| 2356 | →→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃 | Modus ponens 2354, 2355 | |
| 2357 | ↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃 | Modus ponens 2349, 2356 | |
| 2358 | →↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃 | Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃] into biimp | |
| 2359 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃 | Modus ponens 2357, 2358 | |
| 2360 | →↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒 | Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒] into biimp | |
| 2361 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒 | Modus ponens 2353, 2360 | |
| 2362 | →→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃 | Subs [𝜑↗→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒] into ax-1 | |
| 2363 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃 | Modus ponens 2359, 2362 | |
| 2364 | →→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃 | Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃] into ax-2 | |
| 2365 | →→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃 | Modus ponens 2363, 2364 | |
| 2366 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃 | Modus ponens 2361, 2365 | |
| 2367 | →↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒 | Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃] into bicom1 | |
| 2368 | ↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒 | Modus ponens 2357, 2367 | |
| 2369 | →↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒 | Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒] into biimp | |
| 2370 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒 | Modus ponens 2368, 2369 | |
| 2371 | →↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒 | Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒] into bicom1 | |
| 2372 | ↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒 | Modus ponens 2353, 2371 | |
| 2373 | →↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒 | Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒] into biimp | |
| 2374 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒 | Modus ponens 2372, 2373 | |
| 2375 | →→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒 | Subs [𝜑↗→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃] into ax-1 | |
| 2376 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒 | Modus ponens 2374, 2375 | |
| 2377 | →→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒 | Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒] into ax-2 | |
| 2378 | →→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒 | Modus ponens 2376, 2377 | |
| 2379 | →→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒 | Modus ponens 2370, 2378 | |
| 2380 | →→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃 | Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃] into impbi | |
| 2381 | →→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃 | Modus ponens 2366, 2380 | |
| 2382 | ↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃 | Modus ponens 2379, 2381 | |
| 2383 | ↔→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜑𝜒, 𝜒↗→𝜓𝜃] into pm5.74 | |
| 2384 | →↔→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃↔↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃 | Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃, 𝜓↗↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃] into bicom1 | |
| 2385 | ↔↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃 | Modus ponens 2383, 2384 | |
| 2386 | →↔↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃→↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃 | Subs [𝜑↗↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃] into biimp | |
| 2387 | →↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃 | Modus ponens 2385, 2386 | |
| 2388 | →¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃 | Modus ponens 2382, 2387 | |
| 2389 | →↔𝜑𝜓→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒𝜃] into pm3.2im | |
| 2390 | →→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃→↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃 | Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃, 𝜓↗↔𝜒𝜃] into ax-1 | |
| 2391 | →↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃 | Modus ponens 2388, 2390 | |
| 2392 | →→↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃→→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃 | Subs [𝜑↗↔𝜒𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗↔→𝜑𝜒→𝜓𝜃] into ax-2 | |
| 2393 | →→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃 | Modus ponens 2391, 2392 | |
| 2394 | →→→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃→↔𝜑𝜓→→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃 | Subs [𝜑↗→→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2395 | →↔𝜑𝜓→→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃 | Modus ponens 2393, 2394 | |
| 2396 | →→↔𝜑𝜓→→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃→→↔𝜑𝜓→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜑𝜓→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃] into ax-2 | |
| 2397 | →→↔𝜑𝜓→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜑𝜓→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃 | Modus ponens 2395, 2396 | |
| 2398 | →↔𝜑𝜓→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃 | Modus ponens 2389, 2397 | imbi12 |
| 2399 | →→↔𝜑𝜓↔𝜓𝜑→↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑 | Subs [𝜑↗→↔𝜑𝜓↔𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2400 | →→↔𝜓𝜑→𝜓𝜑→↔𝜑𝜓→↔𝜓𝜑→𝜓𝜑 | Subs [𝜑↗→↔𝜓𝜑→𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2401 | →↔𝜑𝜓→↔𝜓𝜑→𝜓𝜑 | Modus ponens 2191, 2400 | |
| 2402 | →→↔𝜑𝜓→↔𝜓𝜑→𝜓𝜑→→↔𝜑𝜓↔𝜓𝜑→↔𝜑𝜓→𝜓𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜓𝜑, 𝜒↗→𝜓𝜑] into ax-2 | |
| 2403 | →→↔𝜑𝜓↔𝜓𝜑→↔𝜑𝜓→𝜓𝜑 | Modus ponens 2401, 2402 | |
| 2404 | →𝜓→↔𝜑𝜓𝜓 | Subs [𝜑↗𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2405 | →→𝜓→↔𝜑𝜓𝜓→𝜓→𝜓→↔𝜑𝜓𝜓 | Subs [𝜑↗→𝜓→↔𝜑𝜓𝜓] into ax-1 | |
| 2406 | →𝜓→𝜓→↔𝜑𝜓𝜓 | Modus ponens 2404, 2405 | |
| 2407 | →→𝜓→𝜓→↔𝜑𝜓𝜓→→𝜓𝜓→𝜓→↔𝜑𝜓𝜓 | Subs [𝜑↗𝜓, 𝜒↗→↔𝜑𝜓𝜓] into ax-2 | |
| 2408 | →→𝜓𝜓→𝜓→↔𝜑𝜓𝜓 | Modus ponens 2406, 2407 | |
| 2409 | →→↔𝜑𝜓→𝜓𝜑→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜒↗𝜑] into ax-2 | |
| 2410 | →→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→𝜓→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑 | Subs [𝜑↗→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑] into ax-1 | |
| 2411 | →𝜓→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑 | Modus ponens 1940, 2410 | |
| 2412 | →→𝜓→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→𝜓→↔𝜑𝜓𝜓→𝜓→↔𝜑𝜓𝜑 | Subs [𝜑↗𝜓, 𝜓↗→↔𝜑𝜓𝜓, 𝜒↗→↔𝜑𝜓𝜑] into ax-2 | |
| 2413 | →→𝜓→↔𝜑𝜓𝜓→𝜓→↔𝜑𝜓𝜑 | Modus ponens 2411, 2412 | |
| 2414 | →𝜓→↔𝜑𝜓𝜑 | Modus ponens 2404, 2413 | |
| 2415 | →↔𝜑𝜓→𝜓↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓] into ax-1 | |
| 2416 | →→↔𝜑𝜓→𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→𝜓↔𝜑𝜓 | Subs [𝜑↗→↔𝜑𝜓→𝜓↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2417 | →↔𝜑𝜓→↔𝜑𝜓→𝜓↔𝜑𝜓 | Modus ponens 2415, 2416 | |
| 2418 | →→↔𝜑𝜓→↔𝜑𝜓→𝜓↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→𝜓↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→𝜓↔𝜑𝜓] into ax-2 | |
| 2419 | →→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→𝜓↔𝜑𝜓 | Modus ponens 2417, 2418 | |
| 2420 | →→𝜓→↔𝜑𝜓𝜑→→𝜓↔𝜑𝜓→𝜓𝜑 | Subs [𝜑↗𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗𝜑] into ax-2 | |
| 2421 | →→𝜓↔𝜑𝜓→𝜓𝜑 | Modus ponens 2414, 2420 | |
| 2422 | →→→𝜓↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜓𝜑 | Subs [𝜑↗→→𝜓↔𝜑𝜓→𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2423 | →↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜓𝜑 | Modus ponens 2421, 2422 | |
| 2424 | →→↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜓𝜑→→↔𝜑𝜓→𝜓↔𝜑𝜓→↔𝜑𝜓→𝜓𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜓↔𝜑𝜓, 𝜒↗→𝜓𝜑] into ax-2 | |
| 2425 | →→↔𝜑𝜓→𝜓↔𝜑𝜓→↔𝜑𝜓→𝜓𝜑 | Modus ponens 2423, 2424 | |
| 2426 | →↔𝜑𝜓→𝜒𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜒] into idd | |
| 2427 | →→→𝜒𝜒→𝜑→𝜒𝜒→↔𝜑𝜓→→𝜒𝜒→𝜑→𝜒𝜒 | Subs [𝜑↗→→𝜒𝜒→𝜑→𝜒𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2428 | →↔𝜑𝜓→→𝜒𝜒→𝜑→𝜒𝜒 | Modus ponens 2222, 2427 | |
| 2429 | →→↔𝜑𝜓→→𝜒𝜒→𝜑→𝜒𝜒→→↔𝜑𝜓→𝜒𝜒→↔𝜑𝜓→𝜑→𝜒𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜒𝜒, 𝜒↗→𝜑→𝜒𝜒] into ax-2 | |
| 2430 | →→↔𝜑𝜓→𝜒𝜒→↔𝜑𝜓→𝜑→𝜒𝜒 | Modus ponens 2428, 2429 | |
| 2431 | →↔𝜑𝜓→𝜑→𝜒𝜒 | Modus ponens 2426, 2430 | |
| 2432 | →→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒→↔𝜑𝜓→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒 | Subs [𝜑↗→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2433 | →↔𝜑𝜓→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒 | Modus ponens 2228, 2432 | |
| 2434 | →→↔𝜑𝜓→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒→→↔𝜑𝜓→𝜑→𝜒𝜒→↔𝜑𝜓→→𝜑𝜒→𝜑𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜑→𝜒𝜒, 𝜒↗→→𝜑𝜒→𝜑𝜒] into ax-2 | |
| 2435 | →→↔𝜑𝜓→𝜑→𝜒𝜒→↔𝜑𝜓→→𝜑𝜒→𝜑𝜒 | Modus ponens 2433, 2434 | |
| 2436 | →↔𝜑𝜓→→𝜑𝜒→𝜑𝜒 | Modus ponens 2431, 2435 | |
| 2437 | →→→𝜓𝜑→→𝜑𝜒→𝜓𝜑→↔𝜑𝜓→→𝜓𝜑→→𝜑𝜒→𝜓𝜑 | Subs [𝜑↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2438 | →↔𝜑𝜓→→𝜓𝜑→→𝜑𝜒→𝜓𝜑 | Modus ponens 2234, 2437 | |
| 2439 | →→↔𝜑𝜓→→𝜓𝜑→→𝜑𝜒→𝜓𝜑→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓→→𝜑𝜒→𝜓𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜓𝜑, 𝜒↗→→𝜑𝜒→𝜓𝜑] into ax-2 | |
| 2440 | →→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓→→𝜑𝜒→𝜓𝜑 | Modus ponens 2438, 2439 | |
| 2441 | →↔𝜑𝜓→→𝜑𝜒→𝜓𝜑 | Modus ponens biimpr, 2440 | |
| 2442 | →→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→↔𝜑𝜓→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2443 | →↔𝜑𝜓→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒 | Modus ponens 2244, 2442 | |
| 2444 | →→↔𝜑𝜓→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→↔𝜑𝜓→→𝜑𝜒→𝜑𝜒→↔𝜑𝜓→→𝜑𝜒→→𝜓𝜑→𝜓𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜑𝜒→𝜑𝜒, 𝜒↗→→𝜑𝜒→→𝜓𝜑→𝜓𝜒] into ax-2 | |
| 2445 | →→↔𝜑𝜓→→𝜑𝜒→𝜑𝜒→↔𝜑𝜓→→𝜑𝜒→→𝜓𝜑→𝜓𝜒 | Modus ponens 2443, 2444 | |
| 2446 | →↔𝜑𝜓→→𝜑𝜒→→𝜓𝜑→𝜓𝜒 | Modus ponens 2436, 2445 | |
| 2447 | →→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2448 | →↔𝜑𝜓→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒 | Modus ponens 2250, 2447 | |
| 2449 | →→↔𝜑𝜓→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜑𝜒→→𝜓𝜑→𝜓𝜒, 𝜒↗→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒] into ax-2 | |
| 2450 | →→↔𝜑𝜓→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒 | Modus ponens 2448, 2449 | |
| 2451 | →↔𝜑𝜓→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒 | Modus ponens 2446, 2450 | |
| 2452 | →→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜑→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜑𝜒→𝜓𝜑, 𝜒↗→→𝜑𝜒→𝜓𝜒] into ax-2 | |
| 2453 | →→↔𝜑𝜓→→𝜑𝜒→𝜓𝜑→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒 | Modus ponens 2451, 2452 | |
| 2454 | →↔𝜑𝜓→→𝜑𝜒→𝜓𝜒 | Modus ponens 2441, 2453 | |
| 2455 | →→↔𝜑𝜓→𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→↔𝜑𝜓→𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2456 | →↔𝜑𝜓→↔𝜑𝜓→𝜑𝜓 | Modus ponens biimp, 2455 | |
| 2457 | →→↔𝜑𝜓→↔𝜑𝜓→𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2 | |
| 2458 | →→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→𝜑𝜓 | Modus ponens 2456, 2457 | |
| 2459 | →→→𝜒𝜒→𝜓→𝜒𝜒→↔𝜑𝜓→→𝜒𝜒→𝜓→𝜒𝜒 | Subs [𝜑↗→→𝜒𝜒→𝜓→𝜒𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2460 | →↔𝜑𝜓→→𝜒𝜒→𝜓→𝜒𝜒 | Modus ponens 51, 2459 | |
| 2461 | →→↔𝜑𝜓→→𝜒𝜒→𝜓→𝜒𝜒→→↔𝜑𝜓→𝜒𝜒→↔𝜑𝜓→𝜓→𝜒𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜒𝜒, 𝜒↗→𝜓→𝜒𝜒] into ax-2 | |
| 2462 | →→↔𝜑𝜓→𝜒𝜒→↔𝜑𝜓→𝜓→𝜒𝜒 | Modus ponens 2460, 2461 | |
| 2463 | →↔𝜑𝜓→𝜓→𝜒𝜒 | Modus ponens 2426, 2462 | |
| 2464 | →→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒→↔𝜑𝜓→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒 | Subs [𝜑↗→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2465 | →↔𝜑𝜓→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒 | Modus ponens 57, 2464 | |
| 2466 | →→↔𝜑𝜓→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒→→↔𝜑𝜓→𝜓→𝜒𝜒→↔𝜑𝜓→→𝜓𝜒→𝜓𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜓→𝜒𝜒, 𝜒↗→→𝜓𝜒→𝜓𝜒] into ax-2 | |
| 2467 | →→↔𝜑𝜓→𝜓→𝜒𝜒→↔𝜑𝜓→→𝜓𝜒→𝜓𝜒 | Modus ponens 2465, 2466 | |
| 2468 | →↔𝜑𝜓→→𝜓𝜒→𝜓𝜒 | Modus ponens 2463, 2467 | |
| 2469 | →→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→↔𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→→𝜓𝜒→𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2470 | →↔𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓 | Modus ponens 63, 2469 | |
| 2471 | →→↔𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→→↔𝜑𝜓→𝜑𝜓→↔𝜑𝜓→→𝜓𝜒→𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜓] into ax-2 | |
| 2472 | →→↔𝜑𝜓→𝜑𝜓→↔𝜑𝜓→→𝜓𝜒→𝜑𝜓 | Modus ponens 2470, 2471 | |
| 2473 | →↔𝜑𝜓→→𝜓𝜒→𝜑𝜓 | Modus ponens biimp, 2472 | |
| 2474 | →→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→↔𝜑𝜓→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2475 | →↔𝜑𝜓→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 72, 2474 | |
| 2476 | →→↔𝜑𝜓→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→↔𝜑𝜓→→𝜓𝜒→𝜓𝜒→↔𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜓𝜒→𝜓𝜒, 𝜒↗→→𝜓𝜒→→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 2477 | →→↔𝜑𝜓→→𝜓𝜒→𝜓𝜒→↔𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 2475, 2476 | |
| 2478 | →↔𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 2468, 2477 | |
| 2479 | →→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→↔𝜑𝜓→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2480 | →↔𝜑𝜓→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Modus ponens 78, 2479 | |
| 2481 | →→↔𝜑𝜓→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→↔𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→↔𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜒↗→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒] into ax-2 | |
| 2482 | →→↔𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→↔𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Modus ponens 2480, 2481 | |
| 2483 | →↔𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Modus ponens 2478, 2482 | |
| 2484 | →→↔𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→↔𝜑𝜓→→𝜓𝜒→𝜑𝜓→↔𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜓𝜒→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜒] into ax-2 | |
| 2485 | →→↔𝜑𝜓→→𝜓𝜒→𝜑𝜓→↔𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Modus ponens 2483, 2484 | |
| 2486 | →↔𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Modus ponens 2473, 2485 | |
| 2487 | →→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→↔𝜑𝜓→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2488 | →↔𝜑𝜓→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒 | Modus ponens 2293, 2487 | |
| 2489 | →→↔𝜑𝜓→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→↔𝜑𝜓→→𝜓𝜒→𝜑𝜒→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜓𝜒→𝜑𝜒, 𝜒↗→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒] into ax-2 | |
| 2490 | →→↔𝜑𝜓→→𝜓𝜒→𝜑𝜒→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒 | Modus ponens 2488, 2489 | |
| 2491 | →↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒 | Modus ponens 2486, 2490 | |
| 2492 | →→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2493 | →↔𝜑𝜓→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2300, 2492 | |
| 2494 | →→↔𝜑𝜓→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒, 𝜒↗→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒] into ax-2 | |
| 2495 | →→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2493, 2494 | |
| 2496 | →↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2491, 2495 | |
| 2497 | →→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→→𝜑𝜒→𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2498 | →→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒, 𝜓↗→→𝜑𝜒→𝜓𝜒] into ax-1 | |
| 2499 | →→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒 | Modus ponens 2497, 2498 | |
| 2500 | →→→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→→→→𝜑𝜒→𝜓𝜒→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→→𝜑𝜒→𝜓𝜒, 𝜓↗→→𝜑𝜒→𝜓𝜒, 𝜒↗→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒] into ax-2 | |
| 2501 | →→→→𝜑𝜒→𝜓𝜒→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒 | Modus ponens 2499, 2500 | |
| 2502 | →→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜑𝜒→𝜓𝜒, 𝜒↗↔→𝜑𝜒→𝜓𝜒] into ax-2 | |
| 2503 | →→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2496, 2502 | |
| 2504 | →→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒, 𝜓↗→→𝜑𝜒→𝜓𝜒] into ax-1 | |
| 2505 | →→→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2503, 2504 | |
| 2506 | →→→→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒→→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→→𝜑𝜒→𝜓𝜒, 𝜓↗→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒, 𝜒↗→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒] into ax-2 | |
| 2507 | →→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2505, 2506 | |
| 2508 | →→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2497, 2507 | |
| 2509 | →→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2510 | →↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2508, 2509 | |
| 2511 | →→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜑𝜒→𝜓𝜒, 𝜒↗→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒] into ax-2 | |
| 2512 | →→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2510, 2511 | |
| 2513 | →↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2454, 2512 | |
| 2514 | →→↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗↔→𝜑𝜒→𝜓𝜒] into ax-2 | |
| 2515 | →→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2513, 2514 | |
| 2516 | →→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2517 | →↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2515, 2516 | |
| 2518 | →→↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→↔𝜑𝜓↔𝜑𝜓, 𝜒↗→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒] into ax-2 | |
| 2519 | →→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒 | Modus ponens 2517, 2518 | |
| 2520 | →↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒 | Modus ponens 1651, 2515 | imbi1 |
| 2521 | →↔𝜑𝜓→𝜒↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜒] into ax-1 | |
| 2522 | →→↔𝜑𝜓→𝜒↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→𝜒↔𝜑𝜓 | Subs [𝜑↗→↔𝜑𝜓→𝜒↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2523 | →↔𝜑𝜓→↔𝜑𝜓→𝜒↔𝜑𝜓 | Modus ponens 2521, 2522 | |
| 2524 | →→↔𝜑𝜓→↔𝜑𝜓→𝜒↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→𝜒↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→𝜒↔𝜑𝜓] into ax-2 | |
| 2525 | →→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→𝜒↔𝜑𝜓 | Modus ponens 2523, 2524 | |
| 2526 | ↔→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓 | Subs [𝜑↗𝜒, 𝜓↗𝜑, 𝜒↗𝜓] into pm5.74 | |
| 2527 | →↔→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓→→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓 | Subs [𝜑↗→𝜒↔𝜑𝜓, 𝜓↗↔→𝜒𝜑→𝜒𝜓] into biimp | |
| 2528 | →→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓 | Modus ponens 2526, 2527 | |
| 2529 | →→→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓→↔𝜑𝜓→→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓 | Subs [𝜑↗→→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2530 | →↔𝜑𝜓→→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓 | Modus ponens 2528, 2529 | |
| 2531 | →→↔𝜑𝜓→→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓→→↔𝜑𝜓→𝜒↔𝜑𝜓→↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜒↔𝜑𝜓, 𝜒↗↔→𝜒𝜑→𝜒𝜓] into ax-2 | |
| 2532 | →→↔𝜑𝜓→𝜒↔𝜑𝜓→↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓 | Modus ponens 2530, 2531 | |
| 2533 | →↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓 | Modus ponens 2521, 2532 | imbi2 |
| 2534 | →↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑 | Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into id | |
| 2535 | →↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Subs [𝜑↗↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into ax-1 | |
| 2536 | →↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Modus ponens 1927, 2535 | |
| 2537 | ↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑 | Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓𝜒, 𝜒↗→↔𝜑𝜓𝜑] into pm5.74 | |
| 2538 | →↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑] into biimp | |
| 2539 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑 | Modus ponens 2537, 2538 | |
| 2540 | ↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑 | Modus ponens 2534, 2539 | |
| 2541 | ↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓𝜑, 𝜒↗→↔𝜑𝜓𝜓] into pm5.74 | |
| 2542 | →↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓, 𝜓↗↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓] into biimp | |
| 2543 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Modus ponens 2541, 2542 | |
| 2544 | ↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Modus ponens 2536, 2543 | |
| 2545 | →↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓] into biimp | |
| 2546 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Modus ponens 2544, 2545 | |
| 2547 | →↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑] into biimp | |
| 2548 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑 | Modus ponens 2540, 2547 | |
| 2549 | →→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Subs [𝜑↗→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒] into ax-1 | |
| 2550 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Modus ponens 2546, 2549 | |
| 2551 | →→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑, 𝜒↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓] into ax-2 | |
| 2552 | →→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Modus ponens 2550, 2551 | |
| 2553 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Modus ponens 2548, 2552 | |
| 2554 | →↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓] into bicom1 | |
| 2555 | ↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑 | Modus ponens 2544, 2554 | |
| 2556 | →↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑] into biimp | |
| 2557 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑 | Modus ponens 2555, 2556 | |
| 2558 | →↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑] into bicom1 | |
| 2559 | ↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒 | Modus ponens 2540, 2558 | |
| 2560 | →↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒] into biimp | |
| 2561 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒 | Modus ponens 2559, 2560 | |
| 2562 | →→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒 | Subs [𝜑↗→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓] into ax-1 | |
| 2563 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒 | Modus ponens 2561, 2562 | |
| 2564 | →→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑, 𝜒↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒] into ax-2 | |
| 2565 | →→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒 | Modus ponens 2563, 2564 | |
| 2566 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒 | Modus ponens 2557, 2565 | |
| 2567 | →→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓] into impbi | |
| 2568 | →→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Modus ponens 2553, 2567 | |
| 2569 | ↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Modus ponens 2566, 2568 | |
| 2570 | ↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓𝜒, 𝜒↗→↔𝜑𝜓𝜓] into pm5.74 | |
| 2571 | →↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓↔↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜓↗↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓] into bicom1 | |
| 2572 | ↔↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓 | Modus ponens 2570, 2571 | |
| 2573 | →↔↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓 | Subs [𝜑↗↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓] into biimp | |
| 2574 | →↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓 | Modus ponens 2572, 2573 | |
| 2575 | →↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓 | Modus ponens 2569, 2574 | |
| 2576 | →↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓 | Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓] into id | |
| 2577 | →↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑 | Subs [𝜑↗↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓] into ax-1 | |
| 2578 | →↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑 | Modus ponens 1938, 2577 | |
| 2579 | ↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓 | Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓𝜒, 𝜒↗→↔𝜑𝜓𝜓] into pm5.74 | |
| 2580 | →↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜓↗↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓] into biimp | |
| 2581 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓 | Modus ponens 2579, 2580 | |
| 2582 | ↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓 | Modus ponens 2576, 2581 | |
| 2583 | ↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑 | Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓𝜓, 𝜒↗→↔𝜑𝜓𝜑] into pm5.74 | |
| 2584 | →↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑, 𝜓↗↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑] into biimp | |
| 2585 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑 | Modus ponens 2583, 2584 | |
| 2586 | ↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑 | Modus ponens 2578, 2585 | |
| 2587 | →↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑] into biimp | |
| 2588 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑 | Modus ponens 2586, 2587 | |
| 2589 | →↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓] into biimp | |
| 2590 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓 | Modus ponens 2582, 2589 | |
| 2591 | →→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑 | Subs [𝜑↗→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒] into ax-1 | |
| 2592 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑 | Modus ponens 2588, 2591 | |
| 2593 | →→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓, 𝜒↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑] into ax-2 | |
| 2594 | →→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑 | Modus ponens 2592, 2593 | |
| 2595 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑 | Modus ponens 2590, 2594 | |
| 2596 | →↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑] into bicom1 | |
| 2597 | ↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓 | Modus ponens 2586, 2596 | |
| 2598 | →↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓] into biimp | |
| 2599 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓 | Modus ponens 2597, 2598 | |
| 2600 | →↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓] into bicom1 | |
| 2601 | ↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒 | Modus ponens 2582, 2600 | |
| 2602 | →↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒] into biimp | |
| 2603 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒 | Modus ponens 2601, 2602 | |
| 2604 | →→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒 | Subs [𝜑↗→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑] into ax-1 | |
| 2605 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒 | Modus ponens 2603, 2604 | |
| 2606 | →→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓, 𝜒↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒] into ax-2 | |
| 2607 | →→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒 | Modus ponens 2605, 2606 | |
| 2608 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒 | Modus ponens 2599, 2607 | |
| 2609 | →→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑] into impbi | |
| 2610 | →→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑 | Modus ponens 2595, 2609 | |
| 2611 | ↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑 | Modus ponens 2608, 2610 | |
| 2612 | ↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑 | Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓𝜒, 𝜒↗→↔𝜑𝜓𝜑] into pm5.74 | |
| 2613 | →↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑↔↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑] into bicom1 | |
| 2614 | ↔↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑 | Modus ponens 2612, 2613 | |
| 2615 | →↔↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑 | Subs [𝜑↗↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into biimp | |
| 2616 | →↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑 | Modus ponens 2614, 2615 | |
| 2617 | →↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑 | Modus ponens 2611, 2616 | |
| 2618 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓 | Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓] into impbi | |
| 2619 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓 | Modus ponens 2575, 2618 | |
| 2620 | ↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓 | Modus ponens 2617, 2619 | |
| 2621 | ↔→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜒, 𝜒↗𝜑] into pm5.74 | |
| 2622 | ↔→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜒, 𝜒↗𝜓] into pm5.74 | |
| 2623 | →↔→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓] into bicom1 | |
| 2624 | ↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 2622, 2623 | |
| 2625 | →↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into biimp | |
| 2626 | →↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 2624, 2625 | |
| 2627 | →↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓 | Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓] into biimp | |
| 2628 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into ax-1 | |
| 2629 | →↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 2626, 2628 | |
| 2630 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜒↗→↔𝜑𝜓↔𝜒𝜓] into ax-2 | |
| 2631 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 2629, 2630 | |
| 2632 | →↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 2575, 2631 | |
| 2633 | →↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓 | Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into bicom1 | |
| 2634 | →↔→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓 | Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓] into biimp | |
| 2635 | →→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓 | Modus ponens 2622, 2634 | |
| 2636 | →↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑 | Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓] into bicom1 | |
| 2637 | ↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑 | Modus ponens 2620, 2636 | |
| 2638 | →↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑 | Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into biimp | |
| 2639 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into ax-1 | |
| 2640 | →→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑 | Modus ponens 2617, 2639 | |
| 2641 | →→→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑 | Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜒↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into ax-2 | |
| 2642 | →→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑 | Modus ponens 2640, 2641 | |
| 2643 | →→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑 | Modus ponens 2635, 2642 | |
| 2644 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓→→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into impbi | |
| 2645 | →→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 2632, 2644 | |
| 2646 | ↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 2643, 2645 | |
| 2647 | →↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into biimp | |
| 2648 | →↔→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑 | Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜑, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into biimp | |
| 2649 | →→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑 | Modus ponens 2621, 2648 | |
| 2650 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜒𝜑] into ax-1 | |
| 2651 | →→↔𝜑𝜓↔𝜒𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 2632, 2650 | |
| 2652 | →→→↔𝜑𝜓↔𝜒𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓→→→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜑, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜒↗→↔𝜑𝜓↔𝜒𝜓] into ax-2 | |
| 2653 | →→→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 2651, 2652 | |
| 2654 | →→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 2649, 2653 | |
| 2655 | →↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑 | Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into bicom1 | |
| 2656 | ↔→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑 | Modus ponens 2646, 2655 | |
| 2657 | →↔→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑 | Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into biimp | |
| 2658 | →↔→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑 | Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜑, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into bicom1 | |
| 2659 | ↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑 | Modus ponens 2621, 2658 | |
| 2660 | →↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑 | Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜑] into biimp | |
| 2661 | →↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑 | Modus ponens 2659, 2660 | |
| 2662 | →→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑→→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑 | Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into ax-1 | |
| 2663 | →→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑 | Modus ponens 2661, 2662 | |
| 2664 | →→→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑→→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑 | Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜒↗→↔𝜑𝜓↔𝜒𝜑] into ax-2 | |
| 2665 | →→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑 | Modus ponens 2663, 2664 | |
| 2666 | →→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑 | Modus ponens 2643, 2665 | |
| 2667 | →→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into impbi | |
| 2668 | →→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 2654, 2667 | |
| 2669 | ↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 2666, 2668 | |
| 2670 | ↔→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒𝜑, 𝜒↗↔𝜒𝜓] into pm5.74 | |
| 2671 | →↔→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓↔↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓 | Subs [𝜑↗→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓] into bicom1 | |
| 2672 | ↔↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓 | Modus ponens 2670, 2671 | |
| 2673 | →↔↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓→↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓 | Subs [𝜑↗↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓] into biimp | |
| 2674 | →↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓 | Modus ponens 2672, 2673 | |
| 2675 | →↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓 | Modus ponens 2669, 2674 | |
| 2676 | ↔↔𝜑𝜒↔𝜒𝜑 | Subs [𝜓↗𝜒] into bicom | |
| 2677 | ↔↔𝜓𝜒↔𝜒𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜒] into bicom | |
| 2678 | →↔↔𝜑𝜒↔𝜒𝜑→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜑 | Subs [𝜑↗↔↔𝜑𝜒↔𝜒𝜑, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2679 | →↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜑 | Modus ponens 2676, 2678 | |
| 2680 | ↔→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜑↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜒, 𝜒↗↔𝜒𝜑] into pm5.74 | |
| 2681 | →↔→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜑↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑→→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜑↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑 | Subs [𝜑↗→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜑, 𝜓↗↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑] into biimp | |
| 2682 | →→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜑↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑 | Modus ponens 2680, 2681 | |
| 2683 | ↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑 | Modus ponens 2679, 2682 | |
| 2684 | →↔→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓] into biimp | |
| 2685 | →→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 2670, 2684 | |
| 2686 | →↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into biimp | |
| 2687 | →↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑 | Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜑] into biimp | |
| 2688 | →→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑 | Modus ponens 2683, 2687 | |
| 2689 | →→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜑𝜒] into ax-1 | |
| 2690 | →→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 2654, 2689 | |
| 2691 | →→→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜑, 𝜒↗→↔𝜑𝜓↔𝜒𝜓] into ax-2 | |
| 2692 | →→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 2690, 2691 | |
| 2693 | →→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 2688, 2692 | |
| 2694 | →↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑 | Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into bicom1 | |
| 2695 | ↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑 | Modus ponens 2669, 2694 | |
| 2696 | →↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑 | Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜒𝜑] into biimp | |
| 2697 | →↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜑] into bicom1 | |
| 2698 | ↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒 | Modus ponens 2683, 2697 | |
| 2699 | →↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜑, 𝜓↗→↔𝜑𝜓↔𝜑𝜒] into biimp | |
| 2700 | →→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒 | Modus ponens 2698, 2699 | |
| 2701 | →→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into ax-1 | |
| 2702 | →→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒 | Modus ponens 2700, 2701 | |
| 2703 | →→→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒→→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜒𝜑, 𝜒↗→↔𝜑𝜓↔𝜑𝜒] into ax-2 | |
| 2704 | →→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒 | Modus ponens 2702, 2703 | |
| 2705 | →→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒 | Modus ponens 2666, 2704 | |
| 2706 | →→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into impbi | |
| 2707 | →→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 2693, 2706 | |
| 2708 | ↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 2705, 2707 | |
| 2709 | ↔→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜒, 𝜒↗↔𝜒𝜓] into pm5.74 | |
| 2710 | →↔→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓↔↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓 | Subs [𝜑↗→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓] into bicom1 | |
| 2711 | ↔↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓 | Modus ponens 2709, 2710 | |
| 2712 | →↔↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓→↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓 | Subs [𝜑↗↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓] into biimp | |
| 2713 | →↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓 | Modus ponens 2711, 2712 | |
| 2714 | →↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓 | Modus ponens 2708, 2713 | |
| 2715 | →↔↔𝜓𝜒↔𝜒𝜓↔↔𝜒𝜓↔𝜓𝜒 | Subs [𝜑↗↔𝜓𝜒, 𝜓↗↔𝜒𝜓] into bicom1 | |
| 2716 | ↔↔𝜒𝜓↔𝜓𝜒 | Modus ponens 2677, 2715 | |
| 2717 | →↔↔𝜒𝜓↔𝜓𝜒→↔𝜑𝜓↔↔𝜒𝜓↔𝜓𝜒 | Subs [𝜑↗↔↔𝜒𝜓↔𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2718 | →↔𝜑𝜓↔↔𝜒𝜓↔𝜓𝜒 | Modus ponens 2716, 2717 | |
| 2719 | →↔→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓] into biimp | |
| 2720 | →→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 2709, 2719 | |
| 2721 | ↔→↔𝜑𝜓↔↔𝜒𝜓↔𝜓𝜒↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒𝜓, 𝜒↗↔𝜓𝜒] into pm5.74 | |
| 2722 | →↔→↔𝜑𝜓↔↔𝜒𝜓↔𝜓𝜒↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒→→↔𝜑𝜓↔↔𝜒𝜓↔𝜓𝜒↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒 | Subs [𝜑↗→↔𝜑𝜓↔↔𝜒𝜓↔𝜓𝜒, 𝜓↗↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒] into biimp | |
| 2723 | →→↔𝜑𝜓↔↔𝜒𝜓↔𝜓𝜒↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒 | Modus ponens 2721, 2722 | |
| 2724 | ↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒 | Modus ponens 2718, 2723 | |
| 2725 | →↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒 | Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜓𝜒] into biimp | |
| 2726 | →→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒 | Modus ponens 2724, 2725 | |
| 2727 | →↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into biimp | |
| 2728 | →→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒→→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒 | Subs [𝜑↗→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒, 𝜓↗→↔𝜑𝜓↔𝜑𝜒] into ax-1 | |
| 2729 | →→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒 | Modus ponens 2726, 2728 | |
| 2730 | →→→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒→→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒 | Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜓, 𝜒↗→↔𝜑𝜓↔𝜓𝜒] into ax-2 | |
| 2731 | →→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒 | Modus ponens 2729, 2730 | |
| 2732 | →→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒 | Modus ponens 2693, 2731 | |
| 2733 | →↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒↔→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜓𝜒] into bicom1 | |
| 2734 | ↔→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 2724, 2733 | |
| 2735 | →↔→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗→↔𝜑𝜓↔𝜓𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into biimp | |
| 2736 | →→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 2734, 2735 | |
| 2737 | →↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into bicom1 | |
| 2738 | ↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒 | Modus ponens 2708, 2737 | |
| 2739 | →↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜑𝜒] into biimp | |
| 2740 | →→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜓𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜓𝜒] into ax-1 | |
| 2741 | →→↔𝜑𝜓↔𝜓𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒 | Modus ponens 2705, 2740 | |
| 2742 | →→→↔𝜑𝜓↔𝜓𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗→↔𝜑𝜓↔𝜓𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜓, 𝜒↗→↔𝜑𝜓↔𝜑𝜒] into ax-2 | |
| 2743 | →→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒 | Modus ponens 2741, 2742 | |
| 2744 | →→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒 | Modus ponens 2736, 2743 | |
| 2745 | →→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒→→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒 | Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜓𝜒] into impbi | |
| 2746 | →→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒 | Modus ponens 2732, 2745 | |
| 2747 | ↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒 | Modus ponens 2744, 2746 | |
| 2748 | ↔→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜒, 𝜒↗↔𝜓𝜒] into pm5.74 | |
| 2749 | →↔→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒↔↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒 | Subs [𝜑↗→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒, 𝜓↗↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒] into bicom1 | |
| 2750 | ↔↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒 | Modus ponens 2748, 2749 | |
| 2751 | →↔↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒→↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒 | Subs [𝜑↗↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒, 𝜓↗→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒] into biimp | |
| 2752 | →↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒 | Modus ponens 2750, 2751 | |
| 2753 | →↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒 | Modus ponens 2747, 2752 | bibi1 |
| 2754 | →↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜒↔𝜓𝜒 | Subs [𝜑↗↔𝜑𝜒, 𝜓↗↔𝜓𝜒] into biimp | |
| 2755 | →→↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜓→↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜒↔𝜓𝜒 | Subs [𝜑↗→↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜒↔𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 2756 | →↔𝜑𝜓→↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜒↔𝜓𝜒 | Modus ponens 2754, 2755 | |
| 2757 | →→↔𝜑𝜓→↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜒↔𝜓𝜒→→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜓→↔𝜑𝜒↔𝜓𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔↔𝜑𝜒↔𝜓𝜒, 𝜒↗→↔𝜑𝜒↔𝜓𝜒] into ax-2 | |
| 2758 | →→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜓→↔𝜑𝜒↔𝜓𝜒 | Modus ponens 2756, 2757 | |
| 2759 | →↔𝜑𝜓→↔𝜑𝜒↔𝜓𝜒 | Modus ponens bibi1, 2758 | bitr3 |
| 2760 | ↔↔𝜑¬𝜓↔¬𝜑¬¬𝜓 | Subs [𝜓↗¬𝜓] into notbi | |
| 2761 | →↔¬𝜑𝜓↔¬𝜑𝜓 | Subs [𝜑↗↔¬𝜑𝜓] into id | |
| 2762 | →↔𝜓¬¬𝜓→↔¬𝜑𝜓↔𝜓¬¬𝜓 | Subs [𝜑↗↔𝜓¬¬𝜓, 𝜓↗↔¬𝜑𝜓] into ax-1 | |
| 2763 | →↔¬𝜑𝜓↔𝜓¬¬𝜓 | Modus ponens 1915, 2762 | |
| 2764 | ↔→↔¬𝜑𝜓↔¬𝜑𝜓↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓 | Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗¬𝜑, 𝜒↗𝜓] into pm5.74 | |
| 2765 | →↔→↔¬𝜑𝜓↔¬𝜑𝜓↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓→→↔¬𝜑𝜓↔¬𝜑𝜓↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓 | Subs [𝜑↗→↔¬𝜑𝜓↔¬𝜑𝜓, 𝜓↗↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓] into biimp | |
| 2766 | →→↔¬𝜑𝜓↔¬𝜑𝜓↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓 | Modus ponens 2764, 2765 | |
| 2767 | ↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓 | Modus ponens 2761, 2766 | |
| 2768 | ↔→↔¬𝜑𝜓↔𝜓¬¬𝜓↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓 | Subs [𝜑↗↔¬𝜑𝜓, 𝜒↗¬¬𝜓] into pm5.74 | |
| 2769 | →↔→↔¬𝜑𝜓↔𝜓¬¬𝜓↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓→→↔¬𝜑𝜓↔𝜓¬¬𝜓↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓 | Subs [𝜑↗→↔¬𝜑𝜓↔𝜓¬¬𝜓, 𝜓↗↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓] into biimp | |
| 2770 | →→↔¬𝜑𝜓↔𝜓¬¬𝜓↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓 | Modus ponens 2768, 2769 | |
| 2771 | ↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓 | Modus ponens 2763, 2770 | |
| 2772 | →↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓 | Subs [𝜑↗→↔¬𝜑𝜓𝜓, 𝜓↗→↔¬𝜑𝜓¬¬𝜓] into biimp | |
| 2773 | →→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓 | Modus ponens 2771, 2772 | |
| 2774 | →↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓→→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓 | Subs [𝜑↗→↔¬𝜑𝜓¬𝜑, 𝜓↗→↔¬𝜑𝜓𝜓] into biimp | |
| 2775 | →→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓 | Modus ponens 2767, 2774 | |
| 2776 | →→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓→→↔¬𝜑𝜓¬𝜑→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓 | Subs [𝜑↗→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓, 𝜓↗→↔¬𝜑𝜓¬𝜑] into ax-1 | |
| 2777 | →→↔¬𝜑𝜓¬𝜑→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓 | Modus ponens 2773, 2776 | |
| 2778 | →→→↔¬𝜑𝜓¬𝜑→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓→→→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓→→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓 | Subs [𝜑↗→↔¬𝜑𝜓¬𝜑, 𝜓↗→↔¬𝜑𝜓𝜓, 𝜒↗→↔¬𝜑𝜓¬¬𝜓] into ax-2 | |
| 2779 | →→→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓→→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓 | Modus ponens 2777, 2778 | |
| 2780 | →→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓 | Modus ponens 2775, 2779 | |
| 2781 | →↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓↔→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓𝜓 | Subs [𝜑↗→↔¬𝜑𝜓𝜓, 𝜓↗→↔¬𝜑𝜓¬¬𝜓] into bicom1 | |
| 2782 | ↔→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓𝜓 | Modus ponens 2771, 2781 | |
| 2783 | →↔→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓𝜓→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓𝜓 | Subs [𝜑↗→↔¬𝜑𝜓¬¬𝜓, 𝜓↗→↔¬𝜑𝜓𝜓] into biimp | |
| 2784 | →→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓𝜓 | Modus ponens 2782, 2783 | |
| 2785 | →↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑 | Subs [𝜑↗→↔¬𝜑𝜓¬𝜑, 𝜓↗→↔¬𝜑𝜓𝜓] into bicom1 | |
| 2786 | ↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑 | Modus ponens 2767, 2785 | |
| 2787 | →↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑 | Subs [𝜑↗→↔¬𝜑𝜓𝜓, 𝜓↗→↔¬𝜑𝜓¬𝜑] into biimp | |
| 2788 | →→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑 | Modus ponens 2786, 2787 | |
| 2789 | →→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑→→↔¬𝜑𝜓¬¬𝜓→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑 | Subs [𝜑↗→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑, 𝜓↗→↔¬𝜑𝜓¬¬𝜓] into ax-1 | |
| 2790 | →→↔¬𝜑𝜓¬¬𝜓→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑 | Modus ponens 2788, 2789 | |
| 2791 | →→→↔¬𝜑𝜓¬¬𝜓→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑→→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓𝜓→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓¬𝜑 | Subs [𝜑↗→↔¬𝜑𝜓¬¬𝜓, 𝜓↗→↔¬𝜑𝜓𝜓, 𝜒↗→↔¬𝜑𝜓¬𝜑] into ax-2 | |
| 2792 | →→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓𝜓→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓¬𝜑 | Modus ponens 2790, 2791 | |
| 2793 | →→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓¬𝜑 | Modus ponens 2784, 2792 | |
| 2794 | →→→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓→→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓¬𝜑↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓 | Subs [𝜑↗→↔¬𝜑𝜓¬𝜑, 𝜓↗→↔¬𝜑𝜓¬¬𝜓] into impbi | |
| 2795 | →→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓¬𝜑↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓 | Modus ponens 2780, 2794 | |
| 2796 | ↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓 | Modus ponens 2793, 2795 | |
| 2797 | ↔→↔¬𝜑𝜓↔¬𝜑¬¬𝜓↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓 | Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗¬𝜑, 𝜒↗¬¬𝜓] into pm5.74 | |
| 2798 | →↔→↔¬𝜑𝜓↔¬𝜑¬¬𝜓↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓↔↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓↔¬𝜑¬¬𝜓 | Subs [𝜑↗→↔¬𝜑𝜓↔¬𝜑¬¬𝜓, 𝜓↗↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓] into bicom1 | |
| 2799 | ↔↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓↔¬𝜑¬¬𝜓 | Modus ponens 2797, 2798 | |
| 2800 | →↔↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓↔¬𝜑¬¬𝜓→↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓↔¬𝜑¬¬𝜓 | Subs [𝜑↗↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓, 𝜓↗→↔¬𝜑𝜓↔¬𝜑¬¬𝜓] into biimp | |
| 2801 | →↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓↔¬𝜑¬¬𝜓 | Modus ponens 2799, 2800 | |
| 2802 | →↔¬𝜑𝜓↔¬𝜑¬¬𝜓 | Modus ponens 2796, 2801 | |
| 2803 | →↔¬𝜑¬¬𝜓↔¬𝜑¬¬𝜓 | Subs [𝜑↗↔¬𝜑¬¬𝜓] into id | |
| 2804 | →↔𝜓¬¬𝜓↔¬¬𝜓𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬¬𝜓] into bicom1 | |
| 2805 | ↔¬¬𝜓𝜓 | Modus ponens 1915, 2804 | |
| 2806 | →↔¬¬𝜓𝜓→↔¬𝜑¬¬𝜓↔¬¬𝜓𝜓 | Subs [𝜑↗↔¬¬𝜓𝜓, 𝜓↗↔¬𝜑¬¬𝜓] into ax-1 | |
| 2807 | →↔¬𝜑¬¬𝜓↔¬¬𝜓𝜓 | Modus ponens 2805, 2806 | |
| 2808 | ↔→↔¬𝜑¬¬𝜓↔¬𝜑¬¬𝜓↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓 | Subs [𝜑↗↔¬𝜑¬¬𝜓, 𝜓↗¬𝜑, 𝜒↗¬¬𝜓] into pm5.74 | |
| 2809 | →↔→↔¬𝜑¬¬𝜓↔¬𝜑¬¬𝜓↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓→→↔¬𝜑¬¬𝜓↔¬𝜑¬¬𝜓↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓 | Subs [𝜑↗→↔¬𝜑¬¬𝜓↔¬𝜑¬¬𝜓, 𝜓↗↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓] into biimp | |
| 2810 | →→↔¬𝜑¬¬𝜓↔¬𝜑¬¬𝜓↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓 | Modus ponens 2808, 2809 | |
| 2811 | ↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓 | Modus ponens 2803, 2810 | |
| 2812 | ↔→↔¬𝜑¬¬𝜓↔¬¬𝜓𝜓↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓 | Subs [𝜑↗↔¬𝜑¬¬𝜓, 𝜓↗¬¬𝜓, 𝜒↗𝜓] into pm5.74 | |
| 2813 | →↔→↔¬𝜑¬¬𝜓↔¬¬𝜓𝜓↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓→→↔¬𝜑¬¬𝜓↔¬¬𝜓𝜓↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓 | Subs [𝜑↗→↔¬𝜑¬¬𝜓↔¬¬𝜓𝜓, 𝜓↗↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓] into biimp | |
| 2814 | →→↔¬𝜑¬¬𝜓↔¬¬𝜓𝜓↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓 | Modus ponens 2812, 2813 | |
| 2815 | ↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓 | Modus ponens 2807, 2814 | |
| 2816 | →↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓 | Subs [𝜑↗→↔¬𝜑¬¬𝜓¬¬𝜓, 𝜓↗→↔¬𝜑¬¬𝜓𝜓] into biimp | |
| 2817 | →→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓 | Modus ponens 2815, 2816 | |
| 2818 | →↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓→→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓 | Subs [𝜑↗→↔¬𝜑¬¬𝜓¬𝜑, 𝜓↗→↔¬𝜑¬¬𝜓¬¬𝜓] into biimp | |
| 2819 | →→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓 | Modus ponens 2811, 2818 | |
| 2820 | →→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓→→↔¬𝜑¬¬𝜓¬𝜑→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓 | Subs [𝜑↗→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓, 𝜓↗→↔¬𝜑¬¬𝜓¬𝜑] into ax-1 | |
| 2821 | →→↔¬𝜑¬¬𝜓¬𝜑→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓 | Modus ponens 2817, 2820 | |
| 2822 | →→→↔¬𝜑¬¬𝜓¬𝜑→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓→→→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓→→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓 | Subs [𝜑↗→↔¬𝜑¬¬𝜓¬𝜑, 𝜓↗→↔¬𝜑¬¬𝜓¬¬𝜓, 𝜒↗→↔¬𝜑¬¬𝜓𝜓] into ax-2 | |
| 2823 | →→→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓→→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓 | Modus ponens 2821, 2822 | |
| 2824 | →→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓 | Modus ponens 2819, 2823 | |
| 2825 | →↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓↔→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬¬𝜓 | Subs [𝜑↗→↔¬𝜑¬¬𝜓¬¬𝜓, 𝜓↗→↔¬𝜑¬¬𝜓𝜓] into bicom1 | |
| 2826 | ↔→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬¬𝜓 | Modus ponens 2815, 2825 | |
| 2827 | →↔→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬¬𝜓→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬¬𝜓 | Subs [𝜑↗→↔¬𝜑¬¬𝜓𝜓, 𝜓↗→↔¬𝜑¬¬𝜓¬¬𝜓] into biimp | |
| 2828 | →→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬¬𝜓 | Modus ponens 2826, 2827 | |
| 2829 | →↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑 | Subs [𝜑↗→↔¬𝜑¬¬𝜓¬𝜑, 𝜓↗→↔¬𝜑¬¬𝜓¬¬𝜓] into bicom1 | |
| 2830 | ↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑 | Modus ponens 2811, 2829 | |
| 2831 | →↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑 | Subs [𝜑↗→↔¬𝜑¬¬𝜓¬¬𝜓, 𝜓↗→↔¬𝜑¬¬𝜓¬𝜑] into biimp | |
| 2832 | →→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑 | Modus ponens 2830, 2831 | |
| 2833 | →→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑→→↔¬𝜑¬¬𝜓𝜓→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑 | Subs [𝜑↗→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑, 𝜓↗→↔¬𝜑¬¬𝜓𝜓] into ax-1 | |
| 2834 | →→↔¬𝜑¬¬𝜓𝜓→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑 | Modus ponens 2832, 2833 | |
| 2835 | →→→↔¬𝜑¬¬𝜓𝜓→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑→→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬¬𝜓→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬𝜑 | Subs [𝜑↗→↔¬𝜑¬¬𝜓𝜓, 𝜓↗→↔¬𝜑¬¬𝜓¬¬𝜓, 𝜒↗→↔¬𝜑¬¬𝜓¬𝜑] into ax-2 | |
| 2836 | →→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬¬𝜓→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬𝜑 | Modus ponens 2834, 2835 | |
| 2837 | →→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬𝜑 | Modus ponens 2828, 2836 | |
| 2838 | →→→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓→→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬𝜑↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓 | Subs [𝜑↗→↔¬𝜑¬¬𝜓¬𝜑, 𝜓↗→↔¬𝜑¬¬𝜓𝜓] into impbi | |
| 2839 | →→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬𝜑↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓 | Modus ponens 2824, 2838 | |
| 2840 | ↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓 | Modus ponens 2837, 2839 | |
| 2841 | ↔→↔¬𝜑¬¬𝜓↔¬𝜑𝜓↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓 | Subs [𝜑↗↔¬𝜑¬¬𝜓, 𝜓↗¬𝜑, 𝜒↗𝜓] into pm5.74 | |
| 2842 | →↔→↔¬𝜑¬¬𝜓↔¬𝜑𝜓↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓↔↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓 | Subs [𝜑↗→↔¬𝜑¬¬𝜓↔¬𝜑𝜓, 𝜓↗↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓] into bicom1 | |
| 2843 | ↔↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓 | Modus ponens 2841, 2842 | |
| 2844 | →↔↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓→↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓 | Subs [𝜑↗↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓, 𝜓↗→↔¬𝜑¬¬𝜓↔¬𝜑𝜓] into biimp | |
| 2845 | →↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓 | Modus ponens 2843, 2844 | |
| 2846 | →↔¬𝜑¬¬𝜓↔¬𝜑𝜓 | Modus ponens 2840, 2845 | |
| 2847 | →→↔¬𝜑𝜓↔¬𝜑¬¬𝜓→→↔¬𝜑¬¬𝜓↔¬𝜑𝜓↔↔¬𝜑𝜓↔¬𝜑¬¬𝜓 | Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗↔¬𝜑¬¬𝜓] into impbi | |
| 2848 | →→↔¬𝜑¬¬𝜓↔¬𝜑𝜓↔↔¬𝜑𝜓↔¬𝜑¬¬𝜓 | Modus ponens 2802, 2847 | |
| 2849 | ↔↔¬𝜑𝜓↔¬𝜑¬¬𝜓 | Modus ponens 2846, 2848 | |
| 2850 | ↔↔¬𝜑𝜓↔𝜓¬𝜑 | Subs [𝜑↗¬𝜑] into bicom | |
| 2851 | →↔↔¬𝜑𝜓↔¬𝜑¬¬𝜓↔↔¬𝜑¬¬𝜓↔¬𝜑𝜓 | Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗↔¬𝜑¬¬𝜓] into bicom1 | |
| 2852 | ↔↔¬𝜑¬¬𝜓↔¬𝜑𝜓 | Modus ponens 2849, 2851 | |
| 2853 | →↔↔¬𝜑¬¬𝜓↔¬𝜑𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓 | Subs [𝜑↗↔¬𝜑¬¬𝜓, 𝜓↗↔¬𝜑𝜓] into biimp | |
| 2854 | →↔↔𝜑¬𝜓↔¬𝜑¬¬𝜓→↔𝜑¬𝜓↔¬𝜑¬¬𝜓 | Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔¬𝜑¬¬𝜓] into biimp | |
| 2855 | →↔𝜑¬𝜓↔¬𝜑¬¬𝜓 | Modus ponens 2760, 2854 | |
| 2856 | →→↔¬𝜑¬¬𝜓↔¬𝜑𝜓→↔𝜑¬𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓 | Subs [𝜑↗→↔¬𝜑¬¬𝜓↔¬𝜑𝜓, 𝜓↗↔𝜑¬𝜓] into ax-1 | |
| 2857 | →↔𝜑¬𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓 | Modus ponens 2846, 2856 | |
| 2858 | →→↔𝜑¬𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓→→↔𝜑¬𝜓↔¬𝜑¬¬𝜓→↔𝜑¬𝜓↔¬𝜑𝜓 | Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔¬𝜑¬¬𝜓, 𝜒↗↔¬𝜑𝜓] into ax-2 | |
| 2859 | →→↔𝜑¬𝜓↔¬𝜑¬¬𝜓→↔𝜑¬𝜓↔¬𝜑𝜓 | Modus ponens 2857, 2858 | |
| 2860 | →↔𝜑¬𝜓↔¬𝜑𝜓 | Modus ponens 2855, 2859 | |
| 2861 | →↔↔¬𝜑¬¬𝜓↔¬𝜑𝜓↔↔¬𝜑𝜓↔¬𝜑¬¬𝜓 | Subs [𝜑↗↔¬𝜑¬¬𝜓, 𝜓↗↔¬𝜑𝜓] into bicom1 | |
| 2862 | →↔↔¬𝜑𝜓↔¬𝜑¬¬𝜓→↔¬𝜑𝜓↔¬𝜑¬¬𝜓 | Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗↔¬𝜑¬¬𝜓] into biimp | |
| 2863 | →↔↔𝜑¬𝜓↔¬𝜑¬¬𝜓↔↔¬𝜑¬¬𝜓↔𝜑¬𝜓 | Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔¬𝜑¬¬𝜓] into bicom1 | |
| 2864 | ↔↔¬𝜑¬¬𝜓↔𝜑¬𝜓 | Modus ponens 2760, 2863 | |
| 2865 | →↔↔¬𝜑¬¬𝜓↔𝜑¬𝜓→↔¬𝜑¬¬𝜓↔𝜑¬𝜓 | Subs [𝜑↗↔¬𝜑¬¬𝜓, 𝜓↗↔𝜑¬𝜓] into biimp | |
| 2866 | →↔¬𝜑¬¬𝜓↔𝜑¬𝜓 | Modus ponens 2864, 2865 | |
| 2867 | →→↔¬𝜑¬¬𝜓↔𝜑¬𝜓→↔¬𝜑𝜓→↔¬𝜑¬¬𝜓↔𝜑¬𝜓 | Subs [𝜑↗→↔¬𝜑¬¬𝜓↔𝜑¬𝜓, 𝜓↗↔¬𝜑𝜓] into ax-1 | |
| 2868 | →↔¬𝜑𝜓→↔¬𝜑¬¬𝜓↔𝜑¬𝜓 | Modus ponens 2866, 2867 | |
| 2869 | →→↔¬𝜑𝜓→↔¬𝜑¬¬𝜓↔𝜑¬𝜓→→↔¬𝜑𝜓↔¬𝜑¬¬𝜓→↔¬𝜑𝜓↔𝜑¬𝜓 | Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗↔¬𝜑¬¬𝜓, 𝜒↗↔𝜑¬𝜓] into ax-2 | |
| 2870 | →→↔¬𝜑𝜓↔¬𝜑¬¬𝜓→↔¬𝜑𝜓↔𝜑¬𝜓 | Modus ponens 2868, 2869 | |
| 2871 | →↔¬𝜑𝜓↔𝜑¬𝜓 | Modus ponens 2802, 2870 | |
| 2872 | →→↔𝜑¬𝜓↔¬𝜑𝜓→→↔¬𝜑𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓↔¬𝜑𝜓 | Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔¬𝜑𝜓] into impbi | |
| 2873 | →→↔¬𝜑𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓↔¬𝜑𝜓 | Modus ponens 2860, 2872 | |
| 2874 | ↔↔𝜑¬𝜓↔¬𝜑𝜓 | Modus ponens 2871, 2873 | |
| 2875 | →↔↔¬𝜑𝜓↔𝜓¬𝜑→↔¬𝜑𝜓↔𝜓¬𝜑 | Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗↔𝜓¬𝜑] into biimp | |
| 2876 | →↔¬𝜑𝜓↔𝜓¬𝜑 | Modus ponens 2850, 2875 | |
| 2877 | →↔↔𝜑¬𝜓↔¬𝜑𝜓→↔𝜑¬𝜓↔¬𝜑𝜓 | Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔¬𝜑𝜓] into biimp | |
| 2878 | →→↔¬𝜑𝜓↔𝜓¬𝜑→↔𝜑¬𝜓→↔¬𝜑𝜓↔𝜓¬𝜑 | Subs [𝜑↗→↔¬𝜑𝜓↔𝜓¬𝜑, 𝜓↗↔𝜑¬𝜓] into ax-1 | |
| 2879 | →↔𝜑¬𝜓→↔¬𝜑𝜓↔𝜓¬𝜑 | Modus ponens 2876, 2878 | |
| 2880 | →→↔𝜑¬𝜓→↔¬𝜑𝜓↔𝜓¬𝜑→→↔𝜑¬𝜓↔¬𝜑𝜓→↔𝜑¬𝜓↔𝜓¬𝜑 | Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔¬𝜑𝜓, 𝜒↗↔𝜓¬𝜑] into ax-2 | |
| 2881 | →→↔𝜑¬𝜓↔¬𝜑𝜓→↔𝜑¬𝜓↔𝜓¬𝜑 | Modus ponens 2879, 2880 | |
| 2882 | →↔𝜑¬𝜓↔𝜓¬𝜑 | Modus ponens 2860, 2881 | |
| 2883 | →↔↔¬𝜑𝜓↔𝜓¬𝜑↔↔𝜓¬𝜑↔¬𝜑𝜓 | Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗↔𝜓¬𝜑] into bicom1 | |
| 2884 | ↔↔𝜓¬𝜑↔¬𝜑𝜓 | Modus ponens 2850, 2883 | |
| 2885 | →↔↔𝜓¬𝜑↔¬𝜑𝜓→↔𝜓¬𝜑↔¬𝜑𝜓 | Subs [𝜑↗↔𝜓¬𝜑, 𝜓↗↔¬𝜑𝜓] into biimp | |
| 2886 | →↔𝜓¬𝜑↔¬𝜑𝜓 | Modus ponens 2884, 2885 | |
| 2887 | →↔↔𝜑¬𝜓↔¬𝜑𝜓↔↔¬𝜑𝜓↔𝜑¬𝜓 | Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔¬𝜑𝜓] into bicom1 | |
| 2888 | ↔↔¬𝜑𝜓↔𝜑¬𝜓 | Modus ponens 2874, 2887 | |
| 2889 | →↔↔¬𝜑𝜓↔𝜑¬𝜓→↔¬𝜑𝜓↔𝜑¬𝜓 | Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗↔𝜑¬𝜓] into biimp | |
| 2890 | →→↔¬𝜑𝜓↔𝜑¬𝜓→↔𝜓¬𝜑→↔¬𝜑𝜓↔𝜑¬𝜓 | Subs [𝜑↗→↔¬𝜑𝜓↔𝜑¬𝜓, 𝜓↗↔𝜓¬𝜑] into ax-1 | |
| 2891 | →↔𝜓¬𝜑→↔¬𝜑𝜓↔𝜑¬𝜓 | Modus ponens 2871, 2890 | |
| 2892 | →→↔𝜓¬𝜑→↔¬𝜑𝜓↔𝜑¬𝜓→→↔𝜓¬𝜑↔¬𝜑𝜓→↔𝜓¬𝜑↔𝜑¬𝜓 | Subs [𝜑↗↔𝜓¬𝜑, 𝜓↗↔¬𝜑𝜓, 𝜒↗↔𝜑¬𝜓] into ax-2 | |
| 2893 | →→↔𝜓¬𝜑↔¬𝜑𝜓→↔𝜓¬𝜑↔𝜑¬𝜓 | Modus ponens 2891, 2892 | |
| 2894 | →↔𝜓¬𝜑↔𝜑¬𝜓 | Modus ponens 2886, 2893 | |
| 2895 | →→↔𝜑¬𝜓↔𝜓¬𝜑→→↔𝜓¬𝜑↔𝜑¬𝜓↔↔𝜑¬𝜓↔𝜓¬𝜑 | Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔𝜓¬𝜑] into impbi | |
| 2896 | →→↔𝜓¬𝜑↔𝜑¬𝜓↔↔𝜑¬𝜓↔𝜓¬𝜑 | Modus ponens 2882, 2895 | |
| 2897 | ↔↔𝜑¬𝜓↔𝜓¬𝜑 | Modus ponens 2894, 2896 | con2bi |
| 2898 | →→¬𝜓𝜑→¬𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜑] into con1 | |
| 2899 | →→→¬𝜑𝜓→¬𝜓𝜑→→→¬𝜓𝜑→¬𝜑𝜓↔→¬𝜑𝜓→¬𝜓𝜑 | Subs [𝜑↗→¬𝜑𝜓, 𝜓↗→¬𝜓𝜑] into impbi | |
| 2900 | →→→¬𝜓𝜑→¬𝜑𝜓↔→¬𝜑𝜓→¬𝜓𝜑 | Modus ponens con1, 2899 | |
| 2901 | ↔→¬𝜑𝜓→¬𝜓𝜑 | Modus ponens 2898, 2900 | con1b |
| 2902 | →→𝜓¬𝜑→𝜑¬𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜑] into con2 | |
| 2903 | →→→𝜑¬𝜓→𝜓¬𝜑→→→𝜓¬𝜑→𝜑¬𝜓↔→𝜑¬𝜓→𝜓¬𝜑 | Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→𝜓¬𝜑] into impbi | |
| 2904 | →→→𝜓¬𝜑→𝜑¬𝜓↔→𝜑¬𝜓→𝜓¬𝜑 | Modus ponens con2, 2903 | |
| 2905 | ↔→𝜑¬𝜓→𝜓¬𝜑 | Modus ponens 2902, 2904 | con2b |
| 2906 | →→𝜓→𝜑𝜓→𝜑→𝜓→𝜑𝜓 | Subs [𝜑↗→𝜓→𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 2907 | →𝜑→𝜓→𝜑𝜓 | Modus ponens 208, 2906 | |
| 2908 | →→→𝜑𝜓𝜓→→𝜓→𝜑𝜓↔→𝜑𝜓𝜓 | Subs [𝜑↗→𝜑𝜓] into impbi | |
| 2909 | →→𝜓→𝜑𝜓→→→𝜑𝜓𝜓→𝜓→𝜑𝜓 | Subs [𝜑↗→𝜓→𝜑𝜓, 𝜓↗→→𝜑𝜓𝜓] into ax-1 | |
| 2910 | →→→𝜓→𝜑𝜓→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→𝜑→→𝜓→𝜑𝜓→→→𝜑𝜓𝜓→𝜓→𝜑𝜓 | Subs [𝜑↗→→𝜓→𝜑𝜓→→→𝜑𝜓𝜓→𝜓→𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 2911 | →𝜑→→𝜓→𝜑𝜓→→→𝜑𝜓𝜓→𝜓→𝜑𝜓 | Modus ponens 2909, 2910 | |
| 2912 | →→𝜑→→𝜓→𝜑𝜓→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→→𝜑→𝜓→𝜑𝜓→𝜑→→→𝜑𝜓𝜓→𝜓→𝜑𝜓 | Subs [𝜓↗→𝜓→𝜑𝜓, 𝜒↗→→→𝜑𝜓𝜓→𝜓→𝜑𝜓] into ax-2 | |
| 2913 | →→𝜑→𝜓→𝜑𝜓→𝜑→→→𝜑𝜓𝜓→𝜓→𝜑𝜓 | Modus ponens 2911, 2912 | |
| 2914 | →𝜑→→→𝜑𝜓𝜓→𝜓→𝜑𝜓 | Modus ponens 2907, 2913 | |
| 2915 | →→→→𝜑𝜓𝜓→→𝜓→𝜑𝜓↔→𝜑𝜓𝜓→→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓 | Subs [𝜑↗→→𝜑𝜓𝜓, 𝜓↗→𝜓→𝜑𝜓, 𝜒↗↔→𝜑𝜓𝜓] into ax-2 | |
| 2916 | →→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓 | Modus ponens 2908, 2915 | |
| 2917 | →→→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓→𝜑→→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓 | Subs [𝜑↗→→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1 | |
| 2918 | →𝜑→→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓 | Modus ponens 2916, 2917 | |
| 2919 | →→𝜑→→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓→→𝜑→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→𝜑→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓 | Subs [𝜓↗→→→𝜑𝜓𝜓→𝜓→𝜑𝜓, 𝜒↗→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓] into ax-2 | |
| 2920 | →→𝜑→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→𝜑→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓 | Modus ponens 2918, 2919 | |
| 2921 | →𝜑→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓 | Modus ponens 2914, 2920 | |
| 2922 | →→→𝜑𝜓𝜓→→𝜑𝜓𝜓 | Subs [𝜑↗→→𝜑𝜓𝜓] into id | |
| 2923 | →→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓 | Subs [𝜑↗→→𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1 | |
| 2924 | →→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓→→→𝜑𝜓𝜓→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓 | Subs [𝜑↗→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓, 𝜓↗→→𝜑𝜓𝜓] into ax-1 | |
| 2925 | →→→𝜑𝜓𝜓→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓 | Modus ponens 2923, 2924 | |
| 2926 | →→→→𝜑𝜓𝜓→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓→→→→𝜑𝜓𝜓→→𝜑𝜓𝜓→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓 | Subs [𝜑↗→→𝜑𝜓𝜓, 𝜓↗→→𝜑𝜓𝜓, 𝜒↗→𝜑→→𝜑𝜓𝜓] into ax-2 | |
| 2927 | →→→→𝜑𝜓𝜓→→𝜑𝜓𝜓→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓 | Modus ponens 2925, 2926 | |
| 2928 | →→𝜑→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓→→𝜑→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓 | Subs [𝜓↗→→𝜑𝜓𝜓, 𝜒↗↔→𝜑𝜓𝜓] into ax-2 | |
| 2929 | →→𝜑→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓 | Modus ponens 2921, 2928 | |
| 2930 | →→→𝜑→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓→→→𝜑𝜓𝜓→→𝜑→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓 | Subs [𝜑↗→→𝜑→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓, 𝜓↗→→𝜑𝜓𝜓] into ax-1 | |
| 2931 | →→→𝜑𝜓𝜓→→𝜑→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓 | Modus ponens 2929, 2930 | |
| 2932 | →→→→𝜑𝜓𝜓→→𝜑→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓→→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓→→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓 | Subs [𝜑↗→→𝜑𝜓𝜓, 𝜓↗→𝜑→→𝜑𝜓𝜓, 𝜒↗→𝜑↔→𝜑𝜓𝜓] into ax-2 | |
| 2933 | →→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓→→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓 | Modus ponens 2931, 2932 | |
| 2934 | →→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓 | Modus ponens 2923, 2933 | |
| 2935 | →→→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓→𝜑→→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓 | Subs [𝜑↗→→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1 | |
| 2936 | →𝜑→→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓 | Modus ponens 2934, 2935 | |
| 2937 | →→𝜑→→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓→→𝜑→→𝜑𝜓𝜓→𝜑→𝜑↔→𝜑𝜓𝜓 | Subs [𝜓↗→→𝜑𝜓𝜓, 𝜒↗→𝜑↔→𝜑𝜓𝜓] into ax-2 | |
| 2938 | →→𝜑→→𝜑𝜓𝜓→𝜑→𝜑↔→𝜑𝜓𝜓 | Modus ponens 2936, 2937 | |
| 2939 | →𝜑→𝜑↔→𝜑𝜓𝜓 | Modus ponens pm2.27, 2938 | |
| 2940 | →→𝜑→𝜑𝜑→𝜑→𝜑→𝜑𝜑 | Subs [𝜑↗→𝜑→𝜑𝜑, 𝜓↗𝜑] into ax-1 | |
| 2941 | →𝜑→𝜑→𝜑𝜑 | Modus ponens 5, 2940 | |
| 2942 | →→𝜑→𝜑→𝜑𝜑→→𝜑𝜑→𝜑→𝜑𝜑 | Subs [𝜓↗𝜑, 𝜒↗→𝜑𝜑] into ax-2 | |
| 2943 | →→𝜑𝜑→𝜑→𝜑𝜑 | Modus ponens 2941, 2942 | |
| 2944 | →→𝜑→𝜑↔→𝜑𝜓𝜓→→𝜑𝜑→𝜑↔→𝜑𝜓𝜓 | Subs [𝜓↗𝜑, 𝜒↗↔→𝜑𝜓𝜓] into ax-2 | |
| 2945 | →→𝜑𝜑→𝜑↔→𝜑𝜓𝜓 | Modus ponens 2939, 2944 | |
| 2946 | →→→𝜑𝜑→𝜑↔→𝜑𝜓𝜓→𝜑→→𝜑𝜑→𝜑↔→𝜑𝜓𝜓 | Subs [𝜑↗→→𝜑𝜑→𝜑↔→𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1 | |
| 2947 | →𝜑→→𝜑𝜑→𝜑↔→𝜑𝜓𝜓 | Modus ponens 2945, 2946 | |
| 2948 | →→𝜑→→𝜑𝜑→𝜑↔→𝜑𝜓𝜓→→𝜑→𝜑𝜑→𝜑→𝜑↔→𝜑𝜓𝜓 | Subs [𝜓↗→𝜑𝜑, 𝜒↗→𝜑↔→𝜑𝜓𝜓] into ax-2 | |
| 2949 | →→𝜑→𝜑𝜑→𝜑→𝜑↔→𝜑𝜓𝜓 | Modus ponens 2947, 2948 | |
| 2950 | →𝜑↔→𝜑𝜓𝜓 | Modus ponens id, 2945 | pm5.5 |
| 2951 | ↔↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓] into bicom | |
| 2952 | →↔↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓→↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜓𝜓, 𝜓↗↔𝜓→𝜑𝜓] into biimp | |
| 2953 | →↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓 | Modus ponens 2951, 2952 | |
| 2954 | →→↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓→𝜑→↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 2955 | →𝜑→↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓 | Modus ponens 2953, 2954 | |
| 2956 | →→𝜑→↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓→→𝜑↔→𝜑𝜓𝜓→𝜑↔𝜓→𝜑𝜓 | Subs [𝜓↗↔→𝜑𝜓𝜓, 𝜒↗↔𝜓→𝜑𝜓] into ax-2 | |
| 2957 | →→𝜑↔→𝜑𝜓𝜓→𝜑↔𝜓→𝜑𝜓 | Modus ponens 2955, 2956 | |
| 2958 | →𝜑↔𝜓→𝜑𝜓 | Modus ponens pm5.5, 2957 | biimt |
| 2959 | ↔↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓 | Subs [𝜑↗𝜓, 𝜓↗→𝜑𝜓] into bicom | |
| 2960 | →↔↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓→↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓 | Subs [𝜑↗↔𝜓→𝜑𝜓, 𝜓↗↔→𝜑𝜓𝜓] into biimp | |
| 2961 | →↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓 | Modus ponens 2959, 2960 | |
| 2962 | →→↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓→𝜑→↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓 | Subs [𝜑↗→↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1 | |
| 2963 | →𝜑→↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓 | Modus ponens 2961, 2962 | |
| 2964 | →→𝜑→↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓→→𝜑↔𝜓→𝜑𝜓→𝜑↔→𝜑𝜓𝜓 | Subs [𝜓↗↔𝜓→𝜑𝜓, 𝜒↗↔→𝜑𝜓𝜓] into ax-2 | |
| 2965 | →→𝜑↔𝜓→𝜑𝜓→𝜑↔→𝜑𝜓𝜓 | Modus ponens 2963, 2964 | |
| 2966 | →¬𝜑↔¬𝜓→¬𝜑¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓] into biimt | |
| 2967 | ↔→𝜓𝜑→¬𝜑¬𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜑] into con34b | |
| 2968 | →↔→𝜓𝜑→¬𝜑¬𝜓↔→¬𝜑¬𝜓→𝜓𝜑 | Subs [𝜑↗→𝜓𝜑, 𝜓↗→¬𝜑¬𝜓] into bicom1 | |
| 2969 | ↔→¬𝜑¬𝜓→𝜓𝜑 | Modus ponens 2967, 2968 | |
| 2970 | →↔→¬𝜑¬𝜓→𝜓𝜑→¬𝜑↔→¬𝜑¬𝜓→𝜓𝜑 | Subs [𝜑↗↔→¬𝜑¬𝜓→𝜓𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 2971 | →¬𝜑↔→¬𝜑¬𝜓→𝜓𝜑 | Modus ponens 2969, 2970 | |
| 2972 | ↔→¬𝜑↔¬𝜓→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓, 𝜒↗→¬𝜑¬𝜓] into pm5.74 | |
| 2973 | →↔→¬𝜑↔¬𝜓→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓→→¬𝜑↔¬𝜓→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑↔¬𝜓→¬𝜑¬𝜓, 𝜓↗↔→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓] into biimp | |
| 2974 | →→¬𝜑↔¬𝜓→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓 | Modus ponens 2972, 2973 | |
| 2975 | ↔→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓 | Modus ponens 2966, 2974 | |
| 2976 | ↔→¬𝜑↔→¬𝜑¬𝜓→𝜓𝜑↔→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗→¬𝜑¬𝜓, 𝜒↗→𝜓𝜑] into pm5.74 | |
| 2977 | →↔→¬𝜑↔→¬𝜑¬𝜓→𝜓𝜑↔→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→→¬𝜑↔→¬𝜑¬𝜓→𝜓𝜑↔→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑 | Subs [𝜑↗→¬𝜑↔→¬𝜑¬𝜓→𝜓𝜑, 𝜓↗↔→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑] into biimp | |
| 2978 | →→¬𝜑↔→¬𝜑¬𝜓→𝜓𝜑↔→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑 | Modus ponens 2976, 2977 | |
| 2979 | ↔→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑 | Modus ponens 2971, 2978 | |
| 2980 | →↔→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑 | Subs [𝜑↗→¬𝜑→¬𝜑¬𝜓, 𝜓↗→¬𝜑→𝜓𝜑] into biimp | |
| 2981 | →→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑 | Modus ponens 2979, 2980 | |
| 2982 | →↔→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑→¬𝜑¬𝜓] into biimp | |
| 2983 | →→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓 | Modus ponens 2975, 2982 | |
| 2984 | →→→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→→¬𝜑¬𝜓→→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑 | Subs [𝜑↗→→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑, 𝜓↗→¬𝜑¬𝜓] into ax-1 | |
| 2985 | →→¬𝜑¬𝜓→→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑 | Modus ponens 2981, 2984 | |
| 2986 | →→→¬𝜑¬𝜓→→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→→→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑→𝜓𝜑 | Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑→¬𝜑¬𝜓, 𝜒↗→¬𝜑→𝜓𝜑] into ax-2 | |
| 2987 | →→→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑→𝜓𝜑 | Modus ponens 2985, 2986 | |
| 2988 | →→¬𝜑¬𝜓→¬𝜑→𝜓𝜑 | Modus ponens 2983, 2987 | |
| 2989 | →↔→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑↔→¬𝜑→𝜓𝜑→¬𝜑→¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑→¬𝜑¬𝜓, 𝜓↗→¬𝜑→𝜓𝜑] into bicom1 | |
| 2990 | ↔→¬𝜑→𝜓𝜑→¬𝜑→¬𝜑¬𝜓 | Modus ponens 2979, 2989 | |
| 2991 | →↔→¬𝜑→𝜓𝜑→¬𝜑→¬𝜑¬𝜓→→¬𝜑→𝜓𝜑→¬𝜑→¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑→𝜓𝜑, 𝜓↗→¬𝜑→¬𝜑¬𝜓] into biimp | |
| 2992 | →→¬𝜑→𝜓𝜑→¬𝜑→¬𝜑¬𝜓 | Modus ponens 2990, 2991 | |
| 2993 | →↔→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓↔→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑→¬𝜑¬𝜓] into bicom1 | |
| 2994 | ↔→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓 | Modus ponens 2975, 2993 | |
| 2995 | →↔→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑→¬𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓] into biimp | |
| 2996 | →→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓 | Modus ponens 2994, 2995 | |
| 2997 | →→→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑→𝜓𝜑→→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓, 𝜓↗→¬𝜑→𝜓𝜑] into ax-1 | |
| 2998 | →→¬𝜑→𝜓𝜑→→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓 | Modus ponens 2996, 2997 | |
| 2999 | →→→¬𝜑→𝜓𝜑→→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓→→→¬𝜑→𝜓𝜑→¬𝜑→¬𝜑¬𝜓→→¬𝜑→𝜓𝜑→¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑→𝜓𝜑, 𝜓↗→¬𝜑→¬𝜑¬𝜓, 𝜒↗→¬𝜑¬𝜓] into ax-2 | |
| 3000 | →→→¬𝜑→𝜓𝜑→¬𝜑→¬𝜑¬𝜓→→¬𝜑→𝜓𝜑→¬𝜑¬𝜓 | Modus ponens 2998, 2999 | |
| 3001 | →→¬𝜑→𝜓𝜑→¬𝜑¬𝜓 | Modus ponens 2992, 3000 | |
| 3002 | →→→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→→→¬𝜑→𝜓𝜑→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑 | Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑→𝜓𝜑] into impbi | |
| 3003 | →→→¬𝜑→𝜓𝜑→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑 | Modus ponens 2988, 3002 | |
| 3004 | ↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑 | Modus ponens 3001, 3003 | |
| 3005 | ↔→¬𝜑↔¬𝜓→𝜓𝜑↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓, 𝜒↗→𝜓𝜑] into pm5.74 | |
| 3006 | →↔→¬𝜑↔¬𝜓→𝜓𝜑↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑↔↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→¬𝜑↔¬𝜓→𝜓𝜑 | Subs [𝜑↗→¬𝜑↔¬𝜓→𝜓𝜑, 𝜓↗↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑] into bicom1 | |
| 3007 | ↔↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→¬𝜑↔¬𝜓→𝜓𝜑 | Modus ponens 3005, 3006 | |
| 3008 | →↔↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→¬𝜑↔¬𝜓→𝜓𝜑→↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→¬𝜑↔¬𝜓→𝜓𝜑 | Subs [𝜑↗↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑, 𝜓↗→¬𝜑↔¬𝜓→𝜓𝜑] into biimp | |
| 3009 | →↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→¬𝜑↔¬𝜓→𝜓𝜑 | Modus ponens 3007, 3008 | |
| 3010 | →¬𝜑↔¬𝜓→𝜓𝜑 | Modus ponens 3004, 3009 | mtt |
| 3011 | →¬𝜓↔¬𝜑→𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜑] into mtt | |
| 3012 | ↔↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗→𝜑𝜓] into bicom | |
| 3013 | →↔↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑→↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑 | Subs [𝜑↗↔¬𝜑→𝜑𝜓, 𝜓↗↔→𝜑𝜓¬𝜑] into biimp | |
| 3014 | →↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑 | Modus ponens 3012, 3013 | |
| 3015 | →→↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑→¬𝜓→↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑 | Subs [𝜑↗→↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1 | |
| 3016 | →¬𝜓→↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑 | Modus ponens 3014, 3015 | |
| 3017 | →→¬𝜓→↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑→→¬𝜓↔¬𝜑→𝜑𝜓→¬𝜓↔→𝜑𝜓¬𝜑 | Subs [𝜑↗¬𝜓, 𝜓↗↔¬𝜑→𝜑𝜓, 𝜒↗↔→𝜑𝜓¬𝜑] into ax-2 | |
| 3018 | →→¬𝜓↔¬𝜑→𝜑𝜓→¬𝜓↔→𝜑𝜓¬𝜑 | Modus ponens 3016, 3017 | |
| 3019 | →¬𝜓↔→𝜑𝜓¬𝜑 | Modus ponens 3011, 3018 | imnot |
| 3020 | →𝜑→↔𝜑𝜓𝜑 | Subs [𝜓↗↔𝜑𝜓] into ax-1 | |
| 3021 | →→𝜑→↔𝜑𝜓𝜑→𝜑→𝜑→↔𝜑𝜓𝜑 | Subs [𝜑↗→𝜑→↔𝜑𝜓𝜑, 𝜓↗𝜑] into ax-1 | |
| 3022 | →𝜑→𝜑→↔𝜑𝜓𝜑 | Modus ponens 3020, 3021 | |
| 3023 | →→𝜑→𝜑→↔𝜑𝜓𝜑→→𝜑𝜑→𝜑→↔𝜑𝜓𝜑 | Subs [𝜓↗𝜑, 𝜒↗→↔𝜑𝜓𝜑] into ax-2 | |
| 3024 | →→𝜑𝜑→𝜑→↔𝜑𝜓𝜑 | Modus ponens 3022, 3023 | |
| 3025 | →→↔𝜑𝜓→𝜑𝜓→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2 | |
| 3026 | →→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→𝜑→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Subs [𝜑↗→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1 | |
| 3027 | →𝜑→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓 | Modus ponens 1929, 3026 | |
| 3028 | →→𝜑→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→𝜑→↔𝜑𝜓𝜑→𝜑→↔𝜑𝜓𝜓 | Subs [𝜓↗→↔𝜑𝜓𝜑, 𝜒↗→↔𝜑𝜓𝜓] into ax-2 | |
| 3029 | →→𝜑→↔𝜑𝜓𝜑→𝜑→↔𝜑𝜓𝜓 | Modus ponens 3027, 3028 | |
| 3030 | →𝜑→↔𝜑𝜓𝜓 | Modus ponens 3020, 3029 | |
| 3031 | →→𝜓↔𝜑𝜓→→↔𝜑𝜓𝜓↔𝜓↔𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗↔𝜑𝜓] into impbi | |
| 3032 | →→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓 | Subs [𝜑↗→↔𝜑𝜓𝜓, 𝜓↗→𝜓↔𝜑𝜓] into ax-1 | |
| 3033 | →→→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→𝜑→→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓 | Subs [𝜑↗→→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1 | |
| 3034 | →𝜑→→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓 | Modus ponens 3032, 3033 | |
| 3035 | →→𝜑→→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→→𝜑→↔𝜑𝜓𝜓→𝜑→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓 | Subs [𝜓↗→↔𝜑𝜓𝜓, 𝜒↗→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓] into ax-2 | |
| 3036 | →→𝜑→↔𝜑𝜓𝜓→𝜑→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓 | Modus ponens 3034, 3035 | |
| 3037 | →𝜑→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓 | Modus ponens 3030, 3036 | |
| 3038 | →→→𝜓↔𝜑𝜓→→↔𝜑𝜓𝜓↔𝜓↔𝜑𝜓→→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓 | Subs [𝜑↗→𝜓↔𝜑𝜓, 𝜓↗→↔𝜑𝜓𝜓, 𝜒↗↔𝜓↔𝜑𝜓] into ax-2 | |
| 3039 | →→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓 | Modus ponens 3031, 3038 | |
| 3040 | →→→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓→𝜑→→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓 | Subs [𝜑↗→→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 3041 | →𝜑→→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓 | Modus ponens 3039, 3040 | |
| 3042 | →→𝜑→→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓→→𝜑→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→𝜑→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓 | Subs [𝜓↗→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓, 𝜒↗→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓] into ax-2 | |
| 3043 | →→𝜑→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→𝜑→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓 | Modus ponens 3041, 3042 | |
| 3044 | →𝜑→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓 | Modus ponens 3037, 3043 | |
| 3045 | →→𝜓↔𝜑𝜓→𝜓↔𝜑𝜓 | Subs [𝜑↗→𝜓↔𝜑𝜓] into id | |
| 3046 | →→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓 | Subs [𝜑↗→𝜓↔𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 3047 | →→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓 | Subs [𝜑↗→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓, 𝜓↗→𝜓↔𝜑𝜓] into ax-1 | |
| 3048 | →→𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓 | Modus ponens 3046, 3047 | |
| 3049 | →→→𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓→→→𝜓↔𝜑𝜓→𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓 | Subs [𝜑↗→𝜓↔𝜑𝜓, 𝜓↗→𝜓↔𝜑𝜓, 𝜒↗→𝜑→𝜓↔𝜑𝜓] into ax-2 | |
| 3050 | →→→𝜓↔𝜑𝜓→𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓 | Modus ponens 3048, 3049 | |
| 3051 | →→𝜑→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓→→𝜑→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓 | Subs [𝜓↗→𝜓↔𝜑𝜓, 𝜒↗↔𝜓↔𝜑𝜓] into ax-2 | |
| 3052 | →→𝜑→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓 | Modus ponens 3044, 3051 | |
| 3053 | →→→𝜑→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→→𝜑→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓 | Subs [𝜑↗→→𝜑→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓, 𝜓↗→𝜓↔𝜑𝜓] into ax-1 | |
| 3054 | →→𝜓↔𝜑𝜓→→𝜑→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓 | Modus ponens 3052, 3053 | |
| 3055 | →→→𝜓↔𝜑𝜓→→𝜑→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓→→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓 | Subs [𝜑↗→𝜓↔𝜑𝜓, 𝜓↗→𝜑→𝜓↔𝜑𝜓, 𝜒↗→𝜑↔𝜓↔𝜑𝜓] into ax-2 | |
| 3056 | →→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓 | Modus ponens 3054, 3055 | |
| 3057 | →→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓 | Modus ponens 3046, 3056 | |
| 3058 | →→→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓→𝜑→→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓 | Subs [𝜑↗→→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 3059 | →𝜑→→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓 | Modus ponens 3057, 3058 | |
| 3060 | →→𝜑→→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓→→𝜑→𝜓↔𝜑𝜓→𝜑→𝜑↔𝜓↔𝜑𝜓 | Subs [𝜓↗→𝜓↔𝜑𝜓, 𝜒↗→𝜑↔𝜓↔𝜑𝜓] into ax-2 | |
| 3061 | →→𝜑→𝜓↔𝜑𝜓→𝜑→𝜑↔𝜓↔𝜑𝜓 | Modus ponens 3059, 3060 | |
| 3062 | →𝜑→𝜑↔𝜓↔𝜑𝜓 | Modus ponens pm5.1im, 3061 | |
| 3063 | →→𝜑→𝜑↔𝜓↔𝜑𝜓→→𝜑𝜑→𝜑↔𝜓↔𝜑𝜓 | Subs [𝜓↗𝜑, 𝜒↗↔𝜓↔𝜑𝜓] into ax-2 | |
| 3064 | →→𝜑𝜑→𝜑↔𝜓↔𝜑𝜓 | Modus ponens 3062, 3063 | |
| 3065 | →→→𝜑𝜑→𝜑↔𝜓↔𝜑𝜓→𝜑→→𝜑𝜑→𝜑↔𝜓↔𝜑𝜓 | Subs [𝜑↗→→𝜑𝜑→𝜑↔𝜓↔𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 3066 | →𝜑→→𝜑𝜑→𝜑↔𝜓↔𝜑𝜓 | Modus ponens 3064, 3065 | |
| 3067 | →→𝜑→→𝜑𝜑→𝜑↔𝜓↔𝜑𝜓→→𝜑→𝜑𝜑→𝜑→𝜑↔𝜓↔𝜑𝜓 | Subs [𝜓↗→𝜑𝜑, 𝜒↗→𝜑↔𝜓↔𝜑𝜓] into ax-2 | |
| 3068 | →→𝜑→𝜑𝜑→𝜑→𝜑↔𝜓↔𝜑𝜓 | Modus ponens 3066, 3067 | |
| 3069 | →𝜑↔𝜓↔𝜑𝜓 | Modus ponens id, 3064 | pm5.501 |
| 3070 | ↔→𝜑↔𝜓↔𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓 | Subs [𝜒↗↔𝜑𝜓] into pm5.74 | |
| 3071 | →↔→𝜑↔𝜓↔𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓→→𝜑↔𝜓↔𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓 | Subs [𝜑↗→𝜑↔𝜓↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜑↔𝜑𝜓] into biimp | |
| 3072 | →→𝜑↔𝜓↔𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓 | Modus ponens 3070, 3071 | |
| 3073 | ↔→𝜑𝜓→𝜑↔𝜑𝜓 | Modus ponens pm5.501, 3072 | ibib |
| 3074 | →↔↔𝜑𝜓↔𝜓𝜑→𝜑↔↔𝜑𝜓↔𝜓𝜑 | Subs [𝜑↗↔↔𝜑𝜓↔𝜓𝜑, 𝜓↗𝜑] into ax-1 | |
| 3075 | →𝜑↔↔𝜑𝜓↔𝜓𝜑 | Modus ponens bicom, 3074 | |
| 3076 | ↔→𝜑↔↔𝜑𝜓↔𝜓𝜑↔→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑 | Subs [𝜓↗↔𝜑𝜓, 𝜒↗↔𝜓𝜑] into pm5.74 | |
| 3077 | →↔→𝜑↔↔𝜑𝜓↔𝜓𝜑↔→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑→→𝜑↔↔𝜑𝜓↔𝜓𝜑↔→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑 | Subs [𝜑↗→𝜑↔↔𝜑𝜓↔𝜓𝜑, 𝜓↗↔→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑] into biimp | |
| 3078 | →→𝜑↔↔𝜑𝜓↔𝜓𝜑↔→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑 | Modus ponens 3076, 3077 | |
| 3079 | ↔→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑 | Modus ponens 3075, 3078 | |
| 3080 | →↔→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑→→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑 | Subs [𝜑↗→𝜑↔𝜑𝜓, 𝜓↗→𝜑↔𝜓𝜑] into biimp | |
| 3081 | →→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑 | Modus ponens 3079, 3080 | |
| 3082 | →↔→𝜑𝜓→𝜑↔𝜑𝜓→→𝜑𝜓→𝜑↔𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑↔𝜑𝜓] into biimp | |
| 3083 | →→→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑→→𝜑𝜓→→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑 | Subs [𝜑↗→→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑, 𝜓↗→𝜑𝜓] into ax-1 | |
| 3084 | →→𝜑𝜓→→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑 | Modus ponens 3081, 3083 | |
| 3085 | →→→𝜑𝜓→→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑→→→𝜑𝜓→𝜑↔𝜑𝜓→→𝜑𝜓→𝜑↔𝜓𝜑 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑↔𝜑𝜓, 𝜒↗→𝜑↔𝜓𝜑] into ax-2 | |
| 3086 | →→→𝜑𝜓→𝜑↔𝜑𝜓→→𝜑𝜓→𝜑↔𝜓𝜑 | Modus ponens 3084, 3085 | |
| 3087 | →→𝜑𝜓→𝜑↔𝜓𝜑 | Modus ponens 1697, 3086 | |
| 3088 | →↔→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑↔→𝜑↔𝜓𝜑→𝜑↔𝜑𝜓 | Subs [𝜑↗→𝜑↔𝜑𝜓, 𝜓↗→𝜑↔𝜓𝜑] into bicom1 | |
| 3089 | ↔→𝜑↔𝜓𝜑→𝜑↔𝜑𝜓 | Modus ponens 3079, 3088 | |
| 3090 | →↔→𝜑↔𝜓𝜑→𝜑↔𝜑𝜓→→𝜑↔𝜓𝜑→𝜑↔𝜑𝜓 | Subs [𝜑↗→𝜑↔𝜓𝜑, 𝜓↗→𝜑↔𝜑𝜓] into biimp | |
| 3091 | →→𝜑↔𝜓𝜑→𝜑↔𝜑𝜓 | Modus ponens 3089, 3090 | |
| 3092 | →↔→𝜑𝜓→𝜑↔𝜑𝜓↔→𝜑↔𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑↔𝜑𝜓] into bicom1 | |
| 3093 | ↔→𝜑↔𝜑𝜓→𝜑𝜓 | Modus ponens ibib, 3092 | |
| 3094 | →↔→𝜑↔𝜑𝜓→𝜑𝜓→→𝜑↔𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑↔𝜑𝜓, 𝜓↗→𝜑𝜓] into biimp | |
| 3095 | →→𝜑↔𝜑𝜓→𝜑𝜓 | Modus ponens 3093, 3094 | |
| 3096 | →→→𝜑↔𝜑𝜓→𝜑𝜓→→𝜑↔𝜓𝜑→→𝜑↔𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→→𝜑↔𝜑𝜓→𝜑𝜓, 𝜓↗→𝜑↔𝜓𝜑] into ax-1 | |
| 3097 | →→𝜑↔𝜓𝜑→→𝜑↔𝜑𝜓→𝜑𝜓 | Modus ponens 3095, 3096 | |
| 3098 | →→→𝜑↔𝜓𝜑→→𝜑↔𝜑𝜓→𝜑𝜓→→→𝜑↔𝜓𝜑→𝜑↔𝜑𝜓→→𝜑↔𝜓𝜑→𝜑𝜓 | Subs [𝜑↗→𝜑↔𝜓𝜑, 𝜓↗→𝜑↔𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2 | |
| 3099 | →→→𝜑↔𝜓𝜑→𝜑↔𝜑𝜓→→𝜑↔𝜓𝜑→𝜑𝜓 | Modus ponens 3097, 3098 | |
| 3100 | →→𝜑↔𝜓𝜑→𝜑𝜓 | Modus ponens 3091, 3099 | |
| 3101 | →→→𝜑𝜓→𝜑↔𝜓𝜑→→→𝜑↔𝜓𝜑→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜓𝜑 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑↔𝜓𝜑] into impbi | |
| 3102 | →→→𝜑↔𝜓𝜑→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜓𝜑 | Modus ponens 3087, 3101 | |
| 3103 | ↔→𝜑𝜓→𝜑↔𝜓𝜑 | Modus ponens 3100, 3102 | ibibr |
| 3104 | ↔→𝜑↔𝜓↔𝜓𝜑↔→𝜑𝜓→𝜑↔𝜓𝜑 | Subs [𝜒↗↔𝜓𝜑] into pm5.74 | |
| 3105 | →↔→𝜑↔𝜓↔𝜓𝜑↔→𝜑𝜓→𝜑↔𝜓𝜑↔↔→𝜑𝜓→𝜑↔𝜓𝜑→𝜑↔𝜓↔𝜓𝜑 | Subs [𝜑↗→𝜑↔𝜓↔𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜑↔𝜓𝜑] into bicom1 | |
| 3106 | ↔↔→𝜑𝜓→𝜑↔𝜓𝜑→𝜑↔𝜓↔𝜓𝜑 | Modus ponens 3104, 3105 | |
| 3107 | →↔↔→𝜑𝜓→𝜑↔𝜓𝜑→𝜑↔𝜓↔𝜓𝜑→↔→𝜑𝜓→𝜑↔𝜓𝜑→𝜑↔𝜓↔𝜓𝜑 | Subs [𝜑↗↔→𝜑𝜓→𝜑↔𝜓𝜑, 𝜓↗→𝜑↔𝜓↔𝜓𝜑] into biimp | |
| 3108 | →↔→𝜑𝜓→𝜑↔𝜓𝜑→𝜑↔𝜓↔𝜓𝜑 | Modus ponens 3106, 3107 | |
| 3109 | →𝜑↔𝜓↔𝜓𝜑 | Modus ponens ibibr, 3108 | |
| 3110 | →↔→𝜑↔𝜓↔𝜓𝜑↔→𝜑𝜓→𝜑↔𝜓𝜑→→𝜑↔𝜓↔𝜓𝜑↔→𝜑𝜓→𝜑↔𝜓𝜑 | Subs [𝜑↗→𝜑↔𝜓↔𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜑↔𝜓𝜑] into biimp | |
| 3111 | →→𝜑↔𝜓↔𝜓𝜑↔→𝜑𝜓→𝜑↔𝜓𝜑 | Modus ponens 3104, 3110 | |
| 3112 | →¬𝜑↔¬𝜓↔¬𝜑¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓] into pm5.501 | |
| 3113 | →↔↔𝜑𝜓↔¬𝜑¬𝜓↔↔¬𝜑¬𝜓↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔¬𝜑¬𝜓] into bicom1 | |
| 3114 | ↔↔¬𝜑¬𝜓↔𝜑𝜓 | Modus ponens notbi, 3113 | |
| 3115 | →↔↔¬𝜑¬𝜓↔𝜑𝜓→¬𝜑↔↔¬𝜑¬𝜓↔𝜑𝜓 | Subs [𝜑↗↔↔¬𝜑¬𝜓↔𝜑𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 3116 | →¬𝜑↔↔¬𝜑¬𝜓↔𝜑𝜓 | Modus ponens 3114, 3115 | |
| 3117 | ↔→¬𝜑↔¬𝜓↔¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓, 𝜒↗↔¬𝜑¬𝜓] into pm5.74 | |
| 3118 | →↔→¬𝜑↔¬𝜓↔¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓→→¬𝜑↔¬𝜓↔¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑↔¬𝜓↔¬𝜑¬𝜓, 𝜓↗↔→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓] into biimp | |
| 3119 | →→¬𝜑↔¬𝜓↔¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓 | Modus ponens 3117, 3118 | |
| 3120 | ↔→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓 | Modus ponens 3112, 3119 | |
| 3121 | ↔→¬𝜑↔↔¬𝜑¬𝜓↔𝜑𝜓↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗↔¬𝜑¬𝜓, 𝜒↗↔𝜑𝜓] into pm5.74 | |
| 3122 | →↔→¬𝜑↔↔¬𝜑¬𝜓↔𝜑𝜓↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→¬𝜑↔↔¬𝜑¬𝜓↔𝜑𝜓↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗→¬𝜑↔↔¬𝜑¬𝜓↔𝜑𝜓, 𝜓↗↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into biimp | |
| 3123 | →→¬𝜑↔↔¬𝜑¬𝜓↔𝜑𝜓↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3121, 3122 | |
| 3124 | ↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3116, 3123 | |
| 3125 | →↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗→¬𝜑↔¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜑𝜓] into biimp | |
| 3126 | →→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3124, 3125 | |
| 3127 | →↔→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔¬𝜑¬𝜓] into biimp | |
| 3128 | →→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓 | Modus ponens 3120, 3127 | |
| 3129 | →→→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→¬𝜑¬𝜓→→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗→→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑¬𝜓] into ax-1 | |
| 3130 | →→¬𝜑¬𝜓→→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3126, 3129 | |
| 3131 | →→→¬𝜑¬𝜓→→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔¬𝜑¬𝜓, 𝜒↗→¬𝜑↔𝜑𝜓] into ax-2 | |
| 3132 | →→→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3130, 3131 | |
| 3133 | →→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3128, 3132 | |
| 3134 | →↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑↔¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜑𝜓] into bicom1 | |
| 3135 | ↔→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜑¬𝜓 | Modus ponens 3124, 3134 | |
| 3136 | →↔→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜑¬𝜓→→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑↔¬𝜑¬𝜓] into biimp | |
| 3137 | →→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜑¬𝜓 | Modus ponens 3135, 3136 | |
| 3138 | →↔→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔¬𝜑¬𝜓] into bicom1 | |
| 3139 | ↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓 | Modus ponens 3120, 3138 | |
| 3140 | →↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑↔¬𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓] into biimp | |
| 3141 | →→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓 | Modus ponens 3139, 3140 | |
| 3142 | →→→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑↔𝜑𝜓→→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜑𝜓] into ax-1 | |
| 3143 | →→¬𝜑↔𝜑𝜓→→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓 | Modus ponens 3141, 3142 | |
| 3144 | →→→¬𝜑↔𝜑𝜓→→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓→→→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜑¬𝜓→→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑↔¬𝜑¬𝜓, 𝜒↗→¬𝜑¬𝜓] into ax-2 | |
| 3145 | →→→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜑¬𝜓→→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓 | Modus ponens 3143, 3144 | |
| 3146 | →→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓 | Modus ponens 3137, 3145 | |
| 3147 | →→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜑𝜓] into impbi | |
| 3148 | →→→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3133, 3147 | |
| 3149 | ↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3146, 3148 | |
| 3150 | ↔→¬𝜑↔¬𝜓↔𝜑𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓, 𝜒↗↔𝜑𝜓] into pm5.74 | |
| 3151 | →↔→¬𝜑↔¬𝜓↔𝜑𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜓↔𝜑𝜓 | Subs [𝜑↗→¬𝜑↔¬𝜓↔𝜑𝜓, 𝜓↗↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into bicom1 | |
| 3152 | ↔↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜓↔𝜑𝜓 | Modus ponens 3150, 3151 | |
| 3153 | →↔↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜓↔𝜑𝜓→↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜓↔𝜑𝜓 | Subs [𝜑↗↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑↔¬𝜓↔𝜑𝜓] into biimp | |
| 3154 | →↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜓↔𝜑𝜓 | Modus ponens 3152, 3153 | |
| 3155 | →¬𝜑↔¬𝜓↔𝜑𝜓 | Modus ponens 3149, 3154 | nbn2 |
| 3156 | →¬𝜓↔¬𝜑↔𝜓𝜑 | Subs [𝜑↗𝜓, 𝜓↗𝜑] into nbn2 | |
| 3157 | ↔↔𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜑] into bicom | |
| 3158 | →↔↔𝜓𝜑↔𝜑𝜓→¬𝜓↔↔𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗↔↔𝜓𝜑↔𝜑𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 3159 | →¬𝜓↔↔𝜓𝜑↔𝜑𝜓 | Modus ponens 3157, 3158 | |
| 3160 | ↔→¬𝜓↔¬𝜑↔𝜓𝜑↔→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜑, 𝜒↗↔𝜓𝜑] into pm5.74 | |
| 3161 | →↔→¬𝜓↔¬𝜑↔𝜓𝜑↔→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑→→¬𝜓↔¬𝜑↔𝜓𝜑↔→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑 | Subs [𝜑↗→¬𝜓↔¬𝜑↔𝜓𝜑, 𝜓↗↔→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑] into biimp | |
| 3162 | →→¬𝜓↔¬𝜑↔𝜓𝜑↔→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑 | Modus ponens 3160, 3161 | |
| 3163 | ↔→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑 | Modus ponens 3156, 3162 | |
| 3164 | ↔→¬𝜓↔↔𝜓𝜑↔𝜑𝜓↔→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗↔𝜓𝜑, 𝜒↗↔𝜑𝜓] into pm5.74 | |
| 3165 | →↔→¬𝜓↔↔𝜓𝜑↔𝜑𝜓↔→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓→→¬𝜓↔↔𝜓𝜑↔𝜑𝜓↔→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓 | Subs [𝜑↗→¬𝜓↔↔𝜓𝜑↔𝜑𝜓, 𝜓↗↔→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓] into biimp | |
| 3166 | →→¬𝜓↔↔𝜓𝜑↔𝜑𝜓↔→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓 | Modus ponens 3164, 3165 | |
| 3167 | ↔→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓 | Modus ponens 3159, 3166 | |
| 3168 | →↔→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓→→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓 | Subs [𝜑↗→¬𝜓↔𝜓𝜑, 𝜓↗→¬𝜓↔𝜑𝜓] into biimp | |
| 3169 | →→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓 | Modus ponens 3167, 3168 | |
| 3170 | →↔→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑→→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑 | Subs [𝜑↗→¬𝜓¬𝜑, 𝜓↗→¬𝜓↔𝜓𝜑] into biimp | |
| 3171 | →→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑 | Modus ponens 3163, 3170 | |
| 3172 | →→→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓→→¬𝜓¬𝜑→→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓 | Subs [𝜑↗→→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓, 𝜓↗→¬𝜓¬𝜑] into ax-1 | |
| 3173 | →→¬𝜓¬𝜑→→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓 | Modus ponens 3169, 3172 | |
| 3174 | →→→¬𝜓¬𝜑→→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓→→→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑→→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓 | Subs [𝜑↗→¬𝜓¬𝜑, 𝜓↗→¬𝜓↔𝜓𝜑, 𝜒↗→¬𝜓↔𝜑𝜓] into ax-2 | |
| 3175 | →→→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑→→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓 | Modus ponens 3173, 3174 | |
| 3176 | →→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓 | Modus ponens 3171, 3175 | |
| 3177 | →↔→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓↔→¬𝜓↔𝜑𝜓→¬𝜓↔𝜓𝜑 | Subs [𝜑↗→¬𝜓↔𝜓𝜑, 𝜓↗→¬𝜓↔𝜑𝜓] into bicom1 | |
| 3178 | ↔→¬𝜓↔𝜑𝜓→¬𝜓↔𝜓𝜑 | Modus ponens 3167, 3177 | |
| 3179 | →↔→¬𝜓↔𝜑𝜓→¬𝜓↔𝜓𝜑→→¬𝜓↔𝜑𝜓→¬𝜓↔𝜓𝜑 | Subs [𝜑↗→¬𝜓↔𝜑𝜓, 𝜓↗→¬𝜓↔𝜓𝜑] into biimp | |
| 3180 | →→¬𝜓↔𝜑𝜓→¬𝜓↔𝜓𝜑 | Modus ponens 3178, 3179 | |
| 3181 | →↔→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑↔→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑 | Subs [𝜑↗→¬𝜓¬𝜑, 𝜓↗→¬𝜓↔𝜓𝜑] into bicom1 | |
| 3182 | ↔→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑 | Modus ponens 3163, 3181 | |
| 3183 | →↔→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑→→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑 | Subs [𝜑↗→¬𝜓↔𝜓𝜑, 𝜓↗→¬𝜓¬𝜑] into biimp | |
| 3184 | →→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑 | Modus ponens 3182, 3183 | |
| 3185 | →→→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑→→¬𝜓↔𝜑𝜓→→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑 | Subs [𝜑↗→→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑, 𝜓↗→¬𝜓↔𝜑𝜓] into ax-1 | |
| 3186 | →→¬𝜓↔𝜑𝜓→→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑 | Modus ponens 3184, 3185 | |
| 3187 | →→→¬𝜓↔𝜑𝜓→→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑→→→¬𝜓↔𝜑𝜓→¬𝜓↔𝜓𝜑→→¬𝜓↔𝜑𝜓→¬𝜓¬𝜑 | Subs [𝜑↗→¬𝜓↔𝜑𝜓, 𝜓↗→¬𝜓↔𝜓𝜑, 𝜒↗→¬𝜓¬𝜑] into ax-2 | |
| 3188 | →→→¬𝜓↔𝜑𝜓→¬𝜓↔𝜓𝜑→→¬𝜓↔𝜑𝜓→¬𝜓¬𝜑 | Modus ponens 3186, 3187 | |
| 3189 | →→¬𝜓↔𝜑𝜓→¬𝜓¬𝜑 | Modus ponens 3180, 3188 | |
| 3190 | →→→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓→→→¬𝜓↔𝜑𝜓→¬𝜓¬𝜑↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓 | Subs [𝜑↗→¬𝜓¬𝜑, 𝜓↗→¬𝜓↔𝜑𝜓] into impbi | |
| 3191 | →→→¬𝜓↔𝜑𝜓→¬𝜓¬𝜑↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓 | Modus ponens 3176, 3190 | |
| 3192 | ↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓 | Modus ponens 3189, 3191 | |
| 3193 | ↔→¬𝜓↔¬𝜑↔𝜑𝜓↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜑, 𝜒↗↔𝜑𝜓] into pm5.74 | |
| 3194 | →↔→¬𝜓↔¬𝜑↔𝜑𝜓↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓↔↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓→¬𝜓↔¬𝜑↔𝜑𝜓 | Subs [𝜑↗→¬𝜓↔¬𝜑↔𝜑𝜓, 𝜓↗↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓] into bicom1 | |
| 3195 | ↔↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓→¬𝜓↔¬𝜑↔𝜑𝜓 | Modus ponens 3193, 3194 | |
| 3196 | →↔↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓→¬𝜓↔¬𝜑↔𝜑𝜓→↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓→¬𝜓↔¬𝜑↔𝜑𝜓 | Subs [𝜑↗↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓, 𝜓↗→¬𝜓↔¬𝜑↔𝜑𝜓] into biimp | |
| 3197 | →↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓→¬𝜓↔¬𝜑↔𝜑𝜓 | Modus ponens 3195, 3196 | |
| 3198 | →¬𝜓↔¬𝜑↔𝜑𝜓 | Modus ponens 3192, 3197 | |
| 3199 | ↔↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗↔𝜑𝜓] into bicom | |
| 3200 | →↔↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑→↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑 | Subs [𝜑↗↔¬𝜑↔𝜑𝜓, 𝜓↗↔↔𝜑𝜓¬𝜑] into biimp | |
| 3201 | →↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑 | Modus ponens 3199, 3200 | |
| 3202 | →→↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑→¬𝜓→↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑 | Subs [𝜑↗→↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1 | |
| 3203 | →¬𝜓→↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑 | Modus ponens 3201, 3202 | |
| 3204 | →→¬𝜓→↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑→→¬𝜓↔¬𝜑↔𝜑𝜓→¬𝜓↔↔𝜑𝜓¬𝜑 | Subs [𝜑↗¬𝜓, 𝜓↗↔¬𝜑↔𝜑𝜓, 𝜒↗↔↔𝜑𝜓¬𝜑] into ax-2 | |
| 3205 | →→¬𝜓↔¬𝜑↔𝜑𝜓→¬𝜓↔↔𝜑𝜓¬𝜑 | Modus ponens 3203, 3204 | |
| 3206 | →¬𝜓↔↔𝜑𝜓¬𝜑 | Modus ponens 3198, 3205 | bibif |
| 3207 | →↔¬𝜓↔𝜑𝜓→¬𝜓↔𝜑𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗↔𝜑𝜓] into biimp | |
| 3208 | →→↔¬𝜓↔𝜑𝜓→¬𝜓↔𝜑𝜓→¬𝜑→↔¬𝜓↔𝜑𝜓→¬𝜓↔𝜑𝜓 | Subs [𝜑↗→↔¬𝜓↔𝜑𝜓→¬𝜓↔𝜑𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 3209 | →¬𝜑→↔¬𝜓↔𝜑𝜓→¬𝜓↔𝜑𝜓 | Modus ponens 3207, 3208 | |
| 3210 | →→¬𝜑→↔¬𝜓↔𝜑𝜓→¬𝜓↔𝜑𝜓→→¬𝜑↔¬𝜓↔𝜑𝜓→¬𝜑→¬𝜓↔𝜑𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗↔¬𝜓↔𝜑𝜓, 𝜒↗→¬𝜓↔𝜑𝜓] into ax-2 | |
| 3211 | →→¬𝜑↔¬𝜓↔𝜑𝜓→¬𝜑→¬𝜓↔𝜑𝜓 | Modus ponens 3209, 3210 | |
| 3212 | →¬𝜑→¬𝜓↔𝜑𝜓 | Modus ponens nbn2, 3211 | pm5.21im |
| 3213 | →𝜑↔¬𝜓↔𝜑¬𝜓 | Subs [𝜓↗¬𝜓] into pm5.501 | |
| 3214 | ↔↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗↔𝜑¬𝜓] into bicom | |
| 3215 | →↔↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓→↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓 | Subs [𝜑↗↔¬𝜓↔𝜑¬𝜓, 𝜓↗↔↔𝜑¬𝜓¬𝜓] into biimp | |
| 3216 | →↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓 | Modus ponens 3214, 3215 | |
| 3217 | →→↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓→𝜑→↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓 | Subs [𝜑↗→↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 3218 | →𝜑→↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓 | Modus ponens 3216, 3217 | |
| 3219 | →→𝜑→↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓→→𝜑↔¬𝜓↔𝜑¬𝜓→𝜑↔↔𝜑¬𝜓¬𝜓 | Subs [𝜓↗↔¬𝜓↔𝜑¬𝜓, 𝜒↗↔↔𝜑¬𝜓¬𝜓] into ax-2 | |
| 3220 | →→𝜑↔¬𝜓↔𝜑¬𝜓→𝜑↔↔𝜑¬𝜓¬𝜓 | Modus ponens 3218, 3219 | |
| 3221 | →𝜑↔↔𝜑¬𝜓¬𝜓 | Modus ponens 3213, 3220 | |
| 3222 | ↔↔𝜓¬↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓 | Subs [𝜑↗𝜓, 𝜓↗↔𝜑¬𝜓] into con2bi | |
| 3223 | →↔↔𝜓¬↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓↔↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗↔𝜓¬↔𝜑¬𝜓, 𝜓↗↔↔𝜑¬𝜓¬𝜓] into bicom1 | |
| 3224 | ↔↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓 | Modus ponens 3222, 3223 | |
| 3225 | →↔↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓→↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗↔↔𝜑¬𝜓¬𝜓, 𝜓↗↔𝜓¬↔𝜑¬𝜓] into biimp | |
| 3226 | →↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓 | Modus ponens 3224, 3225 | |
| 3227 | →→↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓→𝜑→↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗→↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 3228 | →𝜑→↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓 | Modus ponens 3226, 3227 | |
| 3229 | →→𝜑→↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓→→𝜑↔↔𝜑¬𝜓¬𝜓→𝜑↔𝜓¬↔𝜑¬𝜓 | Subs [𝜓↗↔↔𝜑¬𝜓¬𝜓, 𝜒↗↔𝜓¬↔𝜑¬𝜓] into ax-2 | |
| 3230 | →→𝜑↔↔𝜑¬𝜓¬𝜓→𝜑↔𝜓¬↔𝜑¬𝜓 | Modus ponens 3228, 3229 | |
| 3231 | →𝜑↔𝜓¬↔𝜑¬𝜓 | Modus ponens 3221, 3230 | |
| 3232 | ↔↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬↔𝜑¬𝜓] into bicom | |
| 3233 | →↔↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓→↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓 | Subs [𝜑↗↔𝜓¬↔𝜑¬𝜓, 𝜓↗↔¬↔𝜑¬𝜓𝜓] into biimp | |
| 3234 | →↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓 | Modus ponens 3232, 3233 | |
| 3235 | →→↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓→𝜑→↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓 | Subs [𝜑↗→↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓, 𝜓↗𝜑] into ax-1 | |
| 3236 | →𝜑→↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓 | Modus ponens 3234, 3235 | |
| 3237 | →→𝜑→↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓→→𝜑↔𝜓¬↔𝜑¬𝜓→𝜑↔¬↔𝜑¬𝜓𝜓 | Subs [𝜓↗↔𝜓¬↔𝜑¬𝜓, 𝜒↗↔¬↔𝜑¬𝜓𝜓] into ax-2 | |
| 3238 | →→𝜑↔𝜓¬↔𝜑¬𝜓→𝜑↔¬↔𝜑¬𝜓𝜓 | Modus ponens 3236, 3237 | |
| 3239 | →𝜑↔¬↔𝜑¬𝜓𝜓 | Modus ponens 3231, 3238 | |
| 3240 | ↔→𝜑↔¬↔𝜑¬𝜓𝜓↔→𝜑¬↔𝜑¬𝜓→𝜑𝜓 | Subs [𝜓↗¬↔𝜑¬𝜓, 𝜒↗𝜓] into pm5.74 | |
| 3241 | →↔→𝜑↔¬↔𝜑¬𝜓𝜓↔→𝜑¬↔𝜑¬𝜓→𝜑𝜓→→𝜑↔¬↔𝜑¬𝜓𝜓↔→𝜑¬↔𝜑¬𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑↔¬↔𝜑¬𝜓𝜓, 𝜓↗↔→𝜑¬↔𝜑¬𝜓→𝜑𝜓] into biimp | |
| 3242 | →→𝜑↔¬↔𝜑¬𝜓𝜓↔→𝜑¬↔𝜑¬𝜓→𝜑𝜓 | Modus ponens 3240, 3241 | |
| 3243 | ↔→𝜑¬↔𝜑¬𝜓→𝜑𝜓 | Modus ponens 3239, 3242 | |
| 3244 | →↔→𝜑¬↔𝜑¬𝜓→𝜑𝜓→→𝜑¬↔𝜑¬𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑¬↔𝜑¬𝜓, 𝜓↗→𝜑𝜓] into biimp | |
| 3245 | →→𝜑¬↔𝜑¬𝜓→𝜑𝜓 | Modus ponens 3243, 3244 | |
| 3246 | →→→𝜑𝜓→𝜑↔𝜑𝜓→→𝜑¬↔𝜑¬𝜓→→𝜑𝜓→𝜑↔𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→𝜑¬↔𝜑¬𝜓] into ax-1 | |
| 3247 | →→𝜑¬↔𝜑¬𝜓→→𝜑𝜓→𝜑↔𝜑𝜓 | Modus ponens 1697, 3246 | |
| 3248 | →→→𝜑¬↔𝜑¬𝜓→→𝜑𝜓→𝜑↔𝜑𝜓→→→𝜑¬↔𝜑¬𝜓→𝜑𝜓→→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓 | Subs [𝜑↗→𝜑¬↔𝜑¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑↔𝜑𝜓] into ax-2 | |
| 3249 | →→→𝜑¬↔𝜑¬𝜓→𝜑𝜓→→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓 | Modus ponens 3247, 3248 | |
| 3250 | →→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓 | Modus ponens 3245, 3249 | |
| 3251 | →↔→𝜑¬↔𝜑¬𝜓→𝜑𝜓↔→𝜑𝜓→𝜑¬↔𝜑¬𝜓 | Subs [𝜑↗→𝜑¬↔𝜑¬𝜓, 𝜓↗→𝜑𝜓] into bicom1 | |
| 3252 | ↔→𝜑𝜓→𝜑¬↔𝜑¬𝜓 | Modus ponens 3243, 3251 | |
| 3253 | →↔→𝜑𝜓→𝜑¬↔𝜑¬𝜓→→𝜑𝜓→𝜑¬↔𝜑¬𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑¬↔𝜑¬𝜓] into biimp | |
| 3254 | →→𝜑𝜓→𝜑¬↔𝜑¬𝜓 | Modus ponens 3252, 3253 | |
| 3255 | →→→𝜑𝜓→𝜑¬↔𝜑¬𝜓→→𝜑↔𝜑𝜓→→𝜑𝜓→𝜑¬↔𝜑¬𝜓 | Subs [𝜑↗→→𝜑𝜓→𝜑¬↔𝜑¬𝜓, 𝜓↗→𝜑↔𝜑𝜓] into ax-1 | |
| 3256 | →→𝜑↔𝜑𝜓→→𝜑𝜓→𝜑¬↔𝜑¬𝜓 | Modus ponens 3254, 3255 | |
| 3257 | →→→𝜑↔𝜑𝜓→→𝜑𝜓→𝜑¬↔𝜑¬𝜓→→→𝜑↔𝜑𝜓→𝜑𝜓→→𝜑↔𝜑𝜓→𝜑¬↔𝜑¬𝜓 | Subs [𝜑↗→𝜑↔𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑¬↔𝜑¬𝜓] into ax-2 | |
| 3258 | →→→𝜑↔𝜑𝜓→𝜑𝜓→→𝜑↔𝜑𝜓→𝜑¬↔𝜑¬𝜓 | Modus ponens 3256, 3257 | |
| 3259 | →→𝜑↔𝜑𝜓→𝜑¬↔𝜑¬𝜓 | Modus ponens 3095, 3258 | |
| 3260 | →→→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓→→→𝜑↔𝜑𝜓→𝜑¬↔𝜑¬𝜓↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓 | Subs [𝜑↗→𝜑¬↔𝜑¬𝜓, 𝜓↗→𝜑↔𝜑𝜓] into impbi | |
| 3261 | →→→𝜑↔𝜑𝜓→𝜑¬↔𝜑¬𝜓↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓 | Modus ponens 3250, 3260 | |
| 3262 | ↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓 | Modus ponens 3259, 3261 | |
| 3263 | ↔→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓 | Subs [𝜓↗¬↔𝜑¬𝜓, 𝜒↗↔𝜑𝜓] into pm5.74 | |
| 3264 | →↔→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓↔↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓 | Subs [𝜑↗→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓, 𝜓↗↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓] into bicom1 | |
| 3265 | ↔↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓 | Modus ponens 3263, 3264 | |
| 3266 | →↔↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓→↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓 | Subs [𝜑↗↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓, 𝜓↗→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓] into biimp | |
| 3267 | →↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓 | Modus ponens 3265, 3266 | |
| 3268 | →𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓 | Modus ponens 3262, 3267 | |
| 3269 | ↔↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗¬↔𝜑¬𝜓, 𝜓↗↔𝜑𝜓] into bicom | |
| 3270 | →↔↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗↔¬↔𝜑¬𝜓↔𝜑𝜓, 𝜓↗↔↔𝜑𝜓¬↔𝜑¬𝜓] into biimp | |
| 3271 | →↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3269, 3270 | |
| 3272 | →→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓→𝜑→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 3273 | →𝜑→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3271, 3272 | |
| 3274 | →→𝜑→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓→→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓→𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜓↗↔¬↔𝜑¬𝜓↔𝜑𝜓, 𝜒↗↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2 | |
| 3275 | →→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓→𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3273, 3274 | |
| 3276 | →𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3268, 3275 | |
| 3277 | →¬𝜑↔¬¬𝜓↔𝜑¬𝜓 | Subs [𝜓↗¬𝜓] into nbn2 | |
| 3278 | ↔↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓 | Subs [𝜑↗¬¬𝜓, 𝜓↗↔𝜑¬𝜓] into bicom | |
| 3279 | →↔↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓→↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓 | Subs [𝜑↗↔¬¬𝜓↔𝜑¬𝜓, 𝜓↗↔↔𝜑¬𝜓¬¬𝜓] into biimp | |
| 3280 | →↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓 | Modus ponens 3278, 3279 | |
| 3281 | →→↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓→¬𝜑→↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓 | Subs [𝜑↗→↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 3282 | →¬𝜑→↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓 | Modus ponens 3280, 3281 | |
| 3283 | →→¬𝜑→↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓→→¬𝜑↔¬¬𝜓↔𝜑¬𝜓→¬𝜑↔↔𝜑¬𝜓¬¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗↔¬¬𝜓↔𝜑¬𝜓, 𝜒↗↔↔𝜑¬𝜓¬¬𝜓] into ax-2 | |
| 3284 | →→¬𝜑↔¬¬𝜓↔𝜑¬𝜓→¬𝜑↔↔𝜑¬𝜓¬¬𝜓 | Modus ponens 3282, 3283 | |
| 3285 | →¬𝜑↔↔𝜑¬𝜓¬¬𝜓 | Modus ponens 3277, 3284 | |
| 3286 | ↔↔¬𝜓¬↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗↔𝜑¬𝜓] into con2bi | |
| 3287 | →↔↔¬𝜓¬↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓↔↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗↔¬𝜓¬↔𝜑¬𝜓, 𝜓↗↔↔𝜑¬𝜓¬¬𝜓] into bicom1 | |
| 3288 | ↔↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓 | Modus ponens 3286, 3287 | |
| 3289 | →↔↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓→↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗↔↔𝜑¬𝜓¬¬𝜓, 𝜓↗↔¬𝜓¬↔𝜑¬𝜓] into biimp | |
| 3290 | →↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓 | Modus ponens 3288, 3289 | |
| 3291 | →→↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓→¬𝜑→↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗→↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 3292 | →¬𝜑→↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓 | Modus ponens 3290, 3291 | |
| 3293 | →→¬𝜑→↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓→→¬𝜑↔↔𝜑¬𝜓¬¬𝜓→¬𝜑↔¬𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗↔↔𝜑¬𝜓¬¬𝜓, 𝜒↗↔¬𝜓¬↔𝜑¬𝜓] into ax-2 | |
| 3294 | →→¬𝜑↔↔𝜑¬𝜓¬¬𝜓→¬𝜑↔¬𝜓¬↔𝜑¬𝜓 | Modus ponens 3292, 3293 | |
| 3295 | →¬𝜑↔¬𝜓¬↔𝜑¬𝜓 | Modus ponens 3285, 3294 | |
| 3296 | ↔↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬↔𝜑¬𝜓] into bicom | |
| 3297 | →↔↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓→↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓 | Subs [𝜑↗↔¬𝜓¬↔𝜑¬𝜓, 𝜓↗↔¬↔𝜑¬𝜓¬𝜓] into biimp | |
| 3298 | →↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓 | Modus ponens 3296, 3297 | |
| 3299 | →→↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓→¬𝜑→↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓 | Subs [𝜑↗→↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 3300 | →¬𝜑→↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓 | Modus ponens 3298, 3299 | |
| 3301 | →→¬𝜑→↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓→→¬𝜑↔¬𝜓¬↔𝜑¬𝜓→¬𝜑↔¬↔𝜑¬𝜓¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗↔¬𝜓¬↔𝜑¬𝜓, 𝜒↗↔¬↔𝜑¬𝜓¬𝜓] into ax-2 | |
| 3302 | →→¬𝜑↔¬𝜓¬↔𝜑¬𝜓→¬𝜑↔¬↔𝜑¬𝜓¬𝜓 | Modus ponens 3300, 3301 | |
| 3303 | →¬𝜑↔¬↔𝜑¬𝜓¬𝜓 | Modus ponens 3295, 3302 | |
| 3304 | ↔→¬𝜑↔¬↔𝜑¬𝜓¬𝜓↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗¬↔𝜑¬𝜓, 𝜒↗¬𝜓] into pm5.74 | |
| 3305 | →↔→¬𝜑↔¬↔𝜑¬𝜓¬𝜓↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑↔¬↔𝜑¬𝜓¬𝜓↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑↔¬↔𝜑¬𝜓¬𝜓, 𝜓↗↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓] into biimp | |
| 3306 | →→¬𝜑↔¬↔𝜑¬𝜓¬𝜓↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓 | Modus ponens 3304, 3305 | |
| 3307 | ↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓 | Modus ponens 3303, 3306 | |
| 3308 | →↔→¬𝜑↔¬𝜓↔𝜑𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→¬𝜑↔¬𝜓↔𝜑𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗→¬𝜑↔¬𝜓↔𝜑𝜓, 𝜓↗↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into biimp | |
| 3309 | →→¬𝜑↔¬𝜓↔𝜑𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3150, 3308 | |
| 3310 | →↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜑𝜓] into biimp | |
| 3311 | →↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑¬↔𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓] into biimp | |
| 3312 | →→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓 | Modus ponens 3307, 3311 | |
| 3313 | →→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→¬𝜑¬↔𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑¬↔𝜑¬𝜓] into ax-1 | |
| 3314 | →→¬𝜑¬↔𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3133, 3313 | |
| 3315 | →→→¬𝜑¬↔𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗→¬𝜑¬↔𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓, 𝜒↗→¬𝜑↔𝜑𝜓] into ax-2 | |
| 3316 | →→→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3314, 3315 | |
| 3317 | →→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3312, 3316 | |
| 3318 | →↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜑𝜓] into bicom1 | |
| 3319 | ↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓 | Modus ponens 3149, 3318 | |
| 3320 | →↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑¬𝜓] into biimp | |
| 3321 | →↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓 | Subs [𝜑↗→¬𝜑¬↔𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓] into bicom1 | |
| 3322 | ↔→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓 | Modus ponens 3307, 3321 | |
| 3323 | →↔→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓 | Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑¬↔𝜑¬𝜓] into biimp | |
| 3324 | →→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓 | Modus ponens 3322, 3323 | |
| 3325 | →→→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓→→¬𝜑↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓 | Subs [𝜑↗→→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜑𝜓] into ax-1 | |
| 3326 | →→¬𝜑↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓 | Modus ponens 3324, 3325 | |
| 3327 | →→→¬𝜑↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓→→→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→¬𝜑↔𝜑𝜓→¬𝜑¬↔𝜑¬𝜓 | Subs [𝜑↗→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑¬𝜓, 𝜒↗→¬𝜑¬↔𝜑¬𝜓] into ax-2 | |
| 3328 | →→→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→¬𝜑↔𝜑𝜓→¬𝜑¬↔𝜑¬𝜓 | Modus ponens 3326, 3327 | |
| 3329 | →→¬𝜑↔𝜑𝜓→¬𝜑¬↔𝜑¬𝜓 | Modus ponens 3146, 3328 | |
| 3330 | →→→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓→→→¬𝜑↔𝜑𝜓→¬𝜑¬↔𝜑¬𝜓↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗→¬𝜑¬↔𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜑𝜓] into impbi | |
| 3331 | →→→¬𝜑↔𝜑𝜓→¬𝜑¬↔𝜑¬𝜓↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3317, 3330 | |
| 3332 | ↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3329, 3331 | |
| 3333 | ↔→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗¬↔𝜑¬𝜓, 𝜒↗↔𝜑𝜓] into pm5.74 | |
| 3334 | →↔→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓↔↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓 | Subs [𝜑↗→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓, 𝜓↗↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓] into bicom1 | |
| 3335 | ↔↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓 | Modus ponens 3333, 3334 | |
| 3336 | →↔↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓→↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓 | Subs [𝜑↗↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓] into biimp | |
| 3337 | →↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓 | Modus ponens 3335, 3336 | |
| 3338 | →¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓 | Modus ponens 3332, 3337 | |
| 3339 | →→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 3340 | →¬𝜑→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3271, 3339 | |
| 3341 | →→¬𝜑→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓→¬𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗↔¬↔𝜑¬𝜓↔𝜑𝜓, 𝜒↗↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2 | |
| 3342 | →→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓→¬𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3340, 3341 | |
| 3343 | →¬𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3338, 3342 | |
| 3344 | →¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into id | |
| 3345 | →→¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑→¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗→¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 3346 | →¬𝜑→¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3344, 3345 | |
| 3347 | →¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into notnotr | |
| 3348 | →¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 3349 | →→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-1 | |
| 3350 | →¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3348, 3349 | |
| 3351 | →→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜒↗→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2 | |
| 3352 | →→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3350, 3351 | |
| 3353 | →¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3347, 3352 | |
| 3354 | →→¬𝜑→¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜒↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2 | |
| 3355 | →→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3346, 3354 | |
| 3356 | →→→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗→→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-1 | |
| 3357 | →¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3355, 3356 | |
| 3358 | →→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜒↗→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2 | |
| 3359 | →→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3357, 3358 | |
| 3360 | →¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-1 | |
| 3361 | →→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬𝜑→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 3362 | →¬𝜑→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑 | Modus ponens 3360, 3361 | |
| 3363 | →→¬𝜑→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑] into ax-2 | |
| 3364 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑 | Modus ponens 3362, 3363 | |
| 3365 | →→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬𝜑, 𝜒↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2 | |
| 3366 | →→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3353, 3365 | |
| 3367 | →→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 3368 | →¬𝜑→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3366, 3367 | |
| 3369 | →→¬𝜑→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑, 𝜒↗→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2 | |
| 3370 | →→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3368, 3369 | |
| 3371 | →¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3360, 3370 | |
| 3372 | →→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-3 | |
| 3373 | →→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 3374 | →¬𝜑→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3372, 3373 | |
| 3375 | →→¬𝜑→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜒↗→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2 | |
| 3376 | →→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3374, 3375 | |
| 3377 | →¬𝜑→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3371, 3376 | |
| 3378 | →→¬𝜑→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜒↗¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2 | |
| 3379 | →→¬𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3377, 3378 | |
| 3380 | →¬𝜑¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3343, 3379 | |
| 3381 | →→¬𝜑¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬↔↔𝜑𝜓¬↔𝜑¬𝜓𝜑 | Subs [𝜓↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-3 | |
| 3382 | →¬↔↔𝜑𝜓¬↔𝜑¬𝜓𝜑 | Modus ponens 3380, 3381 | |
| 3383 | →→𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗→𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-1 | |
| 3384 | →¬↔↔𝜑𝜓¬↔𝜑¬𝜓→𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3276, 3383 | |
| 3385 | →→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬↔↔𝜑𝜓¬↔𝜑¬𝜓𝜑→¬↔↔𝜑𝜓¬↔𝜑¬𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗𝜑, 𝜒↗↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2 | |
| 3386 | →→¬↔↔𝜑𝜓¬↔𝜑¬𝜓𝜑→¬↔↔𝜑𝜓¬↔𝜑¬𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3384, 3385 | |
| 3387 | →¬↔↔𝜑𝜓¬↔𝜑¬𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3382, 3386 | |
| 3388 | →→¬↔↔𝜑𝜓¬↔𝜑¬𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓 | Subs [𝜑↗↔↔𝜑𝜓¬↔𝜑¬𝜓] into pm2.18 | |
| 3389 | ↔↔𝜑𝜓¬↔𝜑¬𝜓 | Modus ponens 3387, 3388 | pm5.18 |
| 3390 | ↔↔𝜑¬𝜓¬¬↔𝜑¬𝜓 | Subs [𝜑↗↔𝜑¬𝜓] into notnotb | |
| 3391 | →↔↔𝜑𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬↔𝜑¬𝜓] into bicom1 | |
| 3392 | ↔¬↔𝜑¬𝜓↔𝜑𝜓 | Modus ponens pm5.18, 3391 | |
| 3393 | ↔↔¬↔𝜑¬𝜓↔𝜑𝜓↔¬¬↔𝜑¬𝜓¬↔𝜑𝜓 | Subs [𝜑↗¬↔𝜑¬𝜓, 𝜓↗↔𝜑𝜓] into notbi | |
| 3394 | →↔↔¬↔𝜑¬𝜓↔𝜑𝜓↔¬¬↔𝜑¬𝜓¬↔𝜑𝜓→↔¬↔𝜑¬𝜓↔𝜑𝜓↔¬¬↔𝜑¬𝜓¬↔𝜑𝜓 | Subs [𝜑↗↔¬↔𝜑¬𝜓↔𝜑𝜓, 𝜓↗↔¬¬↔𝜑¬𝜓¬↔𝜑𝜓] into biimp | |
| 3395 | →↔¬↔𝜑¬𝜓↔𝜑𝜓↔¬¬↔𝜑¬𝜓¬↔𝜑𝜓 | Modus ponens 3393, 3394 | |
| 3396 | ↔¬¬↔𝜑¬𝜓¬↔𝜑𝜓 | Modus ponens 3392, 3395 | |
| 3397 | →↔¬¬↔𝜑¬𝜓¬↔𝜑𝜓→¬¬↔𝜑¬𝜓¬↔𝜑𝜓 | Subs [𝜑↗¬¬↔𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into biimp | |
| 3398 | →¬¬↔𝜑¬𝜓¬↔𝜑𝜓 | Modus ponens 3396, 3397 | |
| 3399 | →↔↔𝜑¬𝜓¬¬↔𝜑¬𝜓→↔𝜑¬𝜓¬¬↔𝜑¬𝜓 | Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗¬¬↔𝜑¬𝜓] into biimp | |
| 3400 | →↔𝜑¬𝜓¬¬↔𝜑¬𝜓 | Modus ponens 3390, 3399 | |
| 3401 | →→¬¬↔𝜑¬𝜓¬↔𝜑𝜓→↔𝜑¬𝜓→¬¬↔𝜑¬𝜓¬↔𝜑𝜓 | Subs [𝜑↗→¬¬↔𝜑¬𝜓¬↔𝜑𝜓, 𝜓↗↔𝜑¬𝜓] into ax-1 | |
| 3402 | →↔𝜑¬𝜓→¬¬↔𝜑¬𝜓¬↔𝜑𝜓 | Modus ponens 3398, 3401 | |
| 3403 | →→↔𝜑¬𝜓→¬¬↔𝜑¬𝜓¬↔𝜑𝜓→→↔𝜑¬𝜓¬¬↔𝜑¬𝜓→↔𝜑¬𝜓¬↔𝜑𝜓 | Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗¬¬↔𝜑¬𝜓, 𝜒↗¬↔𝜑𝜓] into ax-2 | |
| 3404 | →→↔𝜑¬𝜓¬¬↔𝜑¬𝜓→↔𝜑¬𝜓¬↔𝜑𝜓 | Modus ponens 3402, 3403 | |
| 3405 | →↔𝜑¬𝜓¬↔𝜑𝜓 | Modus ponens 3400, 3404 | |
| 3406 | →↔¬¬↔𝜑¬𝜓¬↔𝜑𝜓↔¬↔𝜑𝜓¬¬↔𝜑¬𝜓 | Subs [𝜑↗¬¬↔𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into bicom1 | |
| 3407 | ↔¬↔𝜑𝜓¬¬↔𝜑¬𝜓 | Modus ponens 3396, 3406 | |
| 3408 | →↔¬↔𝜑𝜓¬¬↔𝜑¬𝜓→¬↔𝜑𝜓¬¬↔𝜑¬𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬¬↔𝜑¬𝜓] into biimp | |
| 3409 | →¬↔𝜑𝜓¬¬↔𝜑¬𝜓 | Modus ponens 3407, 3408 | |
| 3410 | →↔↔𝜑¬𝜓¬¬↔𝜑¬𝜓↔¬¬↔𝜑¬𝜓↔𝜑¬𝜓 | Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗¬¬↔𝜑¬𝜓] into bicom1 | |
| 3411 | ↔¬¬↔𝜑¬𝜓↔𝜑¬𝜓 | Modus ponens 3390, 3410 | |
| 3412 | →↔¬¬↔𝜑¬𝜓↔𝜑¬𝜓→¬¬↔𝜑¬𝜓↔𝜑¬𝜓 | Subs [𝜑↗¬¬↔𝜑¬𝜓, 𝜓↗↔𝜑¬𝜓] into biimp | |
| 3413 | →¬¬↔𝜑¬𝜓↔𝜑¬𝜓 | Modus ponens 3411, 3412 | |
| 3414 | →→¬¬↔𝜑¬𝜓↔𝜑¬𝜓→¬↔𝜑𝜓→¬¬↔𝜑¬𝜓↔𝜑¬𝜓 | Subs [𝜑↗→¬¬↔𝜑¬𝜓↔𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1 | |
| 3415 | →¬↔𝜑𝜓→¬¬↔𝜑¬𝜓↔𝜑¬𝜓 | Modus ponens 3413, 3414 | |
| 3416 | →→¬↔𝜑𝜓→¬¬↔𝜑¬𝜓↔𝜑¬𝜓→→¬↔𝜑𝜓¬¬↔𝜑¬𝜓→¬↔𝜑𝜓↔𝜑¬𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬¬↔𝜑¬𝜓, 𝜒↗↔𝜑¬𝜓] into ax-2 | |
| 3417 | →→¬↔𝜑𝜓¬¬↔𝜑¬𝜓→¬↔𝜑𝜓↔𝜑¬𝜓 | Modus ponens 3415, 3416 | |
| 3418 | →¬↔𝜑𝜓↔𝜑¬𝜓 | Modus ponens 3409, 3417 | |
| 3419 | →→↔𝜑¬𝜓¬↔𝜑𝜓→→¬↔𝜑𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬↔𝜑𝜓 | Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into impbi | |
| 3420 | →→¬↔𝜑𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬↔𝜑𝜓 | Modus ponens 3405, 3419 | |
| 3421 | ↔↔𝜑¬𝜓¬↔𝜑𝜓 | Modus ponens 3418, 3420 | |
| 3422 | →↔↔𝜑¬𝜓¬↔𝜑𝜓↔¬↔𝜑𝜓↔𝜑¬𝜓 | Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into bicom1 | |
| 3423 | ↔¬↔𝜑𝜓↔𝜑¬𝜓 | Modus ponens 3421, 3422 | xor3 |
| 3424 | →↔↔𝜑¬𝜓↔𝜓¬𝜑→↔𝜑¬𝜓↔𝜓¬𝜑 | Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔𝜓¬𝜑] into biimp | |
| 3425 | →↔¬↔𝜑𝜓↔𝜑¬𝜓→¬↔𝜑𝜓↔𝜑¬𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗↔𝜑¬𝜓] into biimp | |
| 3426 | →→↔𝜑¬𝜓↔𝜓¬𝜑→¬↔𝜑𝜓→↔𝜑¬𝜓↔𝜓¬𝜑 | Subs [𝜑↗→↔𝜑¬𝜓↔𝜓¬𝜑, 𝜓↗¬↔𝜑𝜓] into ax-1 | |
| 3427 | →¬↔𝜑𝜓→↔𝜑¬𝜓↔𝜓¬𝜑 | Modus ponens 2882, 3426 | |
| 3428 | →→¬↔𝜑𝜓→↔𝜑¬𝜓↔𝜓¬𝜑→→¬↔𝜑𝜓↔𝜑¬𝜓→¬↔𝜑𝜓↔𝜓¬𝜑 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗↔𝜑¬𝜓, 𝜒↗↔𝜓¬𝜑] into ax-2 | |
| 3429 | →→¬↔𝜑𝜓↔𝜑¬𝜓→¬↔𝜑𝜓↔𝜓¬𝜑 | Modus ponens 3427, 3428 | |
| 3430 | →¬↔𝜑𝜓↔𝜓¬𝜑 | Modus ponens 3418, 3429 | |
| 3431 | →↔↔𝜑¬𝜓↔𝜓¬𝜑↔↔𝜓¬𝜑↔𝜑¬𝜓 | Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔𝜓¬𝜑] into bicom1 | |
| 3432 | ↔↔𝜓¬𝜑↔𝜑¬𝜓 | Modus ponens con2bi, 3431 | |
| 3433 | →↔↔𝜓¬𝜑↔𝜑¬𝜓→↔𝜓¬𝜑↔𝜑¬𝜓 | Subs [𝜑↗↔𝜓¬𝜑, 𝜓↗↔𝜑¬𝜓] into biimp | |
| 3434 | →↔¬↔𝜑𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬↔𝜑𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗↔𝜑¬𝜓] into bicom1 | |
| 3435 | →↔↔𝜑¬𝜓¬↔𝜑𝜓→↔𝜑¬𝜓¬↔𝜑𝜓 | Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into biimp | |
| 3436 | →→↔𝜑¬𝜓¬↔𝜑𝜓→↔𝜓¬𝜑→↔𝜑¬𝜓¬↔𝜑𝜓 | Subs [𝜑↗→↔𝜑¬𝜓¬↔𝜑𝜓, 𝜓↗↔𝜓¬𝜑] into ax-1 | |
| 3437 | →↔𝜓¬𝜑→↔𝜑¬𝜓¬↔𝜑𝜓 | Modus ponens 3405, 3436 | |
| 3438 | →→↔𝜓¬𝜑→↔𝜑¬𝜓¬↔𝜑𝜓→→↔𝜓¬𝜑↔𝜑¬𝜓→↔𝜓¬𝜑¬↔𝜑𝜓 | Subs [𝜑↗↔𝜓¬𝜑, 𝜓↗↔𝜑¬𝜓, 𝜒↗¬↔𝜑𝜓] into ax-2 | |
| 3439 | →→↔𝜓¬𝜑↔𝜑¬𝜓→↔𝜓¬𝜑¬↔𝜑𝜓 | Modus ponens 3437, 3438 | |
| 3440 | →↔𝜓¬𝜑¬↔𝜑𝜓 | Modus ponens 2894, 3439 | |
| 3441 | →→¬↔𝜑𝜓↔𝜓¬𝜑→→↔𝜓¬𝜑¬↔𝜑𝜓↔¬↔𝜑𝜓↔𝜓¬𝜑 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗↔𝜓¬𝜑] into impbi | |
| 3442 | →→↔𝜓¬𝜑¬↔𝜑𝜓↔¬↔𝜑𝜓↔𝜓¬𝜑 | Modus ponens 3430, 3441 | |
| 3443 | ↔¬↔𝜑𝜓↔𝜓¬𝜑 | Modus ponens 3440, 3442 | |
| 3444 | →↔¬↔𝜑𝜓↔𝜓¬𝜑↔↔𝜓¬𝜑¬↔𝜑𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗↔𝜓¬𝜑] into bicom1 | |
| 3445 | ↔↔𝜓¬𝜑¬↔𝜑𝜓 | Modus ponens 3443, 3444 | |
| 3446 | →↔↔𝜓¬𝜑↔¬𝜑𝜓↔↔¬𝜑𝜓↔𝜓¬𝜑 | Subs [𝜑↗↔𝜓¬𝜑, 𝜓↗↔¬𝜑𝜓] into bicom1 | |
| 3447 | →↔↔𝜓¬𝜑¬↔𝜑𝜓→↔𝜓¬𝜑¬↔𝜑𝜓 | Subs [𝜑↗↔𝜓¬𝜑, 𝜓↗¬↔𝜑𝜓] into biimp | |
| 3448 | →→↔𝜓¬𝜑¬↔𝜑𝜓→↔¬𝜑𝜓→↔𝜓¬𝜑¬↔𝜑𝜓 | Subs [𝜑↗→↔𝜓¬𝜑¬↔𝜑𝜓, 𝜓↗↔¬𝜑𝜓] into ax-1 | |
| 3449 | →↔¬𝜑𝜓→↔𝜓¬𝜑¬↔𝜑𝜓 | Modus ponens 3440, 3448 | |
| 3450 | →→↔¬𝜑𝜓→↔𝜓¬𝜑¬↔𝜑𝜓→→↔¬𝜑𝜓↔𝜓¬𝜑→↔¬𝜑𝜓¬↔𝜑𝜓 | Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗↔𝜓¬𝜑, 𝜒↗¬↔𝜑𝜓] into ax-2 | |
| 3451 | →→↔¬𝜑𝜓↔𝜓¬𝜑→↔¬𝜑𝜓¬↔𝜑𝜓 | Modus ponens 3449, 3450 | |
| 3452 | →↔¬𝜑𝜓¬↔𝜑𝜓 | Modus ponens 2876, 3451 | |
| 3453 | →↔↔𝜓¬𝜑¬↔𝜑𝜓↔¬↔𝜑𝜓↔𝜓¬𝜑 | Subs [𝜑↗↔𝜓¬𝜑, 𝜓↗¬↔𝜑𝜓] into bicom1 | |
| 3454 | →↔¬↔𝜑𝜓↔𝜓¬𝜑→¬↔𝜑𝜓↔𝜓¬𝜑 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗↔𝜓¬𝜑] into biimp | |
| 3455 | →→↔𝜓¬𝜑↔¬𝜑𝜓→¬↔𝜑𝜓→↔𝜓¬𝜑↔¬𝜑𝜓 | Subs [𝜑↗→↔𝜓¬𝜑↔¬𝜑𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1 | |
| 3456 | →¬↔𝜑𝜓→↔𝜓¬𝜑↔¬𝜑𝜓 | Modus ponens 2886, 3455 | |
| 3457 | →→¬↔𝜑𝜓→↔𝜓¬𝜑↔¬𝜑𝜓→→¬↔𝜑𝜓↔𝜓¬𝜑→¬↔𝜑𝜓↔¬𝜑𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗↔𝜓¬𝜑, 𝜒↗↔¬𝜑𝜓] into ax-2 | |
| 3458 | →→¬↔𝜑𝜓↔𝜓¬𝜑→¬↔𝜑𝜓↔¬𝜑𝜓 | Modus ponens 3456, 3457 | |
| 3459 | →¬↔𝜑𝜓↔¬𝜑𝜓 | Modus ponens 3430, 3458 | |
| 3460 | →→↔¬𝜑𝜓¬↔𝜑𝜓→→¬↔𝜑𝜓↔¬𝜑𝜓↔↔¬𝜑𝜓¬↔𝜑𝜓 | Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗¬↔𝜑𝜓] into impbi | |
| 3461 | →→¬↔𝜑𝜓↔¬𝜑𝜓↔↔¬𝜑𝜓¬↔𝜑𝜓 | Modus ponens 3452, 3460 | |
| 3462 | ↔↔¬𝜑𝜓¬↔𝜑𝜓 | Modus ponens 3459, 3461 | nbbn |
| 3463 | →↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓] into id | |
| 3464 | →↔→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑𝜓] into ax-1 | |
| 3465 | →↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓 | Modus ponens ibib, 3464 | |
| 3466 | ↔→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑𝜓] into pm5.74 | |
| 3467 | →↔→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑𝜓, 𝜓↗↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓] into biimp | |
| 3468 | →→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓 | Modus ponens 3466, 3467 | |
| 3469 | ↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓 | Modus ponens 3463, 3468 | |
| 3470 | ↔→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑↔𝜑𝜓] into pm5.74 | |
| 3471 | →↔→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓] into biimp | |
| 3472 | →→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓 | Modus ponens 3470, 3471 | |
| 3473 | ↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓 | Modus ponens 3465, 3472 | |
| 3474 | →↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓] into biimp | |
| 3475 | →→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓 | Modus ponens 3473, 3474 | |
| 3476 | →↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓] into biimp | |
| 3477 | →→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓 | Modus ponens 3469, 3476 | |
| 3478 | →→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓 | Subs [𝜑↗→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 3479 | →→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓 | Modus ponens 3475, 3478 | |
| 3480 | →→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓, 𝜒↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓] into ax-2 | |
| 3481 | →→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓 | Modus ponens 3479, 3480 | |
| 3482 | →→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓 | Modus ponens 3477, 3481 | |
| 3483 | →↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓] into bicom1 | |
| 3484 | ↔→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓 | Modus ponens 3473, 3483 | |
| 3485 | →↔→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓] into biimp | |
| 3486 | →→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓 | Modus ponens 3484, 3485 | |
| 3487 | →↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓] into bicom1 | |
| 3488 | ↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒 | Modus ponens 3469, 3487 | |
| 3489 | →↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒] into biimp | |
| 3490 | →→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒 | Modus ponens 3488, 3489 | |
| 3491 | →→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓] into ax-1 | |
| 3492 | →→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒 | Modus ponens 3490, 3491 | |
| 3493 | →→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓, 𝜒↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 3494 | →→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒 | Modus ponens 3492, 3493 | |
| 3495 | →→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒 | Modus ponens 3486, 3494 | |
| 3496 | →→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓] into impbi | |
| 3497 | →→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓 | Modus ponens 3482, 3496 | |
| 3498 | ↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓 | Modus ponens 3495, 3497 | |
| 3499 | ↔→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑↔𝜑𝜓] into pm5.74 | |
| 3500 | →↔→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓↔↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜓↗↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓] into bicom1 | |
| 3501 | ↔↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓 | Modus ponens 3499, 3500 | |
| 3502 | →↔↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓→↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓 | Subs [𝜑↗↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓] into biimp | |
| 3503 | →↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓 | Modus ponens 3501, 3502 | |
| 3504 | →↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓 | Modus ponens 3498, 3503 | |
| 3505 | →↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜒→𝜑↔𝜑𝜓] into id | |
| 3506 | →↔→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑↔𝜑𝜓→𝜑𝜓 | Subs [𝜑↗↔→𝜑↔𝜑𝜓→𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑↔𝜑𝜓] into ax-1 | |
| 3507 | →↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑↔𝜑𝜓→𝜑𝜓 | Modus ponens 3093, 3506 | |
| 3508 | ↔→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑↔𝜑𝜓] into pm5.74 | |
| 3509 | →↔→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜓↗↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓] into biimp | |
| 3510 | →→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓 | Modus ponens 3508, 3509 | |
| 3511 | ↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓 | Modus ponens 3505, 3510 | |
| 3512 | ↔→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑↔𝜑𝜓→𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜓↗→𝜑↔𝜑𝜓, 𝜒↗→𝜑𝜓] into pm5.74 | |
| 3513 | →↔→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑↔𝜑𝜓→𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑↔𝜑𝜓→𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑↔𝜑𝜓→𝜑𝜓, 𝜓↗↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓] into biimp | |
| 3514 | →→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑↔𝜑𝜓→𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓 | Modus ponens 3512, 3513 | |
| 3515 | ↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓 | Modus ponens 3507, 3514 | |
| 3516 | →↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓] into biimp | |
| 3517 | →→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓 | Modus ponens 3515, 3516 | |
| 3518 | →↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓] into biimp | |
| 3519 | →→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓 | Modus ponens 3511, 3518 | |
| 3520 | →→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒] into ax-1 | |
| 3521 | →→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓 | Modus ponens 3517, 3520 | |
| 3522 | →→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓, 𝜒↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓] into ax-2 | |
| 3523 | →→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓 | Modus ponens 3521, 3522 | |
| 3524 | →→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓 | Modus ponens 3519, 3523 | |
| 3525 | →↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓] into bicom1 | |
| 3526 | ↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓 | Modus ponens 3515, 3525 | |
| 3527 | →↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓] into biimp | |
| 3528 | →→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓 | Modus ponens 3526, 3527 | |
| 3529 | →↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓] into bicom1 | |
| 3530 | ↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒 | Modus ponens 3511, 3529 | |
| 3531 | →↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒] into biimp | |
| 3532 | →→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒 | Modus ponens 3530, 3531 | |
| 3533 | →→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓] into ax-1 | |
| 3534 | →→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒 | Modus ponens 3532, 3533 | |
| 3535 | →→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓, 𝜒↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒] into ax-2 | |
| 3536 | →→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒 | Modus ponens 3534, 3535 | |
| 3537 | →→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒 | Modus ponens 3528, 3536 | |
| 3538 | →→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓] into impbi | |
| 3539 | →→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓 | Modus ponens 3524, 3538 | |
| 3540 | ↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓 | Modus ponens 3537, 3539 | |
| 3541 | ↔→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑𝜓] into pm5.74 | |
| 3542 | →↔→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓↔↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓, 𝜓↗↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓] into bicom1 | |
| 3543 | ↔↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓 | Modus ponens 3541, 3542 | |
| 3544 | →↔↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓→↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓] into biimp | |
| 3545 | →↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓 | Modus ponens 3543, 3544 | |
| 3546 | →↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓 | Modus ponens 3540, 3545 | |
| 3547 | →→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑↔𝜑𝜓] into impbi | |
| 3548 | →→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓 | Modus ponens 3504, 3547 | |
| 3549 | ↔↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓 | Modus ponens 3546, 3548 | |
| 3550 | ↔→𝜑↔𝜒𝜓↔→𝜑𝜒→𝜑𝜓 | Subs [𝜓↗𝜒, 𝜒↗𝜓] into pm5.74 | |
| 3551 | ↔→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓 | Subs [𝜓↗𝜒, 𝜒↗↔𝜑𝜓] into pm5.74 | |
| 3552 | →↔→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓↔↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑↔𝜑𝜓] into bicom1 | |
| 3553 | ↔↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3551, 3552 | |
| 3554 | →↔↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into biimp | |
| 3555 | →↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3553, 3554 | |
| 3556 | →↔↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑↔𝜑𝜓] into biimp | |
| 3557 | →→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑𝜓] into ax-1 | |
| 3558 | →↔→𝜑𝜒→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3555, 3557 | |
| 3559 | →→↔→𝜑𝜒→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜒↗→𝜑↔𝜒↔𝜑𝜓] into ax-2 | |
| 3560 | →→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3558, 3559 | |
| 3561 | →↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3504, 3560 | |
| 3562 | →↔↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓↔→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into bicom1 | |
| 3563 | →↔→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓 | Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑↔𝜑𝜓] into biimp | |
| 3564 | →→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓 | Modus ponens 3551, 3563 | |
| 3565 | →↔↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓↔↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑↔𝜑𝜓] into bicom1 | |
| 3566 | ↔↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓 | Modus ponens 3549, 3565 | |
| 3567 | →↔↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑𝜓] into biimp | |
| 3568 | →→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓→→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into ax-1 | |
| 3569 | →→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓 | Modus ponens 3546, 3568 | |
| 3570 | →→→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓→→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜒↗↔→𝜑𝜒→𝜑𝜓] into ax-2 | |
| 3571 | →→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓 | Modus ponens 3569, 3570 | |
| 3572 | →→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓 | Modus ponens 3564, 3571 | |
| 3573 | →→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓→→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into impbi | |
| 3574 | →→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3561, 3573 | |
| 3575 | ↔↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3572, 3574 | |
| 3576 | →↔↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into biimp | |
| 3577 | →↔→𝜑↔𝜒𝜓↔→𝜑𝜒→𝜑𝜓→→𝜑↔𝜒𝜓↔→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑↔𝜒𝜓, 𝜓↗↔→𝜑𝜒→𝜑𝜓] into biimp | |
| 3578 | →→𝜑↔𝜒𝜓↔→𝜑𝜒→𝜑𝜓 | Modus ponens 3550, 3577 | |
| 3579 | →→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜒𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔𝜒𝜓] into ax-1 | |
| 3580 | →→𝜑↔𝜒𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3561, 3579 | |
| 3581 | →→→𝜑↔𝜒𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓→→→𝜑↔𝜒𝜓↔→𝜑𝜒→𝜑𝜓→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→𝜑↔𝜒𝜓, 𝜓↗↔→𝜑𝜒→𝜑𝜓, 𝜒↗→𝜑↔𝜒↔𝜑𝜓] into ax-2 | |
| 3582 | →→→𝜑↔𝜒𝜓↔→𝜑𝜒→𝜑𝜓→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3580, 3581 | |
| 3583 | →→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3578, 3582 | |
| 3584 | →↔↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓↔→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into bicom1 | |
| 3585 | ↔→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓 | Modus ponens 3575, 3584 | |
| 3586 | →↔→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑𝜓] into biimp | |
| 3587 | →↔→𝜑↔𝜒𝜓↔→𝜑𝜒→𝜑𝜓↔↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓 | Subs [𝜑↗→𝜑↔𝜒𝜓, 𝜓↗↔→𝜑𝜒→𝜑𝜓] into bicom1 | |
| 3588 | ↔↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓 | Modus ponens 3550, 3587 | |
| 3589 | →↔↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓 | Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑↔𝜒𝜓] into biimp | |
| 3590 | →↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓 | Modus ponens 3588, 3589 | |
| 3591 | →→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓→→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓 | Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into ax-1 | |
| 3592 | →→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓 | Modus ponens 3590, 3591 | |
| 3593 | →→→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓→→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓 | Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑𝜓, 𝜒↗→𝜑↔𝜒𝜓] into ax-2 | |
| 3594 | →→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓 | Modus ponens 3592, 3593 | |
| 3595 | →→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓 | Modus ponens 3572, 3594 | |
| 3596 | →→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→𝜑↔𝜒𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into impbi | |
| 3597 | →→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3583, 3596 | |
| 3598 | ↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3595, 3597 | |
| 3599 | ↔→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓 | Subs [𝜓↗↔𝜒𝜓, 𝜒↗↔𝜒↔𝜑𝜓] into pm5.74 | |
| 3600 | →↔→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓↔↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓 | Subs [𝜑↗→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓] into bicom1 | |
| 3601 | ↔↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓 | Modus ponens 3599, 3600 | |
| 3602 | →↔↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓→↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓 | Subs [𝜑↗↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓] into biimp | |
| 3603 | →↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓 | Modus ponens 3601, 3602 | |
| 3604 | →𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓 | Modus ponens 3598, 3603 | |
| 3605 | ↔↔↔𝜑𝜓𝜒↔𝜒↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜒] into bicom | |
| 3606 | →↔↔𝜓𝜒↔𝜒𝜓→𝜑↔↔𝜓𝜒↔𝜒𝜓 | Subs [𝜑↗↔↔𝜓𝜒↔𝜒𝜓, 𝜓↗𝜑] into ax-1 | |
| 3607 | →𝜑↔↔𝜓𝜒↔𝜒𝜓 | Modus ponens 2677, 3606 | |
| 3608 | ↔→𝜑↔↔𝜓𝜒↔𝜒𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓 | Subs [𝜓↗↔𝜓𝜒, 𝜒↗↔𝜒𝜓] into pm5.74 | |
| 3609 | →↔→𝜑↔↔𝜓𝜒↔𝜒𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓→→𝜑↔↔𝜓𝜒↔𝜒𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓 | Subs [𝜑↗→𝜑↔↔𝜓𝜒↔𝜒𝜓, 𝜓↗↔→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓] into biimp | |
| 3610 | →→𝜑↔↔𝜓𝜒↔𝜒𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓 | Modus ponens 3608, 3609 | |
| 3611 | ↔→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓 | Modus ponens 3607, 3610 | |
| 3612 | →↔→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓] into biimp | |
| 3613 | →→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3599, 3612 | |
| 3614 | →↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→𝜑↔𝜒𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into biimp | |
| 3615 | →↔→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓→→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜒𝜓] into biimp | |
| 3616 | →→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓 | Modus ponens 3611, 3615 | |
| 3617 | →→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜓𝜒→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔𝜓𝜒] into ax-1 | |
| 3618 | →→𝜑↔𝜓𝜒→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3583, 3617 | |
| 3619 | →→→𝜑↔𝜓𝜒→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→→→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓→→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜒𝜓, 𝜒↗→𝜑↔𝜒↔𝜑𝜓] into ax-2 | |
| 3620 | →→→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓→→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3618, 3619 | |
| 3621 | →→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3616, 3620 | |
| 3622 | →↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓 | Subs [𝜑↗→𝜑↔𝜒𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into bicom1 | |
| 3623 | ↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓 | Modus ponens 3598, 3622 | |
| 3624 | →↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓 | Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔𝜒𝜓] into biimp | |
| 3625 | →↔→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓↔→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜒𝜓] into bicom1 | |
| 3626 | ↔→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒 | Modus ponens 3611, 3625 | |
| 3627 | →↔→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒→→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒 | Subs [𝜑↗→𝜑↔𝜒𝜓, 𝜓↗→𝜑↔𝜓𝜒] into biimp | |
| 3628 | →→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒 | Modus ponens 3626, 3627 | |
| 3629 | →→→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒 | Subs [𝜑↗→→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into ax-1 | |
| 3630 | →→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒 | Modus ponens 3628, 3629 | |
| 3631 | →→→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒→→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒 | Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔𝜒𝜓, 𝜒↗→𝜑↔𝜓𝜒] into ax-2 | |
| 3632 | →→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒 | Modus ponens 3630, 3631 | |
| 3633 | →→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒 | Modus ponens 3595, 3632 | |
| 3634 | →→→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into impbi | |
| 3635 | →→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3621, 3634 | |
| 3636 | ↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3633, 3635 | |
| 3637 | ↔→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓 | Subs [𝜓↗↔𝜓𝜒, 𝜒↗↔𝜒↔𝜑𝜓] into pm5.74 | |
| 3638 | →↔→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓↔↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓 | Subs [𝜑↗→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓] into bicom1 | |
| 3639 | ↔↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓 | Modus ponens 3637, 3638 | |
| 3640 | →↔↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓→↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓 | Subs [𝜑↗↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓] into biimp | |
| 3641 | →↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓 | Modus ponens 3639, 3640 | |
| 3642 | →𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓 | Modus ponens 3636, 3641 | |
| 3643 | →↔↔↔𝜑𝜓𝜒↔𝜒↔𝜑𝜓↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒 | Subs [𝜑↗↔↔𝜑𝜓𝜒, 𝜓↗↔𝜒↔𝜑𝜓] into bicom1 | |
| 3644 | ↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒 | Modus ponens 3605, 3643 | |
| 3645 | →↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒→𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒 | Subs [𝜑↗↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 3646 | →𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒 | Modus ponens 3644, 3645 | |
| 3647 | →↔→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓] into biimp | |
| 3648 | →→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3637, 3647 | |
| 3649 | ↔→𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒 | Subs [𝜓↗↔𝜒↔𝜑𝜓, 𝜒↗↔↔𝜑𝜓𝜒] into pm5.74 | |
| 3650 | →↔→𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒→→𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗→𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒, 𝜓↗↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒] into biimp | |
| 3651 | →→𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3649, 3650 | |
| 3652 | ↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3646, 3651 | |
| 3653 | →↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔↔𝜑𝜓𝜒] into biimp | |
| 3654 | →→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3652, 3653 | |
| 3655 | →↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into biimp | |
| 3656 | →→→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗→→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1 | |
| 3657 | →→𝜑↔𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3654, 3656 | |
| 3658 | →→→𝜑↔𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒→→→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜒↔𝜑𝜓, 𝜒↗→𝜑↔↔𝜑𝜓𝜒] into ax-2 | |
| 3659 | →→→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3657, 3658 | |
| 3660 | →→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3621, 3659 | |
| 3661 | →↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔↔𝜑𝜓𝜒] into bicom1 | |
| 3662 | ↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3652, 3661 | |
| 3663 | →↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into biimp | |
| 3664 | →→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3662, 3663 | |
| 3665 | →↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into bicom1 | |
| 3666 | ↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒 | Modus ponens 3636, 3665 | |
| 3667 | →↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒 | Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔𝜓𝜒] into biimp | |
| 3668 | →→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒→→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒 | Subs [𝜑↗→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔↔𝜑𝜓𝜒] into ax-1 | |
| 3669 | →→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒 | Modus ponens 3633, 3668 | |
| 3670 | →→→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒→→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒 | Subs [𝜑↗→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔𝜒↔𝜑𝜓, 𝜒↗→𝜑↔𝜓𝜒] into ax-2 | |
| 3671 | →→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒 | Modus ponens 3669, 3670 | |
| 3672 | →→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒 | Modus ponens 3664, 3671 | |
| 3673 | →→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔↔𝜑𝜓𝜒] into impbi | |
| 3674 | →→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3660, 3673 | |
| 3675 | ↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3672, 3674 | |
| 3676 | ↔→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒 | Subs [𝜓↗↔𝜓𝜒, 𝜒↗↔↔𝜑𝜓𝜒] into pm5.74 | |
| 3677 | →↔→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒↔↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒 | Subs [𝜑↗→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒, 𝜓↗↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒] into bicom1 | |
| 3678 | ↔↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒 | Modus ponens 3676, 3677 | |
| 3679 | →↔↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒→↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒 | Subs [𝜑↗↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒] into biimp | |
| 3680 | →↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒 | Modus ponens 3678, 3679 | |
| 3681 | →𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒 | Modus ponens 3675, 3680 | |
| 3682 | →𝜑↔↔𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜓↗↔𝜓𝜒] into pm5.501 | |
| 3683 | ↔↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒 | Subs [𝜑↗↔𝜓𝜒, 𝜓↗↔↔𝜑𝜓𝜒] into bicom | |
| 3684 | →↔↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒→↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒 | Subs [𝜑↗↔↔𝜓𝜒↔↔𝜑𝜓𝜒, 𝜓↗↔↔↔𝜑𝜓𝜒↔𝜓𝜒] into biimp | |
| 3685 | →↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒 | Modus ponens 3683, 3684 | |
| 3686 | →→↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒→𝜑→↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒 | Subs [𝜑↗→↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 3687 | →𝜑→↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒 | Modus ponens 3685, 3686 | |
| 3688 | →→𝜑→↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒→→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜓𝜒 | Subs [𝜓↗↔↔𝜓𝜒↔↔𝜑𝜓𝜒, 𝜒↗↔↔↔𝜑𝜓𝜒↔𝜓𝜒] into ax-2 | |
| 3689 | →→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜓𝜒 | Modus ponens 3687, 3688 | |
| 3690 | →𝜑↔↔↔𝜑𝜓𝜒↔𝜓𝜒 | Modus ponens 3681, 3689 | |
| 3691 | ↔→𝜑↔↔↔𝜑𝜓𝜒↔𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒 | Subs [𝜓↗↔↔𝜑𝜓𝜒, 𝜒↗↔𝜓𝜒] into pm5.74 | |
| 3692 | →↔→𝜑↔↔↔𝜑𝜓𝜒↔𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔↔↔𝜑𝜓𝜒↔𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒 | Subs [𝜑↗→𝜑↔↔↔𝜑𝜓𝜒↔𝜓𝜒, 𝜓↗↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒] into biimp | |
| 3693 | →→𝜑↔↔↔𝜑𝜓𝜒↔𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒 | Modus ponens 3691, 3692 | |
| 3694 | ↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒 | Modus ponens 3690, 3693 | |
| 3695 | ↔→𝜑↔↔𝜓𝜒↔𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒 | Subs [𝜓↗↔𝜓𝜒, 𝜒↗↔𝜑↔𝜓𝜒] into pm5.74 | |
| 3696 | →↔→𝜑↔↔𝜓𝜒↔𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→→𝜑↔↔𝜓𝜒↔𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒 | Subs [𝜑↗→𝜑↔↔𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗↔→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒] into biimp | |
| 3697 | →→𝜑↔↔𝜓𝜒↔𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒 | Modus ponens 3695, 3696 | |
| 3698 | ↔→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒 | Modus ponens 3682, 3697 | |
| 3699 | →↔→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜑↔𝜓𝜒] into biimp | |
| 3700 | →→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒 | Modus ponens 3698, 3699 | |
| 3701 | →↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒 | Subs [𝜑↗→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒] into biimp | |
| 3702 | →→→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒 | Subs [𝜑↗→→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒, 𝜓↗→𝜑↔↔𝜑𝜓𝜒] into ax-1 | |
| 3703 | →→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒 | Modus ponens 3700, 3702 | |
| 3704 | →→→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒 | Subs [𝜑↗→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒, 𝜒↗→𝜑↔𝜑↔𝜓𝜒] into ax-2 | |
| 3705 | →→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒 | Modus ponens 3703, 3704 | |
| 3706 | →→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒 | Modus ponens 3672, 3705 | |
| 3707 | →↔→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒↔→𝜑↔𝜑↔𝜓𝜒→𝜑↔𝜓𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜑↔𝜓𝜒] into bicom1 | |
| 3708 | ↔→𝜑↔𝜑↔𝜓𝜒→𝜑↔𝜓𝜒 | Modus ponens 3698, 3707 | |
| 3709 | →↔→𝜑↔𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜑↔𝜓𝜒→𝜑↔𝜓𝜒 | Subs [𝜑↗→𝜑↔𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒] into biimp | |
| 3710 | →→𝜑↔𝜑↔𝜓𝜒→𝜑↔𝜓𝜒 | Modus ponens 3708, 3709 | |
| 3711 | →↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒] into bicom1 | |
| 3712 | →↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔↔𝜑𝜓𝜒] into biimp | |
| 3713 | →→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔𝜑↔𝜓𝜒] into ax-1 | |
| 3714 | →→𝜑↔𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3660, 3713 | |
| 3715 | →→→𝜑↔𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→→→𝜑↔𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗→𝜑↔𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒, 𝜒↗→𝜑↔↔𝜑𝜓𝜒] into ax-2 | |
| 3716 | →→→𝜑↔𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3714, 3715 | |
| 3717 | →→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3710, 3716 | |
| 3718 | →→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→→→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒 | Subs [𝜑↗→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔𝜑↔𝜓𝜒] into impbi | |
| 3719 | →→→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒 | Modus ponens 3706, 3718 | |
| 3720 | ↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒 | Modus ponens 3717, 3719 | |
| 3721 | ↔→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒 | Subs [𝜓↗↔↔𝜑𝜓𝜒, 𝜒↗↔𝜑↔𝜓𝜒] into pm5.74 | |
| 3722 | →↔→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒↔↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜑↗→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒] into bicom1 | |
| 3723 | ↔↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 3721, 3722 | |
| 3724 | →↔↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜑↗↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒, 𝜓↗→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into biimp | |
| 3725 | →↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 3723, 3724 | |
| 3726 | →𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 3720, 3725 | |
| 3727 | ↔↔¬𝜓𝜒¬↔𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗𝜒] into nbbn | |
| 3728 | →↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓 | Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓] into id | |
| 3729 | →↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑¬𝜓] into ax-1 | |
| 3730 | →↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3149, 3729 | |
| 3731 | ↔→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓 | Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗→¬𝜑𝜒, 𝜒↗→¬𝜑¬𝜓] into pm5.74 | |
| 3732 | →↔→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓] into biimp | |
| 3733 | →→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓 | Modus ponens 3731, 3732 | |
| 3734 | ↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓 | Modus ponens 3728, 3733 | |
| 3735 | ↔→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓, 𝜒↗→¬𝜑↔𝜑𝜓] into pm5.74 | |
| 3736 | →↔→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into biimp | |
| 3737 | →→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3735, 3736 | |
| 3738 | ↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3730, 3737 | |
| 3739 | →↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into biimp | |
| 3740 | →→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3738, 3739 | |
| 3741 | →↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓] into biimp | |
| 3742 | →→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓 | Modus ponens 3734, 3741 | |
| 3743 | →→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒] into ax-1 | |
| 3744 | →→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3740, 3743 | |
| 3745 | →→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓, 𝜒↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into ax-2 | |
| 3746 | →→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3744, 3745 | |
| 3747 | →→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3742, 3746 | |
| 3748 | →↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into bicom1 | |
| 3749 | ↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓 | Modus ponens 3738, 3748 | |
| 3750 | →↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓] into biimp | |
| 3751 | →→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓 | Modus ponens 3749, 3750 | |
| 3752 | →↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓] into bicom1 | |
| 3753 | ↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒 | Modus ponens 3734, 3752 | |
| 3754 | →↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒] into biimp | |
| 3755 | →→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒 | Modus ponens 3753, 3754 | |
| 3756 | →→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒 | Subs [𝜑↗→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into ax-1 | |
| 3757 | →→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒 | Modus ponens 3755, 3756 | |
| 3758 | →→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓, 𝜒↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒] into ax-2 | |
| 3759 | →→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒 | Modus ponens 3757, 3758 | |
| 3760 | →→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒 | Modus ponens 3751, 3759 | |
| 3761 | →→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into impbi | |
| 3762 | →→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3747, 3761 | |
| 3763 | ↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3760, 3762 | |
| 3764 | ↔→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗→¬𝜑𝜒, 𝜒↗→¬𝜑↔𝜑𝜓] into pm5.74 | |
| 3765 | →↔→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜓↗↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into bicom1 | |
| 3766 | ↔↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓 | Modus ponens 3764, 3765 | |
| 3767 | →↔↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓 | Subs [𝜑↗↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓] into biimp | |
| 3768 | →↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓 | Modus ponens 3766, 3767 | |
| 3769 | →↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓 | Modus ponens 3763, 3768 | |
| 3770 | →↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓 | Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓] into id | |
| 3771 | →↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓 | Subs [𝜑↗↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓] into ax-1 | |
| 3772 | →↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓 | Modus ponens 3319, 3771 | |
| 3773 | ↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑𝜒, 𝜒↗→¬𝜑↔𝜑𝜓] into pm5.74 | |
| 3774 | →↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜓↗↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓] into biimp | |
| 3775 | →→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3773, 3774 | |
| 3776 | ↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3770, 3775 | |
| 3777 | ↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓 | Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑↔𝜑𝜓, 𝜒↗→¬𝜑¬𝜓] into pm5.74 | |
| 3778 | →↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓, 𝜓↗↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓] into biimp | |
| 3779 | →→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓 | Modus ponens 3777, 3778 | |
| 3780 | ↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓 | Modus ponens 3772, 3779 | |
| 3781 | →↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓] into biimp | |
| 3782 | →→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓 | Modus ponens 3780, 3781 | |
| 3783 | →↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓] into biimp | |
| 3784 | →→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3776, 3783 | |
| 3785 | →→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒] into ax-1 | |
| 3786 | →→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓 | Modus ponens 3782, 3785 | |
| 3787 | →→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓, 𝜒↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓] into ax-2 | |
| 3788 | →→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓 | Modus ponens 3786, 3787 | |
| 3789 | →→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓 | Modus ponens 3784, 3788 | |
| 3790 | →↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓] into bicom1 | |
| 3791 | ↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3780, 3790 | |
| 3792 | →↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓] into biimp | |
| 3793 | →→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3791, 3792 | |
| 3794 | →↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓] into bicom1 | |
| 3795 | ↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒 | Modus ponens 3776, 3794 | |
| 3796 | →↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒] into biimp | |
| 3797 | →→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒 | Modus ponens 3795, 3796 | |
| 3798 | →→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒 | Subs [𝜑↗→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓] into ax-1 | |
| 3799 | →→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒 | Modus ponens 3797, 3798 | |
| 3800 | →→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓, 𝜒↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒] into ax-2 | |
| 3801 | →→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒 | Modus ponens 3799, 3800 | |
| 3802 | →→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒 | Modus ponens 3793, 3801 | |
| 3803 | →→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓] into impbi | |
| 3804 | →→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓 | Modus ponens 3789, 3803 | |
| 3805 | ↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓 | Modus ponens 3802, 3804 | |
| 3806 | ↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓 | Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑𝜒, 𝜒↗→¬𝜑¬𝜓] into pm5.74 | |
| 3807 | →↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓↔↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓] into bicom1 | |
| 3808 | ↔↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓 | Modus ponens 3806, 3807 | |
| 3809 | →↔↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓 | Subs [𝜑↗↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓] into biimp | |
| 3810 | →↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓 | Modus ponens 3808, 3809 | |
| 3811 | →↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓 | Modus ponens 3805, 3810 | |
| 3812 | →→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓 | Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓] into impbi | |
| 3813 | →→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓 | Modus ponens 3769, 3812 | |
| 3814 | ↔↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓 | Modus ponens 3811, 3813 | |
| 3815 | ↔→¬𝜑↔𝜒¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗𝜒, 𝜒↗¬𝜓] into pm5.74 | |
| 3816 | ↔→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗𝜒, 𝜒↗↔𝜑𝜓] into pm5.74 | |
| 3817 | →↔→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓] into bicom1 | |
| 3818 | ↔↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3816, 3817 | |
| 3819 | →↔↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into biimp | |
| 3820 | →↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3818, 3819 | |
| 3821 | →↔↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓 | Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓] into biimp | |
| 3822 | →→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑¬𝜓] into ax-1 | |
| 3823 | →↔→¬𝜑𝜒→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3820, 3822 | |
| 3824 | →→↔→¬𝜑𝜒→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜒↗→¬𝜑↔𝜒↔𝜑𝜓] into ax-2 | |
| 3825 | →→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3823, 3824 | |
| 3826 | →↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3769, 3825 | |
| 3827 | →↔↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓 | Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into bicom1 | |
| 3828 | →↔→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓 | Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓] into biimp | |
| 3829 | →→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓 | Modus ponens 3816, 3828 | |
| 3830 | →↔↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓 | Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓] into bicom1 | |
| 3831 | ↔↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓 | Modus ponens 3814, 3830 | |
| 3832 | →↔↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓 | Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑¬𝜓] into biimp | |
| 3833 | →→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into ax-1 | |
| 3834 | →→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓 | Modus ponens 3811, 3833 | |
| 3835 | →→→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜒↗↔→¬𝜑𝜒→¬𝜑¬𝜓] into ax-2 | |
| 3836 | →→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓 | Modus ponens 3834, 3835 | |
| 3837 | →→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓 | Modus ponens 3829, 3836 | |
| 3838 | →→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into impbi | |
| 3839 | →→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3826, 3838 | |
| 3840 | ↔↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3837, 3839 | |
| 3841 | →↔↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into biimp | |
| 3842 | →↔→¬𝜑↔𝜒¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→→¬𝜑↔𝜒¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑↔𝜒¬𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑¬𝜓] into biimp | |
| 3843 | →→¬𝜑↔𝜒¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓 | Modus ponens 3815, 3842 | |
| 3844 | →→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔𝜒¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔𝜒¬𝜓] into ax-1 | |
| 3845 | →→¬𝜑↔𝜒¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3826, 3844 | |
| 3846 | →→→¬𝜑↔𝜒¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→→→¬𝜑↔𝜒¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→¬𝜑↔𝜒¬𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜒↗→¬𝜑↔𝜒↔𝜑𝜓] into ax-2 | |
| 3847 | →→→¬𝜑↔𝜒¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3845, 3846 | |
| 3848 | →→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3843, 3847 | |
| 3849 | →↔↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓 | Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into bicom1 | |
| 3850 | ↔→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓 | Modus ponens 3840, 3849 | |
| 3851 | →↔→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑¬𝜓] into biimp | |
| 3852 | →↔→¬𝜑↔𝜒¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓 | Subs [𝜑↗→¬𝜑↔𝜒¬𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑¬𝜓] into bicom1 | |
| 3853 | ↔↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓 | Modus ponens 3815, 3852 | |
| 3854 | →↔↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓 | Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜒¬𝜓] into biimp | |
| 3855 | →↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓 | Modus ponens 3853, 3854 | |
| 3856 | →→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓→→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓 | Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into ax-1 | |
| 3857 | →→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓 | Modus ponens 3855, 3856 | |
| 3858 | →→→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓→→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓 | Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜒↗→¬𝜑↔𝜒¬𝜓] into ax-2 | |
| 3859 | →→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓 | Modus ponens 3857, 3858 | |
| 3860 | →→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓 | Modus ponens 3837, 3859 | |
| 3861 | →→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→¬𝜑↔𝜒¬𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into impbi | |
| 3862 | →→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3848, 3861 | |
| 3863 | ↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3860, 3862 | |
| 3864 | ↔→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗↔𝜒¬𝜓, 𝜒↗↔𝜒↔𝜑𝜓] into pm5.74 | |
| 3865 | →↔→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓↔↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓 | Subs [𝜑↗→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓] into bicom1 | |
| 3866 | ↔↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓 | Modus ponens 3864, 3865 | |
| 3867 | →↔↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓→↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓 | Subs [𝜑↗↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓] into biimp | |
| 3868 | →↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓 | Modus ponens 3866, 3867 | |
| 3869 | →¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓 | Modus ponens 3863, 3868 | |
| 3870 | ↔↔¬𝜓𝜒↔𝜒¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗𝜒] into bicom | |
| 3871 | →↔↔¬𝜓𝜒↔𝜒¬𝜓→¬𝜑↔↔¬𝜓𝜒↔𝜒¬𝜓 | Subs [𝜑↗↔↔¬𝜓𝜒↔𝜒¬𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 3872 | →¬𝜑↔↔¬𝜓𝜒↔𝜒¬𝜓 | Modus ponens 3870, 3871 | |
| 3873 | ↔→¬𝜑↔↔¬𝜓𝜒↔𝜒¬𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗↔¬𝜓𝜒, 𝜒↗↔𝜒¬𝜓] into pm5.74 | |
| 3874 | →↔→¬𝜑↔↔¬𝜓𝜒↔𝜒¬𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓→→¬𝜑↔↔¬𝜓𝜒↔𝜒¬𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓 | Subs [𝜑↗→¬𝜑↔↔¬𝜓𝜒↔𝜒¬𝜓, 𝜓↗↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓] into biimp | |
| 3875 | →→¬𝜑↔↔¬𝜓𝜒↔𝜒¬𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓 | Modus ponens 3873, 3874 | |
| 3876 | ↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓 | Modus ponens 3872, 3875 | |
| 3877 | →↔→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓] into biimp | |
| 3878 | →→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3864, 3877 | |
| 3879 | →↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→¬𝜑↔𝜒¬𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into biimp | |
| 3880 | →↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓 | Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔𝜒¬𝜓] into biimp | |
| 3881 | →→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓 | Modus ponens 3876, 3880 | |
| 3882 | →→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔¬𝜓𝜒] into ax-1 | |
| 3883 | →→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3848, 3882 | |
| 3884 | →→→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔𝜒¬𝜓, 𝜒↗→¬𝜑↔𝜒↔𝜑𝜓] into ax-2 | |
| 3885 | →→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3883, 3884 | |
| 3886 | →→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3881, 3885 | |
| 3887 | →↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓 | Subs [𝜑↗→¬𝜑↔𝜒¬𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into bicom1 | |
| 3888 | ↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓 | Modus ponens 3863, 3887 | |
| 3889 | →↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓 | Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔𝜒¬𝜓] into biimp | |
| 3890 | →↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒 | Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔𝜒¬𝜓] into bicom1 | |
| 3891 | ↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒 | Modus ponens 3876, 3890 | |
| 3892 | →↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒 | Subs [𝜑↗→¬𝜑↔𝜒¬𝜓, 𝜓↗→¬𝜑↔¬𝜓𝜒] into biimp | |
| 3893 | →→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒 | Modus ponens 3891, 3892 | |
| 3894 | →→→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒 | Subs [𝜑↗→→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into ax-1 | |
| 3895 | →→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒 | Modus ponens 3893, 3894 | |
| 3896 | →→→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒→→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒 | Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔𝜒¬𝜓, 𝜒↗→¬𝜑↔¬𝜓𝜒] into ax-2 | |
| 3897 | →→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒 | Modus ponens 3895, 3896 | |
| 3898 | →→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒 | Modus ponens 3860, 3897 | |
| 3899 | →→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into impbi | |
| 3900 | →→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3886, 3899 | |
| 3901 | ↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3898, 3900 | |
| 3902 | ↔→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗↔¬𝜓𝜒, 𝜒↗↔𝜒↔𝜑𝜓] into pm5.74 | |
| 3903 | →↔→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓↔↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓 | Subs [𝜑↗→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓] into bicom1 | |
| 3904 | ↔↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓 | Modus ponens 3902, 3903 | |
| 3905 | →↔↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓→↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓 | Subs [𝜑↗↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓] into biimp | |
| 3906 | →↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓 | Modus ponens 3904, 3905 | |
| 3907 | →¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓 | Modus ponens 3901, 3906 | |
| 3908 | →↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒→¬𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒 | Subs [𝜑↗↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒, 𝜓↗¬𝜑] into ax-1 | |
| 3909 | →¬𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒 | Modus ponens 3644, 3908 | |
| 3910 | →↔→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓] into biimp | |
| 3911 | →→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3902, 3910 | |
| 3912 | ↔→¬𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗¬𝜑, 𝜓↗↔𝜒↔𝜑𝜓, 𝜒↗↔↔𝜑𝜓𝜒] into pm5.74 | |
| 3913 | →↔→¬𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗→¬𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒, 𝜓↗↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒] into biimp | |
| 3914 | →→¬𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3912, 3913 | |
| 3915 | ↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3909, 3914 | |
| 3916 | →↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into biimp | |
| 3917 | →→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3915, 3916 | |
| 3918 | →↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into biimp | |
| 3919 | →→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔¬𝜓𝜒] into ax-1 | |
| 3920 | →→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3917, 3919 | |
| 3921 | →→→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒→→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜒↗→¬𝜑↔↔𝜑𝜓𝜒] into ax-2 | |
| 3922 | →→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3920, 3921 | |
| 3923 | →→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3886, 3922 | |
| 3924 | →↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into bicom1 | |
| 3925 | ↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3915, 3924 | |
| 3926 | →↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into biimp | |
| 3927 | →→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓 | Modus ponens 3925, 3926 | |
| 3928 | →↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒 | Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into bicom1 | |
| 3929 | ↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒 | Modus ponens 3901, 3928 | |
| 3930 | →↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒 | Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔¬𝜓𝜒] into biimp | |
| 3931 | →→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒 | Subs [𝜑↗→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into ax-1 | |
| 3932 | →→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒 | Modus ponens 3898, 3931 | |
| 3933 | →→→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒 | Subs [𝜑↗→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜒↗→¬𝜑↔¬𝜓𝜒] into ax-2 | |
| 3934 | →→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒 | Modus ponens 3932, 3933 | |
| 3935 | →→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒 | Modus ponens 3927, 3934 | |
| 3936 | →→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into impbi | |
| 3937 | →→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3923, 3936 | |
| 3938 | ↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3935, 3937 | |
| 3939 | ↔→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗¬𝜑, 𝜓↗↔¬𝜓𝜒, 𝜒↗↔↔𝜑𝜓𝜒] into pm5.74 | |
| 3940 | →↔→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒↔↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒 | Subs [𝜑↗→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒, 𝜓↗↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒] into bicom1 | |
| 3941 | ↔↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒 | Modus ponens 3939, 3940 | |
| 3942 | →↔↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒→↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒 | Subs [𝜑↗↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒] into biimp | |
| 3943 | →↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒 | Modus ponens 3941, 3942 | |
| 3944 | →¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒 | Modus ponens 3938, 3943 | |
| 3945 | →↔↔¬𝜓𝜒¬↔𝜓𝜒↔¬↔𝜓𝜒↔¬𝜓𝜒 | Subs [𝜑↗↔¬𝜓𝜒, 𝜓↗¬↔𝜓𝜒] into bicom1 | |
| 3946 | ↔¬↔𝜓𝜒↔¬𝜓𝜒 | Modus ponens 3727, 3945 | |
| 3947 | →↔¬↔𝜓𝜒↔¬𝜓𝜒→¬𝜑↔¬↔𝜓𝜒↔¬𝜓𝜒 | Subs [𝜑↗↔¬↔𝜓𝜒↔¬𝜓𝜒, 𝜓↗¬𝜑] into ax-1 | |
| 3948 | →¬𝜑↔¬↔𝜓𝜒↔¬𝜓𝜒 | Modus ponens 3946, 3947 | |
| 3949 | ↔→¬𝜑↔¬↔𝜓𝜒↔¬𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒 | Subs [𝜑↗¬𝜑, 𝜓↗¬↔𝜓𝜒, 𝜒↗↔¬𝜓𝜒] into pm5.74 | |
| 3950 | →↔→¬𝜑↔¬↔𝜓𝜒↔¬𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒→→¬𝜑↔¬↔𝜓𝜒↔¬𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒 | Subs [𝜑↗→¬𝜑↔¬↔𝜓𝜒↔¬𝜓𝜒, 𝜓↗↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒] into biimp | |
| 3951 | →→¬𝜑↔¬↔𝜓𝜒↔¬𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒 | Modus ponens 3949, 3950 | |
| 3952 | ↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒 | Modus ponens 3948, 3951 | |
| 3953 | →↔→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒, 𝜓↗↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒] into biimp | |
| 3954 | →→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3939, 3953 | |
| 3955 | →↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into biimp | |
| 3956 | →↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒 | Subs [𝜑↗→¬𝜑¬↔𝜓𝜒, 𝜓↗→¬𝜑↔¬𝜓𝜒] into biimp | |
| 3957 | →→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒 | Modus ponens 3952, 3956 | |
| 3958 | →→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑¬↔𝜓𝜒→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑¬↔𝜓𝜒] into ax-1 | |
| 3959 | →→¬𝜑¬↔𝜓𝜒→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3923, 3958 | |
| 3960 | →→→¬𝜑¬↔𝜓𝜒→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗→¬𝜑¬↔𝜓𝜒, 𝜓↗→¬𝜑↔¬𝜓𝜒, 𝜒↗→¬𝜑↔↔𝜑𝜓𝜒] into ax-2 | |
| 3961 | →→→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3959, 3960 | |
| 3962 | →→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3957, 3961 | |
| 3963 | →↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒 | Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into bicom1 | |
| 3964 | ↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒 | Modus ponens 3938, 3963 | |
| 3965 | →↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒 | Subs [𝜑↗→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔¬𝜓𝜒] into biimp | |
| 3966 | →↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒 | Subs [𝜑↗→¬𝜑¬↔𝜓𝜒, 𝜓↗→¬𝜑↔¬𝜓𝜒] into bicom1 | |
| 3967 | ↔→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒 | Modus ponens 3952, 3966 | |
| 3968 | →↔→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒 | Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑¬↔𝜓𝜒] into biimp | |
| 3969 | →→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒 | Modus ponens 3967, 3968 | |
| 3970 | →→→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒 | Subs [𝜑↗→→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into ax-1 | |
| 3971 | →→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒 | Modus ponens 3969, 3970 | |
| 3972 | →→→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒 | Subs [𝜑↗→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔¬𝜓𝜒, 𝜒↗→¬𝜑¬↔𝜓𝜒] into ax-2 | |
| 3973 | →→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒 | Modus ponens 3971, 3972 | |
| 3974 | →→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒 | Modus ponens 3935, 3973 | |
| 3975 | →→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗→¬𝜑¬↔𝜓𝜒, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into impbi | |
| 3976 | →→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3962, 3975 | |
| 3977 | ↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3974, 3976 | |
| 3978 | ↔→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗¬𝜑, 𝜓↗¬↔𝜓𝜒, 𝜒↗↔↔𝜑𝜓𝜒] into pm5.74 | |
| 3979 | →↔→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒↔↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒 | Subs [𝜑↗→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒, 𝜓↗↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒] into bicom1 | |
| 3980 | ↔↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒 | Modus ponens 3978, 3979 | |
| 3981 | →↔↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒→↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒 | Subs [𝜑↗↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒] into biimp | |
| 3982 | →↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒 | Modus ponens 3980, 3981 | |
| 3983 | →¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒 | Modus ponens 3977, 3982 | |
| 3984 | →¬𝜑↔¬↔𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜓↗↔𝜓𝜒] into nbn2 | |
| 3985 | ↔↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒 | Subs [𝜑↗¬↔𝜓𝜒, 𝜓↗↔↔𝜑𝜓𝜒] into bicom | |
| 3986 | →↔↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒→↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒 | Subs [𝜑↗↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒, 𝜓↗↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒] into biimp | |
| 3987 | →↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒 | Modus ponens 3985, 3986 | |
| 3988 | →→↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒→¬𝜑→↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒 | Subs [𝜑↗→↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒, 𝜓↗¬𝜑] into ax-1 | |
| 3989 | →¬𝜑→↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒 | Modus ponens 3987, 3988 | |
| 3990 | →→¬𝜑→↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒→→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒→¬𝜑↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒 | Subs [𝜑↗¬𝜑, 𝜓↗↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒, 𝜒↗↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒] into ax-2 | |
| 3991 | →→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒→¬𝜑↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒 | Modus ponens 3989, 3990 | |
| 3992 | →¬𝜑↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒 | Modus ponens 3983, 3991 | |
| 3993 | ↔→¬𝜑↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒 | Subs [𝜑↗¬𝜑, 𝜓↗↔↔𝜑𝜓𝜒, 𝜒↗¬↔𝜓𝜒] into pm5.74 | |
| 3994 | →↔→¬𝜑↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒 | Subs [𝜑↗→¬𝜑↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒, 𝜓↗↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒] into biimp | |
| 3995 | →→¬𝜑↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒 | Modus ponens 3993, 3994 | |
| 3996 | ↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒 | Modus ponens 3992, 3995 | |
| 3997 | ↔→¬𝜑↔¬↔𝜓𝜒↔𝜑↔𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒 | Subs [𝜑↗¬𝜑, 𝜓↗¬↔𝜓𝜒, 𝜒↗↔𝜑↔𝜓𝜒] into pm5.74 | |
| 3998 | →↔→¬𝜑↔¬↔𝜓𝜒↔𝜑↔𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→→¬𝜑↔¬↔𝜓𝜒↔𝜑↔𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒 | Subs [𝜑↗→¬𝜑↔¬↔𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒] into biimp | |
| 3999 | →→¬𝜑↔¬↔𝜓𝜒↔𝜑↔𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒 | Modus ponens 3997, 3998 | |
| 4000 | ↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒 | Modus ponens 3984, 3999 | |
| 4001 | →↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒 | Subs [𝜑↗→¬𝜑¬↔𝜓𝜒, 𝜓↗→¬𝜑↔𝜑↔𝜓𝜒] into biimp | |
| 4002 | →→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒 | Modus ponens 4000, 4001 | |
| 4003 | →↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒 | Subs [𝜑↗→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑¬↔𝜓𝜒] into biimp | |
| 4004 | →→→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒 | Subs [𝜑↗→→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into ax-1 | |
| 4005 | →→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒 | Modus ponens 4002, 4004 | |
| 4006 | →→→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒 | Subs [𝜑↗→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑¬↔𝜓𝜒, 𝜒↗→¬𝜑↔𝜑↔𝜓𝜒] into ax-2 | |
| 4007 | →→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒 | Modus ponens 4005, 4006 | |
| 4008 | →→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒 | Modus ponens 3974, 4007 | |
| 4009 | →↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒↔→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑¬↔𝜓𝜒 | Subs [𝜑↗→¬𝜑¬↔𝜓𝜒, 𝜓↗→¬𝜑↔𝜑↔𝜓𝜒] into bicom1 | |
| 4010 | ↔→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑¬↔𝜓𝜒 | Modus ponens 4000, 4009 | |
| 4011 | →↔→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑¬↔𝜓𝜒 | Subs [𝜑↗→¬𝜑↔𝜑↔𝜓𝜒, 𝜓↗→¬𝜑¬↔𝜓𝜒] into biimp | |
| 4012 | →→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑¬↔𝜓𝜒 | Modus ponens 4010, 4011 | |
| 4013 | →↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑¬↔𝜓𝜒] into bicom1 | |
| 4014 | →↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗→¬𝜑¬↔𝜓𝜒, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into biimp | |
| 4015 | →→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔𝜑↔𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔𝜑↔𝜓𝜒] into ax-1 | |
| 4016 | →→¬𝜑↔𝜑↔𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Modus ponens 3962, 4015 | |
| 4017 | →→→¬𝜑↔𝜑↔𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Subs [𝜑↗→¬𝜑↔𝜑↔𝜓𝜒, 𝜓↗→¬𝜑¬↔𝜓𝜒, 𝜒↗→¬𝜑↔↔𝜑𝜓𝜒] into ax-2 | |
| 4018 | →→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Modus ponens 4016, 4017 | |
| 4019 | →→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒 | Modus ponens 4012, 4018 | |
| 4020 | →→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒 | Subs [𝜑↗→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔𝜑↔𝜓𝜒] into impbi | |
| 4021 | →→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒 | Modus ponens 4008, 4020 | |
| 4022 | ↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒 | Modus ponens 4019, 4021 | |
| 4023 | ↔→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒 | Subs [𝜑↗¬𝜑, 𝜓↗↔↔𝜑𝜓𝜒, 𝜒↗↔𝜑↔𝜓𝜒] into pm5.74 | |
| 4024 | →↔→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒↔↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜑↗→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒] into bicom1 | |
| 4025 | ↔↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 4023, 4024 | |
| 4026 | →↔↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜑↗↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒, 𝜓↗→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into biimp | |
| 4027 | →↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 4025, 4026 | |
| 4028 | →¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 4022, 4027 | |
| 4029 | →¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜑↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into id | |
| 4030 | →→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜑↗→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬𝜑] into ax-1 | |
| 4031 | →¬𝜑→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 4029, 4030 | |
| 4032 | →¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜑↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into notnotr | |
| 4033 | →¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜑↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬𝜑] into ax-1 | |
| 4034 | →→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜑↗→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-1 | |
| 4035 | →¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 4033, 4034 | |
| 4036 | →→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜑↗¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜒↗→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-2 | |
| 4037 | →→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 4035, 4036 | |
| 4038 | →¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 4032, 4037 | |
| 4039 | →→¬𝜑→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜑↗¬𝜑, 𝜓↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜒↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-2 | |
| 4040 | →→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 4031, 4039 | |
| 4041 | →→→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜑↗→→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-1 | |
| 4042 | →¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 4040, 4041 | |
| 4043 | →→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜑↗¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜒↗→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-2 | |
| 4044 | →→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 4042, 4043 | |
| 4045 | →¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-1 | |
| 4046 | →→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬𝜑→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 4047 | →¬𝜑→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑 | Modus ponens 4045, 4046 | |
| 4048 | →→¬𝜑→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑] into ax-2 | |
| 4049 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑 | Modus ponens 4047, 4048 | |
| 4050 | →→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜑↗¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬𝜑, 𝜒↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-2 | |
| 4051 | →→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 4038, 4050 | |
| 4052 | →→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜑↗→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬𝜑] into ax-1 | |
| 4053 | →¬𝜑→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 4051, 4052 | |
| 4054 | →→¬𝜑→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑, 𝜒↗→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-2 | |
| 4055 | →→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 4053, 4054 | |
| 4056 | →¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 4045, 4055 | |
| 4057 | →→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜑↗¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-3 | |
| 4058 | →→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜑↗→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬𝜑] into ax-1 | |
| 4059 | →¬𝜑→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 4057, 4058 | |
| 4060 | →→¬𝜑→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜒↗→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-2 | |
| 4061 | →→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 4059, 4060 | |
| 4062 | →¬𝜑→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 4056, 4061 | |
| 4063 | →→¬𝜑→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜑↗¬𝜑, 𝜓↗↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜒↗¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-2 | |
| 4064 | →→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 4062, 4063 | |
| 4065 | →¬𝜑¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 4028, 4064 | |
| 4066 | →→¬𝜑¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒𝜑 | Subs [𝜓↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-3 | |
| 4067 | →¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒𝜑 | Modus ponens 4065, 4066 | |
| 4068 | →→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜑↗→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-1 | |
| 4069 | →¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 3726, 4068 | |
| 4070 | →→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒𝜑→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜑↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗𝜑, 𝜒↗↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-2 | |
| 4071 | →→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒𝜑→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 4069, 4070 | |
| 4072 | →¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 4067, 4071 | |
| 4073 | →→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Subs [𝜑↗↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into pm2.18 | |
| 4074 | ↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒 | Modus ponens 4072, 4073 | biass |
| 4075 | →↔𝜒↔𝜑𝜓↔𝜒↔𝜑𝜓 | Subs [𝜑↗↔𝜒↔𝜑𝜓] into id | |
| 4076 | →↔↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑 | Subs [𝜑↗↔↔𝜑𝜓↔𝜓𝜑, 𝜓↗↔𝜒↔𝜑𝜓] into ax-1 | |
| 4077 | →↔𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑 | Modus ponens bicom, 4076 | |
| 4078 | ↔→↔𝜒↔𝜑𝜓↔𝜒↔𝜑𝜓↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓 | Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗𝜒, 𝜒↗↔𝜑𝜓] into pm5.74 | |
| 4079 | →↔→↔𝜒↔𝜑𝜓↔𝜒↔𝜑𝜓↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓→→↔𝜒↔𝜑𝜓↔𝜒↔𝜑𝜓↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓 | Subs [𝜑↗→↔𝜒↔𝜑𝜓↔𝜒↔𝜑𝜓, 𝜓↗↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓] into biimp | |
| 4080 | →→↔𝜒↔𝜑𝜓↔𝜒↔𝜑𝜓↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓 | Modus ponens 4078, 4079 | |
| 4081 | ↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓 | Modus ponens 4075, 4080 | |
| 4082 | ↔→↔𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑 | Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗↔𝜓𝜑] into pm5.74 | |
| 4083 | →↔→↔𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑→→↔𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑 | Subs [𝜑↗→↔𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑, 𝜓↗↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑] into biimp | |
| 4084 | →→↔𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑 | Modus ponens 4082, 4083 | |
| 4085 | ↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑 | Modus ponens 4077, 4084 | |
| 4086 | →↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑 | Subs [𝜑↗→↔𝜒↔𝜑𝜓↔𝜑𝜓, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜓𝜑] into biimp | |
| 4087 | →→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑 | Modus ponens 4085, 4086 | |
| 4088 | →↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓→→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓 | Subs [𝜑↗→↔𝜒↔𝜑𝜓𝜒, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜑𝜓] into biimp | |
| 4089 | →→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓 | Modus ponens 4081, 4088 | |
| 4090 | →→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑→→↔𝜒↔𝜑𝜓𝜒→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑 | Subs [𝜑↗→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑, 𝜓↗→↔𝜒↔𝜑𝜓𝜒] into ax-1 | |
| 4091 | →→↔𝜒↔𝜑𝜓𝜒→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑 | Modus ponens 4087, 4090 | |
| 4092 | →→→↔𝜒↔𝜑𝜓𝜒→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑→→→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓→→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑 | Subs [𝜑↗→↔𝜒↔𝜑𝜓𝜒, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜑𝜓, 𝜒↗→↔𝜒↔𝜑𝜓↔𝜓𝜑] into ax-2 | |
| 4093 | →→→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓→→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑 | Modus ponens 4091, 4092 | |
| 4094 | →→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑 | Modus ponens 4089, 4093 | |
| 4095 | →↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑↔→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜑𝜓 | Subs [𝜑↗→↔𝜒↔𝜑𝜓↔𝜑𝜓, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜓𝜑] into bicom1 | |
| 4096 | ↔→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜑𝜓 | Modus ponens 4085, 4095 | |
| 4097 | →↔→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜑𝜓→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜑𝜓 | Subs [𝜑↗→↔𝜒↔𝜑𝜓↔𝜓𝜑, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜑𝜓] into biimp | |
| 4098 | →→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜑𝜓 | Modus ponens 4096, 4097 | |
| 4099 | →↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒 | Subs [𝜑↗→↔𝜒↔𝜑𝜓𝜒, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜑𝜓] into bicom1 | |
| 4100 | ↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒 | Modus ponens 4081, 4099 | |
| 4101 | →↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒 | Subs [𝜑↗→↔𝜒↔𝜑𝜓↔𝜑𝜓, 𝜓↗→↔𝜒↔𝜑𝜓𝜒] into biimp | |
| 4102 | →→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒 | Modus ponens 4100, 4101 | |
| 4103 | →→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒→→↔𝜒↔𝜑𝜓↔𝜓𝜑→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒 | Subs [𝜑↗→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜓𝜑] into ax-1 | |
| 4104 | →→↔𝜒↔𝜑𝜓↔𝜓𝜑→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒 | Modus ponens 4102, 4103 | |
| 4105 | →→→↔𝜒↔𝜑𝜓↔𝜓𝜑→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒→→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜑𝜓→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓𝜒 | Subs [𝜑↗→↔𝜒↔𝜑𝜓↔𝜓𝜑, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜑𝜓, 𝜒↗→↔𝜒↔𝜑𝜓𝜒] into ax-2 | |
| 4106 | →→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜑𝜓→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓𝜒 | Modus ponens 4104, 4105 | |
| 4107 | →→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓𝜒 | Modus ponens 4098, 4106 | |
| 4108 | →→→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑→→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓𝜒↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑 | Subs [𝜑↗→↔𝜒↔𝜑𝜓𝜒, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜓𝜑] into impbi | |
| 4109 | →→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓𝜒↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑 | Modus ponens 4094, 4108 | |
| 4110 | ↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑 | Modus ponens 4107, 4109 | |
| 4111 | ↔→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑 | Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗𝜒, 𝜒↗↔𝜓𝜑] into pm5.74 | |
| 4112 | →↔→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑↔↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑 | Subs [𝜑↗→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑, 𝜓↗↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑] into bicom1 | |
| 4113 | ↔↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑 | Modus ponens 4111, 4112 | |
| 4114 | →↔↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑→↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑 | Subs [𝜑↗↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑] into biimp | |
| 4115 | →↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑 | Modus ponens 4113, 4114 | |
| 4116 | →↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑 | Modus ponens 4110, 4115 | |
| 4117 | →↔𝜒↔𝜓𝜑↔𝜒↔𝜓𝜑 | Subs [𝜑↗↔𝜒↔𝜓𝜑] into id | |
| 4118 | →↔↔𝜑𝜓↔𝜓𝜑↔↔𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜓𝜑] into bicom1 | |
| 4119 | →↔↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔↔𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗↔↔𝜓𝜑↔𝜑𝜓, 𝜓↗↔𝜒↔𝜓𝜑] into ax-1 | |
| 4120 | →↔𝜒↔𝜓𝜑↔↔𝜓𝜑↔𝜑𝜓 | Modus ponens 3157, 4119 | |
| 4121 | ↔→↔𝜒↔𝜓𝜑↔𝜒↔𝜓𝜑↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑 | Subs [𝜑↗↔𝜒↔𝜓𝜑, 𝜓↗𝜒, 𝜒↗↔𝜓𝜑] into pm5.74 | |
| 4122 | →↔→↔𝜒↔𝜓𝜑↔𝜒↔𝜓𝜑↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑→→↔𝜒↔𝜓𝜑↔𝜒↔𝜓𝜑↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑 | Subs [𝜑↗→↔𝜒↔𝜓𝜑↔𝜒↔𝜓𝜑, 𝜓↗↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑] into biimp | |
| 4123 | →→↔𝜒↔𝜓𝜑↔𝜒↔𝜓𝜑↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑 | Modus ponens 4121, 4122 | |
| 4124 | ↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑 | Modus ponens 4117, 4123 | |
| 4125 | ↔→↔𝜒↔𝜓𝜑↔↔𝜓𝜑↔𝜑𝜓↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗↔𝜒↔𝜓𝜑, 𝜓↗↔𝜓𝜑, 𝜒↗↔𝜑𝜓] into pm5.74 | |
| 4126 | →↔→↔𝜒↔𝜓𝜑↔↔𝜓𝜑↔𝜑𝜓↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓→→↔𝜒↔𝜓𝜑↔↔𝜓𝜑↔𝜑𝜓↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→↔𝜒↔𝜓𝜑↔↔𝜓𝜑↔𝜑𝜓, 𝜓↗↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓] into biimp | |
| 4127 | →→↔𝜒↔𝜓𝜑↔↔𝜓𝜑↔𝜑𝜓↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓 | Modus ponens 4125, 4126 | |
| 4128 | ↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓 | Modus ponens 4120, 4127 | |
| 4129 | →↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→↔𝜒↔𝜓𝜑↔𝜓𝜑, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜑𝜓] into biimp | |
| 4130 | →→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓 | Modus ponens 4128, 4129 | |
| 4131 | →↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑→→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑 | Subs [𝜑↗→↔𝜒↔𝜓𝜑𝜒, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜓𝜑] into biimp | |
| 4132 | →→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑 | Modus ponens 4124, 4131 | |
| 4133 | →→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓→→↔𝜒↔𝜓𝜑𝜒→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓, 𝜓↗→↔𝜒↔𝜓𝜑𝜒] into ax-1 | |
| 4134 | →→↔𝜒↔𝜓𝜑𝜒→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓 | Modus ponens 4130, 4133 | |
| 4135 | →→→↔𝜒↔𝜓𝜑𝜒→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓→→→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑→→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→↔𝜒↔𝜓𝜑𝜒, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜓𝜑, 𝜒↗→↔𝜒↔𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 4136 | →→→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑→→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓 | Modus ponens 4134, 4135 | |
| 4137 | →→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓 | Modus ponens 4132, 4136 | |
| 4138 | →↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓↔→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜓𝜑 | Subs [𝜑↗→↔𝜒↔𝜓𝜑↔𝜓𝜑, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜑𝜓] into bicom1 | |
| 4139 | ↔→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜓𝜑 | Modus ponens 4128, 4138 | |
| 4140 | →↔→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜓𝜑→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜓𝜑 | Subs [𝜑↗→↔𝜒↔𝜓𝜑↔𝜑𝜓, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜓𝜑] into biimp | |
| 4141 | →→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜓𝜑 | Modus ponens 4139, 4140 | |
| 4142 | →↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒 | Subs [𝜑↗→↔𝜒↔𝜓𝜑𝜒, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜓𝜑] into bicom1 | |
| 4143 | ↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒 | Modus ponens 4124, 4142 | |
| 4144 | →↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒 | Subs [𝜑↗→↔𝜒↔𝜓𝜑↔𝜓𝜑, 𝜓↗→↔𝜒↔𝜓𝜑𝜒] into biimp | |
| 4145 | →→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒 | Modus ponens 4143, 4144 | |
| 4146 | →→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒→→↔𝜒↔𝜓𝜑↔𝜑𝜓→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒 | Subs [𝜑↗→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜑𝜓] into ax-1 | |
| 4147 | →→↔𝜒↔𝜓𝜑↔𝜑𝜓→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒 | Modus ponens 4145, 4146 | |
| 4148 | →→→↔𝜒↔𝜓𝜑↔𝜑𝜓→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒→→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜓𝜑→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑𝜒 | Subs [𝜑↗→↔𝜒↔𝜓𝜑↔𝜑𝜓, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜓𝜑, 𝜒↗→↔𝜒↔𝜓𝜑𝜒] into ax-2 | |
| 4149 | →→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜓𝜑→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑𝜒 | Modus ponens 4147, 4148 | |
| 4150 | →→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑𝜒 | Modus ponens 4141, 4149 | |
| 4151 | →→→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓→→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑𝜒↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→↔𝜒↔𝜓𝜑𝜒, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜑𝜓] into impbi | |
| 4152 | →→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑𝜒↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓 | Modus ponens 4137, 4151 | |
| 4153 | ↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓 | Modus ponens 4150, 4152 | |
| 4154 | ↔→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗↔𝜒↔𝜓𝜑, 𝜓↗𝜒, 𝜒↗↔𝜑𝜓] into pm5.74 | |
| 4155 | →↔→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓↔↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓] into bicom1 | |
| 4156 | ↔↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓 | Modus ponens 4154, 4155 | |
| 4157 | →↔↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓→↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓] into biimp | |
| 4158 | →↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓 | Modus ponens 4156, 4157 | |
| 4159 | →↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓 | Modus ponens 4153, 4158 | |
| 4160 | →→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑→→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓↔↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑 | Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔𝜒↔𝜓𝜑] into impbi | |
| 4161 | →→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓↔↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑 | Modus ponens 4116, 4160 | |
| 4162 | ↔↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑 | Modus ponens 4159, 4161 | |
| 4163 | ↔↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒 | Subs [𝜑↗𝜒, 𝜓↗↔𝜓𝜑] into bicom | |
| 4164 | →↔↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒 | Subs [𝜑↗↔𝜒↔𝜓𝜑, 𝜓↗↔↔𝜓𝜑𝜒] into biimp | |
| 4165 | →↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒 | Modus ponens 4163, 4164 | |
| 4166 | →↔↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑 | Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔𝜒↔𝜓𝜑] into biimp | |
| 4167 | →→↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒→↔𝜒↔𝜑𝜓→↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒 | Subs [𝜑↗→↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒, 𝜓↗↔𝜒↔𝜑𝜓] into ax-1 | |
| 4168 | →↔𝜒↔𝜑𝜓→↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒 | Modus ponens 4165, 4167 | |
| 4169 | →→↔𝜒↔𝜑𝜓→↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒→→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒 | Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔𝜒↔𝜓𝜑, 𝜒↗↔↔𝜓𝜑𝜒] into ax-2 | |
| 4170 | →→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒 | Modus ponens 4168, 4169 | |
| 4171 | →↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒 | Modus ponens 4116, 4170 | |
| 4172 | →↔↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒↔↔↔𝜓𝜑𝜒↔𝜒↔𝜓𝜑 | Subs [𝜑↗↔𝜒↔𝜓𝜑, 𝜓↗↔↔𝜓𝜑𝜒] into bicom1 | |
| 4173 | ↔↔↔𝜓𝜑𝜒↔𝜒↔𝜓𝜑 | Modus ponens 4163, 4172 | |
| 4174 | →↔↔↔𝜓𝜑𝜒↔𝜒↔𝜓𝜑→↔↔𝜓𝜑𝜒↔𝜒↔𝜓𝜑 | Subs [𝜑↗↔↔𝜓𝜑𝜒, 𝜓↗↔𝜒↔𝜓𝜑] into biimp | |
| 4175 | →↔↔𝜓𝜑𝜒↔𝜒↔𝜓𝜑 | Modus ponens 4173, 4174 | |
| 4176 | →↔↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑↔↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔𝜒↔𝜓𝜑] into bicom1 | |
| 4177 | ↔↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓 | Modus ponens 4162, 4176 | |
| 4178 | →↔↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗↔𝜒↔𝜓𝜑, 𝜓↗↔𝜒↔𝜑𝜓] into biimp | |
| 4179 | →→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓→↔↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓 | Subs [𝜑↗→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔↔𝜓𝜑𝜒] into ax-1 | |
| 4180 | →↔↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓 | Modus ponens 4159, 4179 | |
| 4181 | →→↔↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓→→↔↔𝜓𝜑𝜒↔𝜒↔𝜓𝜑→↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓 | Subs [𝜑↗↔↔𝜓𝜑𝜒, 𝜓↗↔𝜒↔𝜓𝜑, 𝜒↗↔𝜒↔𝜑𝜓] into ax-2 | |
| 4182 | →→↔↔𝜓𝜑𝜒↔𝜒↔𝜓𝜑→↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓 | Modus ponens 4180, 4181 | |
| 4183 | →↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓 | Modus ponens 4175, 4182 | |
| 4184 | →→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒→→↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓↔↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒 | Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔↔𝜓𝜑𝜒] into impbi | |
| 4185 | →→↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓↔↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒 | Modus ponens 4171, 4184 | |
| 4186 | ↔↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒 | Modus ponens 4183, 4185 | |
| 4187 | →↔↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒 | Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔↔𝜓𝜑𝜒] into biimp | |
| 4188 | →↔↔↔𝜑𝜓𝜒↔𝜒↔𝜑𝜓→↔↔𝜑𝜓𝜒↔𝜒↔𝜑𝜓 | Subs [𝜑↗↔↔𝜑𝜓𝜒, 𝜓↗↔𝜒↔𝜑𝜓] into biimp | |
| 4189 | →↔↔𝜑𝜓𝜒↔𝜒↔𝜑𝜓 | Modus ponens 3605, 4188 | |
| 4190 | →→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒→↔↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒 | Subs [𝜑↗→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒, 𝜓↗↔↔𝜑𝜓𝜒] into ax-1 | |
| 4191 | →↔↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒 | Modus ponens 4171, 4190 | |
| 4192 | →→↔↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒→→↔↔𝜑𝜓𝜒↔𝜒↔𝜑𝜓→↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒 | Subs [𝜑↗↔↔𝜑𝜓𝜒, 𝜓↗↔𝜒↔𝜑𝜓, 𝜒↗↔↔𝜓𝜑𝜒] into ax-2 | |
| 4193 | →→↔↔𝜑𝜓𝜒↔𝜒↔𝜑𝜓→↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒 | Modus ponens 4191, 4192 | |
| 4194 | →↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒 | Modus ponens 4189, 4193 | |
| 4195 | →↔↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒↔↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓 | Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔↔𝜓𝜑𝜒] into bicom1 | |
| 4196 | ↔↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓 | Modus ponens 4186, 4195 | |
| 4197 | →↔↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓→↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓 | Subs [𝜑↗↔↔𝜓𝜑𝜒, 𝜓↗↔𝜒↔𝜑𝜓] into biimp | |
| 4198 | →↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒 | Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔↔𝜑𝜓𝜒] into biimp | |
| 4199 | →↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒 | Modus ponens 3644, 4198 | |
| 4200 | →→↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒→↔↔𝜓𝜑𝜒→↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒 | Subs [𝜑↗→↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒, 𝜓↗↔↔𝜓𝜑𝜒] into ax-1 | |
| 4201 | →↔↔𝜓𝜑𝜒→↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒 | Modus ponens 4199, 4200 | |
| 4202 | →→↔↔𝜓𝜑𝜒→↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒→→↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒 | Subs [𝜑↗↔↔𝜓𝜑𝜒, 𝜓↗↔𝜒↔𝜑𝜓, 𝜒↗↔↔𝜑𝜓𝜒] into ax-2 | |
| 4203 | →→↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒 | Modus ponens 4201, 4202 | |
| 4204 | →↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒 | Modus ponens 4183, 4203 | |
| 4205 | →→↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒→→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒 | Subs [𝜑↗↔↔𝜑𝜓𝜒, 𝜓↗↔↔𝜓𝜑𝜒] into impbi | |
| 4206 | →→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒 | Modus ponens 4194, 4205 | |
| 4207 | ↔↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒 | Modus ponens 4204, 4206 | |
| 4208 | ↔↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒 | Subs [𝜑↗𝜓, 𝜓↗𝜑] into biass | |
| 4209 | →↔↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒→↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒 | Subs [𝜑↗↔↔𝜓𝜑𝜒, 𝜓↗↔𝜓↔𝜑𝜒] into biimp | |
| 4210 | →↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒 | Modus ponens 4208, 4209 | |
| 4211 | →↔↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒→↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒 | Subs [𝜑↗↔↔𝜑𝜓𝜒, 𝜓↗↔↔𝜓𝜑𝜒] into biimp | |
| 4212 | →→↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒→↔↔𝜑𝜓𝜒→↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒 | Subs [𝜑↗→↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒, 𝜓↗↔↔𝜑𝜓𝜒] into ax-1 | |
| 4213 | →↔↔𝜑𝜓𝜒→↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒 | Modus ponens 4210, 4212 | |
| 4214 | →→↔↔𝜑𝜓𝜒→↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒→→↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒→↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒 | Subs [𝜑↗↔↔𝜑𝜓𝜒, 𝜓↗↔↔𝜓𝜑𝜒, 𝜒↗↔𝜓↔𝜑𝜒] into ax-2 | |
| 4215 | →→↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒→↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒 | Modus ponens 4213, 4214 | |
| 4216 | →↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒 | Modus ponens 4194, 4215 | |
| 4217 | →↔↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒↔↔𝜓↔𝜑𝜒↔↔𝜓𝜑𝜒 | Subs [𝜑↗↔↔𝜓𝜑𝜒, 𝜓↗↔𝜓↔𝜑𝜒] into bicom1 | |
| 4218 | ↔↔𝜓↔𝜑𝜒↔↔𝜓𝜑𝜒 | Modus ponens 4208, 4217 | |
| 4219 | →↔↔𝜓↔𝜑𝜒↔↔𝜓𝜑𝜒→↔𝜓↔𝜑𝜒↔↔𝜓𝜑𝜒 | Subs [𝜑↗↔𝜓↔𝜑𝜒, 𝜓↗↔↔𝜓𝜑𝜒] into biimp | |
| 4220 | →↔𝜓↔𝜑𝜒↔↔𝜓𝜑𝜒 | Modus ponens 4218, 4219 | |
| 4221 | →↔↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒↔↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒 | Subs [𝜑↗↔↔𝜑𝜓𝜒, 𝜓↗↔↔𝜓𝜑𝜒] into bicom1 | |
| 4222 | ↔↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒 | Modus ponens 4207, 4221 | |
| 4223 | →↔↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒 | Subs [𝜑↗↔↔𝜓𝜑𝜒, 𝜓↗↔↔𝜑𝜓𝜒] into biimp | |
| 4224 | →→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒→↔𝜓↔𝜑𝜒→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒 | Subs [𝜑↗→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒, 𝜓↗↔𝜓↔𝜑𝜒] into ax-1 | |
| 4225 | →↔𝜓↔𝜑𝜒→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒 | Modus ponens 4204, 4224 | |
| 4226 | →→↔𝜓↔𝜑𝜒→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒→→↔𝜓↔𝜑𝜒↔↔𝜓𝜑𝜒→↔𝜓↔𝜑𝜒↔↔𝜑𝜓𝜒 | Subs [𝜑↗↔𝜓↔𝜑𝜒, 𝜓↗↔↔𝜓𝜑𝜒, 𝜒↗↔↔𝜑𝜓𝜒] into ax-2 | |
| 4227 | →→↔𝜓↔𝜑𝜒↔↔𝜓𝜑𝜒→↔𝜓↔𝜑𝜒↔↔𝜑𝜓𝜒 | Modus ponens 4225, 4226 | |
| 4228 | →↔𝜓↔𝜑𝜒↔↔𝜑𝜓𝜒 | Modus ponens 4220, 4227 | |
| 4229 | →→↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒→→↔𝜓↔𝜑𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒 | Subs [𝜑↗↔↔𝜑𝜓𝜒, 𝜓↗↔𝜓↔𝜑𝜒] into impbi | |
| 4230 | →→↔𝜓↔𝜑𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒 | Modus ponens 4216, 4229 | |
| 4231 | ↔↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒 | Modus ponens 4228, 4230 | |
| 4232 | ↔↔↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒↔↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜒, 𝜒↗↔𝜓↔𝜑𝜒] into biass | |
| 4233 | →↔↔↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒↔↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒→↔↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒↔↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒 | Subs [𝜑↗↔↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒, 𝜓↗↔↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒] into biimp | |
| 4234 | →↔↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒↔↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒 | Modus ponens 4232, 4233 | |
| 4235 | ↔↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒 | Modus ponens 4231, 4234 | |
| 4236 | ↔↔↔𝜒𝜓↔𝜑𝜒↔𝜒↔𝜓↔𝜑𝜒 | Subs [𝜑↗𝜒, 𝜒↗↔𝜑𝜒] into biass | |
| 4237 | →↔↔↔𝜒𝜓↔𝜑𝜒↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒 | Subs [𝜑↗↔↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔𝜒↔𝜓↔𝜑𝜒] into bicom1 | |
| 4238 | ↔↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒 | Modus ponens 4236, 4237 | |
| 4239 | →↔↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒→↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒 | Subs [𝜑↗↔𝜒↔𝜓↔𝜑𝜒, 𝜓↗↔↔𝜒𝜓↔𝜑𝜒] into biimp | |
| 4240 | →↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒 | Modus ponens 4238, 4239 | |
| 4241 | →↔↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒↔𝜓↔𝜑𝜒] into biimp | |
| 4242 | →↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒 | Modus ponens 4235, 4241 | |
| 4243 | →→↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒→↔𝜑𝜓→↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒 | Subs [𝜑↗→↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 4244 | →↔𝜑𝜓→↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒 | Modus ponens 4240, 4243 | |
| 4245 | →→↔𝜑𝜓→↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒→↔𝜑𝜓↔↔𝜒𝜓↔𝜑𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒↔𝜓↔𝜑𝜒, 𝜒↗↔↔𝜒𝜓↔𝜑𝜒] into ax-2 | |
| 4246 | →→↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒→↔𝜑𝜓↔↔𝜒𝜓↔𝜑𝜒 | Modus ponens 4244, 4245 | |
| 4247 | →↔𝜑𝜓↔↔𝜒𝜓↔𝜑𝜒 | Modus ponens 4242, 4246 | |
| 4248 | →↔↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒↔↔↔𝜒𝜓↔𝜑𝜒↔𝜒↔𝜓↔𝜑𝜒 | Subs [𝜑↗↔𝜒↔𝜓↔𝜑𝜒, 𝜓↗↔↔𝜒𝜓↔𝜑𝜒] into bicom1 | |
| 4249 | →↔↔↔𝜒𝜓↔𝜑𝜒↔𝜒↔𝜓↔𝜑𝜒→↔↔𝜒𝜓↔𝜑𝜒↔𝜒↔𝜓↔𝜑𝜒 | Subs [𝜑↗↔↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔𝜒↔𝜓↔𝜑𝜒] into biimp | |
| 4250 | →↔↔𝜒𝜓↔𝜑𝜒↔𝜒↔𝜓↔𝜑𝜒 | Modus ponens 4236, 4249 | |
| 4251 | →↔↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒↔𝜓↔𝜑𝜒] into bicom1 | |
| 4252 | ↔↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓 | Modus ponens 4235, 4251 | |
| 4253 | →↔↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓→↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓 | Subs [𝜑↗↔𝜒↔𝜓↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into biimp | |
| 4254 | →↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓 | Modus ponens 4252, 4253 | |
| 4255 | →→↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓→↔↔𝜒𝜓↔𝜑𝜒→↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓 | Subs [𝜑↗→↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓, 𝜓↗↔↔𝜒𝜓↔𝜑𝜒] into ax-1 | |
| 4256 | →↔↔𝜒𝜓↔𝜑𝜒→↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓 | Modus ponens 4254, 4255 | |
| 4257 | →→↔↔𝜒𝜓↔𝜑𝜒→↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓→→↔↔𝜒𝜓↔𝜑𝜒↔𝜒↔𝜓↔𝜑𝜒→↔↔𝜒𝜓↔𝜑𝜒↔𝜑𝜓 | Subs [𝜑↗↔↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔𝜒↔𝜓↔𝜑𝜒, 𝜒↗↔𝜑𝜓] into ax-2 | |
| 4258 | →→↔↔𝜒𝜓↔𝜑𝜒↔𝜒↔𝜓↔𝜑𝜒→↔↔𝜒𝜓↔𝜑𝜒↔𝜑𝜓 | Modus ponens 4256, 4257 | |
| 4259 | →↔↔𝜒𝜓↔𝜑𝜒↔𝜑𝜓 | Modus ponens 4250, 4258 | |
| 4260 | →→↔𝜑𝜓↔↔𝜒𝜓↔𝜑𝜒→→↔↔𝜒𝜓↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔↔𝜒𝜓↔𝜑𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔↔𝜒𝜓↔𝜑𝜒] into impbi | |
| 4261 | →→↔↔𝜒𝜓↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔↔𝜒𝜓↔𝜑𝜒 | Modus ponens 4247, 4260 | |
| 4262 | ↔↔𝜑𝜓↔↔𝜒𝜓↔𝜑𝜒 | Modus ponens 4259, 4261 | biluk |
| 4263 | ↔↔𝜑𝜑¬↔𝜑¬𝜑 | Subs [𝜓↗𝜑] into pm5.18 | |
| 4264 | →↔↔𝜑𝜑¬↔𝜑¬𝜑→↔𝜑𝜑¬↔𝜑¬𝜑 | Subs [𝜑↗↔𝜑𝜑, 𝜓↗¬↔𝜑¬𝜑] into biimp | |
| 4265 | →↔𝜑𝜑¬↔𝜑¬𝜑 | Modus ponens 4263, 4264 | |
| 4266 | ¬↔𝜑¬𝜑 | Modus ponens biid, 4265 | pm5.19 |
| 4267 | →→𝜓→𝜑𝜒→𝜑→𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗𝜑] into pm2.04 | |
| 4268 | →→→𝜑→𝜓𝜒→𝜓→𝜑𝜒→→→𝜓→𝜑𝜒→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜓→𝜑𝜒] into impbi | |
| 4269 | →→→𝜓→𝜑𝜒→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→𝜓→𝜑𝜒 | Modus ponens pm2.04, 4268 | |
| 4270 | ↔→𝜑→𝜓𝜒→𝜓→𝜑𝜒 | Modus ponens 4267, 4269 | bi2.04 |
| 4271 | ↔→𝜑↔→𝜑𝜓𝜓↔→𝜑→𝜑𝜓→𝜑𝜓 | Subs [𝜓↗→𝜑𝜓, 𝜒↗𝜓] into pm5.74 | |
| 4272 | →↔→𝜑↔→𝜑𝜓𝜓↔→𝜑→𝜑𝜓→𝜑𝜓→→𝜑↔→𝜑𝜓𝜓↔→𝜑→𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑↔→𝜑𝜓𝜓, 𝜓↗↔→𝜑→𝜑𝜓→𝜑𝜓] into biimp | |
| 4273 | →→𝜑↔→𝜑𝜓𝜓↔→𝜑→𝜑𝜓→𝜑𝜓 | Modus ponens 4271, 4272 | |
| 4274 | ↔→𝜑→𝜑𝜓→𝜑𝜓 | Modus ponens pm5.5, 4273 | pm5.4 |
| 4275 | →→→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into impbi | |
| 4276 | →→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens ax-2, 4275 | |
| 4277 | ↔→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens pm2.86, 4276 | imdi |
| 4278 | →↔→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒↔→→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into bicom1 | |
| 4279 | ↔→→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒 | Modus ponens imdi, 4278 | pm5.41 |
| 4280 | →↔→𝜑𝜓𝜒↔→𝜑→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒, 𝜒↗𝜑] into imbi2 | |
| 4281 | →↔→𝜑→𝜑𝜓→𝜑𝜓↔→𝜑𝜓→𝜑→𝜑𝜓 | Subs [𝜑↗→𝜑→𝜑𝜓, 𝜓↗→𝜑𝜓] into bicom1 | |
| 4282 | ↔→𝜑𝜓→𝜑→𝜑𝜓 | Modus ponens pm5.4, 4281 | |
| 4283 | →↔→𝜑𝜓→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑→𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜓→𝜑→𝜑𝜓, 𝜓↗↔→𝜑𝜓𝜒] into ax-1 | |
| 4284 | →↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑→𝜑𝜓 | Modus ponens 4282, 4283 | |
| 4285 | ↔→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑→𝜑𝜓↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜓𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑→𝜑𝜓] into pm5.74 | |
| 4286 | →↔→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑→𝜑𝜓↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑→𝜑𝜓↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑→𝜑𝜓, 𝜓↗↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓] into biimp | |
| 4287 | →→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑→𝜑𝜓↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓 | Modus ponens 4285, 4286 | |
| 4288 | ↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓 | Modus ponens 4284, 4287 | |
| 4289 | ↔→↔→𝜑𝜓𝜒↔→𝜑→𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒 | Subs [𝜑↗↔→𝜑𝜓𝜒, 𝜓↗→𝜑→𝜑𝜓, 𝜒↗→𝜑𝜒] into pm5.74 | |
| 4290 | →↔→↔→𝜑𝜓𝜒↔→𝜑→𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→→↔→𝜑𝜓𝜒↔→𝜑→𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→↔→𝜑𝜓𝜒↔→𝜑→𝜑𝜓→𝜑𝜒, 𝜓↗↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒] into biimp | |
| 4291 | →→↔→𝜑𝜓𝜒↔→𝜑→𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒 | Modus ponens 4289, 4290 | |
| 4292 | ↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒 | Modus ponens 4280, 4291 | |
| 4293 | →↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓, 𝜓↗→↔→𝜑𝜓𝜒→𝜑𝜒] into biimp | |
| 4294 | →→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒 | Modus ponens 4292, 4293 | |
| 4295 | →↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑𝜓, 𝜓↗→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓] into biimp | |
| 4296 | →→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓 | Modus ponens 4288, 4295 | |
| 4297 | →→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→→↔→𝜑𝜓𝜒→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒, 𝜓↗→↔→𝜑𝜓𝜒→𝜑𝜓] into ax-1 | |
| 4298 | →→↔→𝜑𝜓𝜒→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒 | Modus ponens 4294, 4297 | |
| 4299 | →→→↔→𝜑𝜓𝜒→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→→→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑𝜓, 𝜓↗→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓, 𝜒↗→↔→𝜑𝜓𝜒→𝜑𝜒] into ax-2 | |
| 4300 | →→→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒 | Modus ponens 4298, 4299 | |
| 4301 | →→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒 | Modus ponens 4296, 4300 | |
| 4302 | →↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒↔→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓, 𝜓↗→↔→𝜑𝜓𝜒→𝜑𝜒] into bicom1 | |
| 4303 | ↔→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓 | Modus ponens 4292, 4302 | |
| 4304 | →↔→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑𝜒, 𝜓↗→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓] into biimp | |
| 4305 | →→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓 | Modus ponens 4303, 4304 | |
| 4306 | →↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑𝜓, 𝜓↗→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓] into bicom1 | |
| 4307 | ↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓 | Modus ponens 4288, 4306 | |
| 4308 | →↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓, 𝜓↗→↔→𝜑𝜓𝜒→𝜑𝜓] into biimp | |
| 4309 | →→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓 | Modus ponens 4307, 4308 | |
| 4310 | →→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑𝜒→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓, 𝜓↗→↔→𝜑𝜓𝜒→𝜑𝜒] into ax-1 | |
| 4311 | →→↔→𝜑𝜓𝜒→𝜑𝜒→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓 | Modus ponens 4309, 4310 | |
| 4312 | →→→↔→𝜑𝜓𝜒→𝜑𝜒→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓→→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑𝜒, 𝜓↗→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓, 𝜒↗→↔→𝜑𝜓𝜒→𝜑𝜓] into ax-2 | |
| 4313 | →→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑𝜓 | Modus ponens 4311, 4312 | |
| 4314 | →→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑𝜓 | Modus ponens 4305, 4313 | |
| 4315 | →→→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑𝜓↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑𝜓, 𝜓↗→↔→𝜑𝜓𝜒→𝜑𝜒] into impbi | |
| 4316 | →→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑𝜓↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒 | Modus ponens 4301, 4315 | |
| 4317 | ↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒 | Modus ponens 4314, 4316 | |
| 4318 | ↔→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒 | Subs [𝜑↗↔→𝜑𝜓𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜒] into pm5.74 | |
| 4319 | →↔→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒↔↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒, 𝜓↗↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒] into bicom1 | |
| 4320 | ↔↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Modus ponens 4318, 4319 | |
| 4321 | →↔↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒→↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒, 𝜓↗→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒] into biimp | |
| 4322 | →↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Modus ponens 4320, 4321 | |
| 4323 | →↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒 | Modus ponens 4317, 4322 | |
| 4324 | →↔→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒↔↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into bicom1 | |
| 4325 | ↔↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒 | Modus ponens pm5.74, 4324 | |
| 4326 | →↔↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒 | Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑↔𝜓𝜒] into biimp | |
| 4327 | →→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒→↔→𝜑𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒 | Subs [𝜑↗→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒, 𝜓↗↔→𝜑𝜓𝜒] into ax-1 | |
| 4328 | →↔→𝜑𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒 | Modus ponens 1905, 4327 | |
| 4329 | →→↔→𝜑𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒→→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑↔𝜓𝜒 | Subs [𝜑↗↔→𝜑𝜓𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜑↔𝜓𝜒] into ax-2 | |
| 4330 | →→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑↔𝜓𝜒 | Modus ponens 4328, 4329 | |
| 4331 | →↔→𝜑𝜓𝜒→𝜑↔𝜓𝜒 | Modus ponens 4323, 4330 | imbibi |
| 4332 | →→→𝜑¬𝜑¬𝜑→→¬𝜑→𝜑¬𝜑↔→𝜑¬𝜑¬𝜑 | Subs [𝜑↗→𝜑¬𝜑, 𝜓↗¬𝜑] into impbi | |
| 4333 | →→¬𝜑→𝜑¬𝜑↔→𝜑¬𝜑¬𝜑 | Modus ponens pm2.01, 4332 | |
| 4334 | ↔→𝜑¬𝜑¬𝜑 | Modus ponens 414, 4333 | pm4.8 |
| 4335 | →→→¬𝜑𝜑𝜑→→𝜑→¬𝜑𝜑↔→¬𝜑𝜑𝜑 | Subs [𝜑↗→¬𝜑𝜑, 𝜓↗𝜑] into impbi | |
| 4336 | →→𝜑→¬𝜑𝜑↔→¬𝜑𝜑𝜑 | Modus ponens pm2.18, 4335 | |
| 4337 | ↔→¬𝜑𝜑𝜑 | Modus ponens 322, 4336 | pm4.81 |
| 4338 | ↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃 | Subs [𝜑↗→𝜑𝜒, 𝜒↗𝜃] into bi2.04 | |
| 4339 | →𝜑↔→𝜑𝜒𝜒 | Subs [𝜓↗𝜒] into pm5.5 | |
| 4340 | ↔↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒 | Subs [𝜑↗→𝜑𝜒, 𝜓↗𝜒] into bicom | |
| 4341 | →↔↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒→↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒 | Subs [𝜑↗↔→𝜑𝜒𝜒, 𝜓↗↔𝜒→𝜑𝜒] into biimp | |
| 4342 | →↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒 | Modus ponens 4340, 4341 | |
| 4343 | →→↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒→𝜑→↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒 | Subs [𝜑↗→↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒, 𝜓↗𝜑] into ax-1 | |
| 4344 | →𝜑→↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒 | Modus ponens 4342, 4343 | |
| 4345 | →→𝜑→↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒→→𝜑↔→𝜑𝜒𝜒→𝜑↔𝜒→𝜑𝜒 | Subs [𝜓↗↔→𝜑𝜒𝜒, 𝜒↗↔𝜒→𝜑𝜒] into ax-2 | |
| 4346 | →→𝜑↔→𝜑𝜒𝜒→𝜑↔𝜒→𝜑𝜒 | Modus ponens 4344, 4345 | |
| 4347 | →𝜑↔𝜒→𝜑𝜒 | Modus ponens 4339, 4346 | |
| 4348 | →↔𝜒→𝜑𝜒→𝜒→𝜑𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜒] into biimp | |
| 4349 | →→↔𝜒→𝜑𝜒→𝜒→𝜑𝜒→𝜑→↔𝜒→𝜑𝜒→𝜒→𝜑𝜒 | Subs [𝜑↗→↔𝜒→𝜑𝜒→𝜒→𝜑𝜒, 𝜓↗𝜑] into ax-1 | |
| 4350 | →𝜑→↔𝜒→𝜑𝜒→𝜒→𝜑𝜒 | Modus ponens 4348, 4349 | |
| 4351 | →→𝜑→↔𝜒→𝜑𝜒→𝜒→𝜑𝜒→→𝜑↔𝜒→𝜑𝜒→𝜑→𝜒→𝜑𝜒 | Subs [𝜓↗↔𝜒→𝜑𝜒, 𝜒↗→𝜒→𝜑𝜒] into ax-2 | |
| 4352 | →→𝜑↔𝜒→𝜑𝜒→𝜑→𝜒→𝜑𝜒 | Modus ponens 4350, 4351 | |
| 4353 | →𝜑→𝜒→𝜑𝜒 | Modus ponens 4347, 4352 | |
| 4354 | →→𝜒→𝜑𝜒→𝜒→𝜒→𝜑𝜒 | Subs [𝜑↗→𝜒→𝜑𝜒, 𝜓↗𝜒] into ax-1 | |
| 4355 | →𝜒→𝜒→𝜑𝜒 | Modus ponens 1834, 4354 | |
| 4356 | →→𝜒→𝜒→𝜑𝜒→→𝜒𝜒→𝜒→𝜑𝜒 | Subs [𝜑↗𝜒, 𝜓↗𝜒, 𝜒↗→𝜑𝜒] into ax-2 | |
| 4357 | →→𝜒𝜒→𝜒→𝜑𝜒 | Modus ponens 4355, 4356 | |
| 4358 | →→𝜑→𝜒→𝜑𝜒→→𝜑𝜒→𝜑→𝜑𝜒 | Subs [𝜓↗𝜒, 𝜒↗→𝜑𝜒] into ax-2 | |
| 4359 | →→𝜑𝜒→𝜑→𝜑𝜒 | Modus ponens 4353, 4358 | |
| 4360 | →→→𝜑𝜒→𝜑→𝜑𝜒→𝜒→→𝜑𝜒→𝜑→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜒→𝜑→𝜑𝜒, 𝜓↗𝜒] into ax-1 | |
| 4361 | →𝜒→→𝜑𝜒→𝜑→𝜑𝜒 | Modus ponens 4359, 4360 | |
| 4362 | →→𝜒→→𝜑𝜒→𝜑→𝜑𝜒→→𝜒→𝜑𝜒→𝜒→𝜑→𝜑𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑→𝜑𝜒] into ax-2 | |
| 4363 | →→𝜒→𝜑𝜒→𝜒→𝜑→𝜑𝜒 | Modus ponens 4361, 4362 | |
| 4364 | →𝜒→𝜑→𝜑𝜒 | Modus ponens 1834, 4363 | |
| 4365 | →→𝜒→𝜑→𝜑𝜒→→𝜒𝜑→𝜒→𝜑𝜒 | Subs [𝜑↗𝜒, 𝜓↗𝜑, 𝜒↗→𝜑𝜒] into ax-2 | |
| 4366 | →→𝜒𝜑→𝜒→𝜑𝜒 | Modus ponens 4364, 4365 | |
| 4367 | →→→𝜒𝜑→𝜒→𝜑𝜒→𝜑→→𝜒𝜑→𝜒→𝜑𝜒 | Subs [𝜑↗→→𝜒𝜑→𝜒→𝜑𝜒, 𝜓↗𝜑] into ax-1 | |
| 4368 | →𝜑→→𝜒𝜑→𝜒→𝜑𝜒 | Modus ponens 4366, 4367 | |
| 4369 | →→𝜑→→𝜒𝜑→𝜒→𝜑𝜒→→𝜑→𝜒𝜑→𝜑→𝜒→𝜑𝜒 | Subs [𝜓↗→𝜒𝜑, 𝜒↗→𝜒→𝜑𝜒] into ax-2 | |
| 4370 | →→𝜑→𝜒𝜑→𝜑→𝜒→𝜑𝜒 | Modus ponens 4368, 4369 | |
| 4371 | →𝜑→𝜃𝜃 | Subs [𝜓↗𝜃] into idd | |
| 4372 | →→𝜃𝜃→→𝜑𝜒→𝜃𝜃 | Subs [𝜑↗→𝜃𝜃, 𝜓↗→𝜑𝜒] into ax-1 | |
| 4373 | →→→𝜃𝜃→→𝜑𝜒→𝜃𝜃→𝜑→→𝜃𝜃→→𝜑𝜒→𝜃𝜃 | Subs [𝜑↗→→𝜃𝜃→→𝜑𝜒→𝜃𝜃, 𝜓↗𝜑] into ax-1 | |
| 4374 | →𝜑→→𝜃𝜃→→𝜑𝜒→𝜃𝜃 | Modus ponens 4372, 4373 | |
| 4375 | →→𝜑→→𝜃𝜃→→𝜑𝜒→𝜃𝜃→→𝜑→𝜃𝜃→𝜑→→𝜑𝜒→𝜃𝜃 | Subs [𝜓↗→𝜃𝜃, 𝜒↗→→𝜑𝜒→𝜃𝜃] into ax-2 | |
| 4376 | →→𝜑→𝜃𝜃→𝜑→→𝜑𝜒→𝜃𝜃 | Modus ponens 4374, 4375 | |
| 4377 | →𝜑→→𝜑𝜒→𝜃𝜃 | Modus ponens 4371, 4376 | |
| 4378 | →→→𝜑𝜒→𝜃𝜃→→→𝜑𝜒𝜃→→𝜑𝜒𝜃 | Subs [𝜑↗→𝜑𝜒, 𝜓↗𝜃, 𝜒↗𝜃] into ax-2 | |
| 4379 | →→→→𝜑𝜒→𝜃𝜃→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→𝜑𝜒→𝜃𝜃→→→𝜑𝜒𝜃→→𝜑𝜒𝜃 | Subs [𝜑↗→→→𝜑𝜒→𝜃𝜃→→→𝜑𝜒𝜃→→𝜑𝜒𝜃, 𝜓↗𝜑] into ax-1 | |
| 4380 | →𝜑→→→𝜑𝜒→𝜃𝜃→→→𝜑𝜒𝜃→→𝜑𝜒𝜃 | Modus ponens 4378, 4379 | |
| 4381 | →→𝜑→→→𝜑𝜒→𝜃𝜃→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→→𝜑→→𝜑𝜒→𝜃𝜃→𝜑→→→𝜑𝜒𝜃→→𝜑𝜒𝜃 | Subs [𝜓↗→→𝜑𝜒→𝜃𝜃, 𝜒↗→→→𝜑𝜒𝜃→→𝜑𝜒𝜃] into ax-2 | |
| 4382 | →→𝜑→→𝜑𝜒→𝜃𝜃→𝜑→→→𝜑𝜒𝜃→→𝜑𝜒𝜃 | Modus ponens 4380, 4381 | |
| 4383 | →𝜑→→→𝜑𝜒𝜃→→𝜑𝜒𝜃 | Modus ponens 4377, 4382 | |
| 4384 | →→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒→𝜑𝜒 | Subs [𝜑↗→𝜒→𝜑𝜒, 𝜓↗→→𝜑𝜒𝜃] into ax-1 | |
| 4385 | →→→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→𝜑→→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒→𝜑𝜒 | Subs [𝜑↗→→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒→𝜑𝜒, 𝜓↗𝜑] into ax-1 | |
| 4386 | →𝜑→→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒→𝜑𝜒 | Modus ponens 4384, 4385 | |
| 4387 | →→𝜑→→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→𝜑→𝜒→𝜑𝜒→𝜑→→→𝜑𝜒𝜃→𝜒→𝜑𝜒 | Subs [𝜓↗→𝜒→𝜑𝜒, 𝜒↗→→→𝜑𝜒𝜃→𝜒→𝜑𝜒] into ax-2 | |
| 4388 | →→𝜑→𝜒→𝜑𝜒→𝜑→→→𝜑𝜒𝜃→𝜒→𝜑𝜒 | Modus ponens 4386, 4387 | |
| 4389 | →𝜑→→→𝜑𝜒𝜃→𝜒→𝜑𝜒 | Modus ponens 4353, 4388 | |
| 4390 | →→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃 | Subs [𝜑↗→𝜑𝜒, 𝜓↗𝜃] into imim2 | |
| 4391 | →→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃 | Subs [𝜑↗→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃, 𝜓↗→→𝜑𝜒𝜃] into ax-1 | |
| 4392 | →→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃 | Modus ponens 4390, 4391 | |
| 4393 | →→→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃 | Subs [𝜑↗→→𝜑𝜒𝜃, 𝜓↗→→𝜑𝜒𝜃, 𝜒↗→→𝜒→𝜑𝜒→𝜒𝜃] into ax-2 | |
| 4394 | →→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃 | Modus ponens 4392, 4393 | |
| 4395 | →→→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃 | Subs [𝜑↗→→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃, 𝜓↗𝜑] into ax-1 | |
| 4396 | →𝜑→→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃 | Modus ponens 4394, 4395 | |
| 4397 | →→𝜑→→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→𝜑→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃 | Subs [𝜓↗→→→𝜑𝜒𝜃→→𝜑𝜒𝜃, 𝜒↗→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃] into ax-2 | |
| 4398 | →→𝜑→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃 | Modus ponens 4396, 4397 | |
| 4399 | →𝜑→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃 | Modus ponens 4383, 4398 | |
| 4400 | →→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃 | Subs [𝜑↗→→𝜑𝜒𝜃, 𝜓↗→𝜒→𝜑𝜒, 𝜒↗→𝜒𝜃] into ax-2 | |
| 4401 | →→→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃 | Subs [𝜑↗→→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗𝜑] into ax-1 | |
| 4402 | →𝜑→→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃 | Modus ponens 4400, 4401 | |
| 4403 | →→𝜑→→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃 | Subs [𝜓↗→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃, 𝜒↗→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃] into ax-2 | |
| 4404 | →→𝜑→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃 | Modus ponens 4402, 4403 | |
| 4405 | →𝜑→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃 | Modus ponens 4399, 4404 | |
| 4406 | →→𝜑→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→𝜑→→→𝜑𝜒𝜃→𝜒𝜃 | Subs [𝜓↗→→→𝜑𝜒𝜃→𝜒→𝜑𝜒, 𝜒↗→→→𝜑𝜒𝜃→𝜒𝜃] into ax-2 | |
| 4407 | →→𝜑→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→𝜑→→→𝜑𝜒𝜃→𝜒𝜃 | Modus ponens 4405, 4406 | |
| 4408 | →𝜑→→→𝜑𝜒𝜃→𝜒𝜃 | Modus ponens 4389, 4407 | |
| 4409 | →↔→𝜑𝜒𝜒→→𝜑𝜒𝜒 | Subs [𝜑↗→𝜑𝜒, 𝜓↗𝜒] into biimp | |
| 4410 | →→↔→𝜑𝜒𝜒→→𝜑𝜒𝜒→𝜑→↔→𝜑𝜒𝜒→→𝜑𝜒𝜒 | Subs [𝜑↗→↔→𝜑𝜒𝜒→→𝜑𝜒𝜒, 𝜓↗𝜑] into ax-1 | |
| 4411 | →𝜑→↔→𝜑𝜒𝜒→→𝜑𝜒𝜒 | Modus ponens 4409, 4410 | |
| 4412 | →→𝜑→↔→𝜑𝜒𝜒→→𝜑𝜒𝜒→→𝜑↔→𝜑𝜒𝜒→𝜑→→𝜑𝜒𝜒 | Subs [𝜓↗↔→𝜑𝜒𝜒, 𝜒↗→→𝜑𝜒𝜒] into ax-2 | |
| 4413 | →→𝜑↔→𝜑𝜒𝜒→𝜑→→𝜑𝜒𝜒 | Modus ponens 4411, 4412 | |
| 4414 | →→𝜃𝜃→𝜒→𝜃𝜃 | Subs [𝜑↗→𝜃𝜃, 𝜓↗𝜒] into ax-1 | |
| 4415 | →→→𝜃𝜃→𝜒→𝜃𝜃→𝜑→→𝜃𝜃→𝜒→𝜃𝜃 | Subs [𝜑↗→→𝜃𝜃→𝜒→𝜃𝜃, 𝜓↗𝜑] into ax-1 | |
| 4416 | →𝜑→→𝜃𝜃→𝜒→𝜃𝜃 | Modus ponens 4414, 4415 | |
| 4417 | →→𝜑→→𝜃𝜃→𝜒→𝜃𝜃→→𝜑→𝜃𝜃→𝜑→𝜒→𝜃𝜃 | Subs [𝜓↗→𝜃𝜃, 𝜒↗→𝜒→𝜃𝜃] into ax-2 | |
| 4418 | →→𝜑→𝜃𝜃→𝜑→𝜒→𝜃𝜃 | Modus ponens 4416, 4417 | |
| 4419 | →𝜑→𝜒→𝜃𝜃 | Modus ponens 4371, 4418 | |
| 4420 | →→𝜒→𝜃𝜃→→𝜒𝜃→𝜒𝜃 | Subs [𝜑↗𝜒, 𝜓↗𝜃, 𝜒↗𝜃] into ax-2 | |
| 4421 | →→→𝜒→𝜃𝜃→→𝜒𝜃→𝜒𝜃→𝜑→→𝜒→𝜃𝜃→→𝜒𝜃→𝜒𝜃 | Subs [𝜑↗→→𝜒→𝜃𝜃→→𝜒𝜃→𝜒𝜃, 𝜓↗𝜑] into ax-1 | |
| 4422 | →𝜑→→𝜒→𝜃𝜃→→𝜒𝜃→𝜒𝜃 | Modus ponens 4420, 4421 | |
| 4423 | →→𝜑→→𝜒→𝜃𝜃→→𝜒𝜃→𝜒𝜃→→𝜑→𝜒→𝜃𝜃→𝜑→→𝜒𝜃→𝜒𝜃 | Subs [𝜓↗→𝜒→𝜃𝜃, 𝜒↗→→𝜒𝜃→𝜒𝜃] into ax-2 | |
| 4424 | →→𝜑→𝜒→𝜃𝜃→𝜑→→𝜒𝜃→𝜒𝜃 | Modus ponens 4422, 4423 | |
| 4425 | →𝜑→→𝜒𝜃→𝜒𝜃 | Modus ponens 4419, 4424 | |
| 4426 | →→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜒 | Subs [𝜑↗→→𝜑𝜒𝜒, 𝜓↗→𝜒𝜃] into ax-1 | |
| 4427 | →→→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜒→𝜑→→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜒 | Subs [𝜑↗→→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜒, 𝜓↗𝜑] into ax-1 | |
| 4428 | →𝜑→→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜒 | Modus ponens 4426, 4427 | |
| 4429 | →→𝜑→→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜒𝜃→→𝜑𝜒𝜒 | Subs [𝜓↗→→𝜑𝜒𝜒, 𝜒↗→→𝜒𝜃→→𝜑𝜒𝜒] into ax-2 | |
| 4430 | →→𝜑→→𝜑𝜒𝜒→𝜑→→𝜒𝜃→→𝜑𝜒𝜒 | Modus ponens 4428, 4429 | |
| 4431 | →𝜑→→𝜒𝜃→→𝜑𝜒𝜒 | Modus ponens 264, 4430 | |
| 4432 | →→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃 | Subs [𝜑↗𝜒, 𝜓↗𝜃, 𝜒↗→𝜑𝜒] into imim2 | |
| 4433 | →→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃 | Subs [𝜑↗→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1 | |
| 4434 | →→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃 | Modus ponens 4432, 4433 | |
| 4435 | →→→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃 | Subs [𝜑↗→𝜒𝜃, 𝜓↗→𝜒𝜃, 𝜒↗→→→𝜑𝜒𝜒→→𝜑𝜒𝜃] into ax-2 | |
| 4436 | →→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃 | Modus ponens 4434, 4435 | |
| 4437 | →→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→𝜑→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃 | Subs [𝜑↗→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃, 𝜓↗𝜑] into ax-1 | |
| 4438 | →𝜑→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃 | Modus ponens 4436, 4437 | |
| 4439 | →→𝜑→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→𝜑→→𝜒𝜃→𝜒𝜃→𝜑→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃 | Subs [𝜓↗→→𝜒𝜃→𝜒𝜃, 𝜒↗→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃] into ax-2 | |
| 4440 | →→𝜑→→𝜒𝜃→𝜒𝜃→𝜑→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃 | Modus ponens 4438, 4439 | |
| 4441 | →𝜑→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃 | Modus ponens 4425, 4440 | |
| 4442 | →→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃 | Subs [𝜑↗→𝜒𝜃, 𝜓↗→→𝜑𝜒𝜒, 𝜒↗→→𝜑𝜒𝜃] into ax-2 | |
| 4443 | →→→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃 | Subs [𝜑↗→→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃, 𝜓↗𝜑] into ax-1 | |
| 4444 | →𝜑→→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃 | Modus ponens 4442, 4443 | |
| 4445 | →→𝜑→→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃→→𝜑→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→𝜑→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃 | Subs [𝜓↗→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃, 𝜒↗→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃] into ax-2 | |
| 4446 | →→𝜑→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→𝜑→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃 | Modus ponens 4444, 4445 | |
| 4447 | →𝜑→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃 | Modus ponens 4441, 4446 | |
| 4448 | →→𝜑→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃→→𝜑→→𝜒𝜃→→𝜑𝜒𝜒→𝜑→→𝜒𝜃→→𝜑𝜒𝜃 | Subs [𝜓↗→→𝜒𝜃→→𝜑𝜒𝜒, 𝜒↗→→𝜒𝜃→→𝜑𝜒𝜃] into ax-2 | |
| 4449 | →→𝜑→→𝜒𝜃→→𝜑𝜒𝜒→𝜑→→𝜒𝜃→→𝜑𝜒𝜃 | Modus ponens 4447, 4448 | |
| 4450 | →𝜑→→𝜒𝜃→→𝜑𝜒𝜃 | Modus ponens 4431, 4449 | |
| 4451 | →→→→𝜑𝜒𝜃→𝜒𝜃→→→𝜒𝜃→→𝜑𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃 | Subs [𝜑↗→→𝜑𝜒𝜃, 𝜓↗→𝜒𝜃] into impbi | |
| 4452 | →→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃 | Subs [𝜑↗→→𝜒𝜃→→𝜑𝜒𝜃, 𝜓↗→→→𝜑𝜒𝜃→𝜒𝜃] into ax-1 | |
| 4453 | →→→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃 | Subs [𝜑↗→→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃, 𝜓↗𝜑] into ax-1 | |
| 4454 | →𝜑→→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃 | Modus ponens 4452, 4453 | |
| 4455 | →→𝜑→→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→→𝜑→→𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃 | Subs [𝜓↗→→𝜒𝜃→→𝜑𝜒𝜃, 𝜒↗→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃] into ax-2 | |
| 4456 | →→𝜑→→𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃 | Modus ponens 4454, 4455 | |
| 4457 | →𝜑→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃 | Modus ponens 4450, 4456 | |
| 4458 | →→→→→𝜑𝜒𝜃→𝜒𝜃→→→𝜒𝜃→→𝜑𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃→→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃 | Subs [𝜑↗→→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗→→𝜒𝜃→→𝜑𝜒𝜃, 𝜒↗↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-2 | |
| 4459 | →→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃 | Modus ponens 4451, 4458 | |
| 4460 | →→→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃 | Subs [𝜑↗→→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗𝜑] into ax-1 | |
| 4461 | →𝜑→→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃 | Modus ponens 4459, 4460 | |
| 4462 | →→𝜑→→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃 | Subs [𝜓↗→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃, 𝜒↗→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-2 | |
| 4463 | →→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃 | Modus ponens 4461, 4462 | |
| 4464 | →𝜑→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃 | Modus ponens 4457, 4463 | |
| 4465 | →→→→𝜑𝜒𝜃→𝜒𝜃→→→𝜑𝜒𝜃→𝜒𝜃 | Subs [𝜑↗→→→𝜑𝜒𝜃→𝜒𝜃] into id | |
| 4466 | →→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃 | Subs [𝜑↗→→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗𝜑] into ax-1 | |
| 4467 | →→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃 | Subs [𝜑↗→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗→→→𝜑𝜒𝜃→𝜒𝜃] into ax-1 | |
| 4468 | →→→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃 | Modus ponens 4466, 4467 | |
| 4469 | →→→→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→→→→→𝜑𝜒𝜃→𝜒𝜃→→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃 | Subs [𝜑↗→→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗→→→𝜑𝜒𝜃→𝜒𝜃, 𝜒↗→𝜑→→→𝜑𝜒𝜃→𝜒𝜃] into ax-2 | |
| 4470 | →→→→→𝜑𝜒𝜃→𝜒𝜃→→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃 | Modus ponens 4468, 4469 | |
| 4471 | →→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃 | Subs [𝜓↗→→→𝜑𝜒𝜃→𝜒𝜃, 𝜒↗↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-2 | |
| 4472 | →→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃 | Modus ponens 4464, 4471 | |
| 4473 | →→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃 | Subs [𝜑↗→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗→→→𝜑𝜒𝜃→𝜒𝜃] into ax-1 | |
| 4474 | →→→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃 | Modus ponens 4472, 4473 | |
| 4475 | →→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃 | Subs [𝜑↗→→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗→𝜑→→→𝜑𝜒𝜃→𝜒𝜃, 𝜒↗→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-2 | |
| 4476 | →→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃 | Modus ponens 4474, 4475 | |
| 4477 | →→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃 | Modus ponens 4466, 4476 | |
| 4478 | →→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃 | Subs [𝜑↗→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗𝜑] into ax-1 | |
| 4479 | →𝜑→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃 | Modus ponens 4477, 4478 | |
| 4480 | →→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃 | Subs [𝜓↗→→→𝜑𝜒𝜃→𝜒𝜃, 𝜒↗→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-2 | |
| 4481 | →→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃 | Modus ponens 4479, 4480 | |
| 4482 | →𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃 | Modus ponens 4408, 4481 | |
| 4483 | →→𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→→𝜑𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃 | Subs [𝜓↗𝜑, 𝜒↗↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-2 | |
| 4484 | →→𝜑𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃 | Modus ponens 4482, 4483 | |
| 4485 | →→→𝜑𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→𝜑𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃 | Subs [𝜑↗→→𝜑𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗𝜑] into ax-1 | |
| 4486 | →𝜑→→𝜑𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃 | Modus ponens 4484, 4485 | |
| 4487 | →→𝜑→→𝜑𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→𝜑𝜑→𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃 | Subs [𝜓↗→𝜑𝜑, 𝜒↗→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-2 | |
| 4488 | →→𝜑→𝜑𝜑→𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃 | Modus ponens 4486, 4487 | |
| 4489 | →𝜑↔→→𝜑𝜒𝜃→𝜒𝜃 | Modus ponens id, 4484 | |
| 4490 | →→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→𝜓→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃 | Subs [𝜑↗→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-1 | |
| 4491 | →𝜓→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃 | Modus ponens 4489, 4490 | |
| 4492 | →→𝜓→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→→𝜓𝜑→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃 | Subs [𝜑↗𝜓, 𝜓↗𝜑, 𝜒↗↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-2 | |
| 4493 | →→𝜓𝜑→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃 | Modus ponens 4491, 4492 | |
| 4494 | ↔→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃 | Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜒𝜃, 𝜒↗→𝜒𝜃] into pm5.74 | |
| 4495 | →↔→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃→→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃 | Subs [𝜑↗→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃] into biimp | |
| 4496 | →→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃 | Modus ponens 4494, 4495 | |
| 4497 | →→→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃→→𝜓𝜑→→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃 | Subs [𝜑↗→→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃, 𝜓↗→𝜓𝜑] into ax-1 | |
| 4498 | →→𝜓𝜑→→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃 | Modus ponens 4496, 4497 | |
| 4499 | →→→𝜓𝜑→→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃→→→𝜓𝜑→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃→→𝜓𝜑↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃 | Subs [𝜑↗→𝜓𝜑, 𝜓↗→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃, 𝜒↗↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃] into ax-2 | |
| 4500 | →→→𝜓𝜑→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃→→𝜓𝜑↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃 | Modus ponens 4498, 4499 | |
| 4501 | →→𝜓𝜑↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃 | Modus ponens 4493, 4500 | |
| 4502 | →↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃 | Subs [𝜑↗↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃, 𝜓↗→𝜓𝜑] into ax-1 | |
| 4503 | →→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃 | Modus ponens 4338, 4502 | |
| 4504 | ↔→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃 | Subs [𝜑↗→𝜓𝜑, 𝜓↗→→𝜑𝜒→𝜓𝜃, 𝜒↗→𝜓→→𝜑𝜒𝜃] into pm5.74 | |
| 4505 | →↔→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃 | Subs [𝜑↗→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃, 𝜓↗↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃] into biimp | |
| 4506 | →→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃 | Modus ponens 4504, 4505 | |
| 4507 | ↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃 | Modus ponens 4503, 4506 | |
| 4508 | ↔→→𝜓𝜑↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃 | Subs [𝜑↗→𝜓𝜑, 𝜓↗→𝜓→→𝜑𝜒𝜃, 𝜒↗→𝜓→𝜒𝜃] into pm5.74 | |
| 4509 | →↔→→𝜓𝜑↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→→𝜓𝜑↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃 | Subs [𝜑↗→→𝜓𝜑↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃, 𝜓↗↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃] into biimp | |
| 4510 | →→→𝜓𝜑↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃 | Modus ponens 4508, 4509 | |
| 4511 | ↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃 | Modus ponens 4501, 4510 | |
| 4512 | →↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃 | Subs [𝜑↗→→𝜓𝜑→𝜓→→𝜑𝜒𝜃, 𝜓↗→→𝜓𝜑→𝜓→𝜒𝜃] into biimp | |
| 4513 | →→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃 | Modus ponens 4511, 4512 | |
| 4514 | →↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃 | Subs [𝜑↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜃, 𝜓↗→→𝜓𝜑→𝜓→→𝜑𝜒𝜃] into biimp | |
| 4515 | →→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃 | Modus ponens 4507, 4514 | |
| 4516 | →→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃 | Subs [𝜑↗→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃, 𝜓↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜃] into ax-1 | |
| 4517 | →→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃 | Modus ponens 4513, 4516 | |
| 4518 | →→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃 | Subs [𝜑↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜃, 𝜓↗→→𝜓𝜑→𝜓→→𝜑𝜒𝜃, 𝜒↗→→𝜓𝜑→𝜓→𝜒𝜃] into ax-2 | |
| 4519 | →→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃 | Modus ponens 4517, 4518 | |
| 4520 | →→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃 | Modus ponens 4515, 4519 | |
| 4521 | →↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃↔→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃 | Subs [𝜑↗→→𝜓𝜑→𝜓→→𝜑𝜒𝜃, 𝜓↗→→𝜓𝜑→𝜓→𝜒𝜃] into bicom1 | |
| 4522 | ↔→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃 | Modus ponens 4511, 4521 | |
| 4523 | →↔→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃 | Subs [𝜑↗→→𝜓𝜑→𝜓→𝜒𝜃, 𝜓↗→→𝜓𝜑→𝜓→→𝜑𝜒𝜃] into biimp | |
| 4524 | →→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃 | Modus ponens 4522, 4523 | |
| 4525 | →↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃 | Subs [𝜑↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜃, 𝜓↗→→𝜓𝜑→𝜓→→𝜑𝜒𝜃] into bicom1 | |
| 4526 | ↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃 | Modus ponens 4507, 4525 | |
| 4527 | →↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃 | Subs [𝜑↗→→𝜓𝜑→𝜓→→𝜑𝜒𝜃, 𝜓↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜃] into biimp | |
| 4528 | →→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃 | Modus ponens 4526, 4527 | |
| 4529 | →→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→→𝜓𝜑→𝜓→𝜒𝜃→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃 | Subs [𝜑↗→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃, 𝜓↗→→𝜓𝜑→𝜓→𝜒𝜃] into ax-1 | |
| 4530 | →→→𝜓𝜑→𝜓→𝜒𝜃→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃 | Modus ponens 4528, 4529 | |
| 4531 | →→→→𝜓𝜑→𝜓→𝜒𝜃→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃 | Subs [𝜑↗→→𝜓𝜑→𝜓→𝜒𝜃, 𝜓↗→→𝜓𝜑→𝜓→→𝜑𝜒𝜃, 𝜒↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜃] into ax-2 | |
| 4532 | →→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃 | Modus ponens 4530, 4531 | |
| 4533 | →→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃 | Modus ponens 4524, 4532 | |
| 4534 | →→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃 | Subs [𝜑↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜃, 𝜓↗→→𝜓𝜑→𝜓→𝜒𝜃] into impbi | |
| 4535 | →→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃 | Modus ponens 4520, 4534 | |
| 4536 | ↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃 | Modus ponens 4533, 4535 | |
| 4537 | ↔→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃 | Subs [𝜑↗→𝜓𝜑, 𝜓↗→→𝜑𝜒→𝜓𝜃, 𝜒↗→𝜓→𝜒𝜃] into pm5.74 | |
| 4538 | →↔→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃↔↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃 | Subs [𝜑↗→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃, 𝜓↗↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃] into bicom1 | |
| 4539 | ↔↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃 | Modus ponens 4537, 4538 | |
| 4540 | →↔↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃→↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃 | Subs [𝜑↗↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃, 𝜓↗→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃] into biimp | |
| 4541 | →↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃 | Modus ponens 4539, 4540 | |
| 4542 | →→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃 | Modus ponens 4536, 4541 | imim21b |
| 4543 | →↔⋀𝜑𝜓¬→𝜑¬𝜓↔¬→𝜑¬𝜓⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓] into bicom1 | |
| 4544 | ↔¬→𝜑¬𝜓⋀𝜑𝜓 | Modus ponens df-an, 4543 | pm4.63 |
| 4545 | ↔¬→¬𝜑¬𝜓⋀¬𝜑𝜓 | Subs [𝜑↗¬𝜑] into pm4.63 | pm4.67 |
| 4546 | ↔→𝜑¬𝜓¬¬→𝜑¬𝜓 | Subs [𝜑↗→𝜑¬𝜓] into notnotb | |
| 4547 | ↔↔¬→𝜑¬𝜓⋀𝜑𝜓↔¬¬→𝜑¬𝜓¬⋀𝜑𝜓 | Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗⋀𝜑𝜓] into notbi | |
| 4548 | →↔↔¬→𝜑¬𝜓⋀𝜑𝜓↔¬¬→𝜑¬𝜓¬⋀𝜑𝜓→↔¬→𝜑¬𝜓⋀𝜑𝜓↔¬¬→𝜑¬𝜓¬⋀𝜑𝜓 | Subs [𝜑↗↔¬→𝜑¬𝜓⋀𝜑𝜓, 𝜓↗↔¬¬→𝜑¬𝜓¬⋀𝜑𝜓] into biimp | |
| 4549 | →↔¬→𝜑¬𝜓⋀𝜑𝜓↔¬¬→𝜑¬𝜓¬⋀𝜑𝜓 | Modus ponens 4547, 4548 | |
| 4550 | ↔¬¬→𝜑¬𝜓¬⋀𝜑𝜓 | Modus ponens pm4.63, 4549 | |
| 4551 | →↔¬¬→𝜑¬𝜓¬⋀𝜑𝜓→¬¬→𝜑¬𝜓¬⋀𝜑𝜓 | Subs [𝜑↗¬¬→𝜑¬𝜓, 𝜓↗¬⋀𝜑𝜓] into biimp | |
| 4552 | →¬¬→𝜑¬𝜓¬⋀𝜑𝜓 | Modus ponens 4550, 4551 | |
| 4553 | →↔→𝜑¬𝜓¬¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Subs [𝜑↗→𝜑¬𝜓, 𝜓↗¬¬→𝜑¬𝜓] into biimp | |
| 4554 | →→𝜑¬𝜓¬¬→𝜑¬𝜓 | Modus ponens 4546, 4553 | |
| 4555 | →→¬¬→𝜑¬𝜓¬⋀𝜑𝜓→→𝜑¬𝜓→¬¬→𝜑¬𝜓¬⋀𝜑𝜓 | Subs [𝜑↗→¬¬→𝜑¬𝜓¬⋀𝜑𝜓, 𝜓↗→𝜑¬𝜓] into ax-1 | |
| 4556 | →→𝜑¬𝜓→¬¬→𝜑¬𝜓¬⋀𝜑𝜓 | Modus ponens 4552, 4555 | |
| 4557 | →→→𝜑¬𝜓→¬¬→𝜑¬𝜓¬⋀𝜑𝜓→→→𝜑¬𝜓¬¬→𝜑¬𝜓→→𝜑¬𝜓¬⋀𝜑𝜓 | Subs [𝜑↗→𝜑¬𝜓, 𝜓↗¬¬→𝜑¬𝜓, 𝜒↗¬⋀𝜑𝜓] into ax-2 | |
| 4558 | →→→𝜑¬𝜓¬¬→𝜑¬𝜓→→𝜑¬𝜓¬⋀𝜑𝜓 | Modus ponens 4556, 4557 | |
| 4559 | →→𝜑¬𝜓¬⋀𝜑𝜓 | Modus ponens 4554, 4558 | |
| 4560 | →↔¬¬→𝜑¬𝜓¬⋀𝜑𝜓↔¬⋀𝜑𝜓¬¬→𝜑¬𝜓 | Subs [𝜑↗¬¬→𝜑¬𝜓, 𝜓↗¬⋀𝜑𝜓] into bicom1 | |
| 4561 | ↔¬⋀𝜑𝜓¬¬→𝜑¬𝜓 | Modus ponens 4550, 4560 | |
| 4562 | →↔¬⋀𝜑𝜓¬¬→𝜑¬𝜓→¬⋀𝜑𝜓¬¬→𝜑¬𝜓 | Subs [𝜑↗¬⋀𝜑𝜓, 𝜓↗¬¬→𝜑¬𝜓] into biimp | |
| 4563 | →¬⋀𝜑𝜓¬¬→𝜑¬𝜓 | Modus ponens 4561, 4562 | |
| 4564 | →↔→𝜑¬𝜓¬¬→𝜑¬𝜓↔¬¬→𝜑¬𝜓→𝜑¬𝜓 | Subs [𝜑↗→𝜑¬𝜓, 𝜓↗¬¬→𝜑¬𝜓] into bicom1 | |
| 4565 | ↔¬¬→𝜑¬𝜓→𝜑¬𝜓 | Modus ponens 4546, 4564 | |
| 4566 | →↔¬¬→𝜑¬𝜓→𝜑¬𝜓→¬¬→𝜑¬𝜓→𝜑¬𝜓 | Subs [𝜑↗¬¬→𝜑¬𝜓, 𝜓↗→𝜑¬𝜓] into biimp | |
| 4567 | →→¬¬→𝜑¬𝜓→𝜑¬𝜓→¬⋀𝜑𝜓→¬¬→𝜑¬𝜓→𝜑¬𝜓 | Subs [𝜑↗→¬¬→𝜑¬𝜓→𝜑¬𝜓, 𝜓↗¬⋀𝜑𝜓] into ax-1 | |
| 4568 | →¬⋀𝜑𝜓→¬¬→𝜑¬𝜓→𝜑¬𝜓 | Modus ponens 501, 4567 | |
| 4569 | →→¬⋀𝜑𝜓→¬¬→𝜑¬𝜓→𝜑¬𝜓→→¬⋀𝜑𝜓¬¬→𝜑¬𝜓→¬⋀𝜑𝜓→𝜑¬𝜓 | Subs [𝜑↗¬⋀𝜑𝜓, 𝜓↗¬¬→𝜑¬𝜓, 𝜒↗→𝜑¬𝜓] into ax-2 | |
| 4570 | →→¬⋀𝜑𝜓¬¬→𝜑¬𝜓→¬⋀𝜑𝜓→𝜑¬𝜓 | Modus ponens 4568, 4569 | |
| 4571 | →¬⋀𝜑𝜓→𝜑¬𝜓 | Modus ponens 4563, 4570 | |
| 4572 | →→→𝜑¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓→𝜑¬𝜓↔→𝜑¬𝜓¬⋀𝜑𝜓 | Subs [𝜑↗→𝜑¬𝜓, 𝜓↗¬⋀𝜑𝜓] into impbi | |
| 4573 | →→¬⋀𝜑𝜓→𝜑¬𝜓↔→𝜑¬𝜓¬⋀𝜑𝜓 | Modus ponens 4559, 4572 | |
| 4574 | ↔→𝜑¬𝜓¬⋀𝜑𝜓 | Modus ponens 4571, 4573 | imnan |
| 4575 | →↔𝜓¬¬𝜓→𝜑↔𝜓¬¬𝜓 | Subs [𝜑↗↔𝜓¬¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 4576 | →𝜑↔𝜓¬¬𝜓 | Modus ponens 1915, 4575 | |
| 4577 | ↔→𝜑↔𝜓¬¬𝜓↔→𝜑𝜓→𝜑¬¬𝜓 | Subs [𝜒↗¬¬𝜓] into pm5.74 | |
| 4578 | →↔→𝜑↔𝜓¬¬𝜓↔→𝜑𝜓→𝜑¬¬𝜓→→𝜑↔𝜓¬¬𝜓↔→𝜑𝜓→𝜑¬¬𝜓 | Subs [𝜑↗→𝜑↔𝜓¬¬𝜓, 𝜓↗↔→𝜑𝜓→𝜑¬¬𝜓] into biimp | |
| 4579 | →→𝜑↔𝜓¬¬𝜓↔→𝜑𝜓→𝜑¬¬𝜓 | Modus ponens 4577, 4578 | |
| 4580 | ↔→𝜑𝜓→𝜑¬¬𝜓 | Modus ponens 4576, 4579 | |
| 4581 | ↔→𝜑¬¬𝜓¬⋀𝜑¬𝜓 | Subs [𝜓↗¬𝜓] into imnan | |
| 4582 | →↔→𝜑¬¬𝜓¬⋀𝜑¬𝜓→→𝜑¬¬𝜓¬⋀𝜑¬𝜓 | Subs [𝜑↗→𝜑¬¬𝜓, 𝜓↗¬⋀𝜑¬𝜓] into biimp | |
| 4583 | →→𝜑¬¬𝜓¬⋀𝜑¬𝜓 | Modus ponens 4581, 4582 | |
| 4584 | →↔→𝜑𝜓→𝜑¬¬𝜓→→𝜑𝜓→𝜑¬¬𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑¬¬𝜓] into biimp | |
| 4585 | →→𝜑𝜓→𝜑¬¬𝜓 | Modus ponens 4580, 4584 | |
| 4586 | →→→𝜑¬¬𝜓¬⋀𝜑¬𝜓→→𝜑𝜓→→𝜑¬¬𝜓¬⋀𝜑¬𝜓 | Subs [𝜑↗→→𝜑¬¬𝜓¬⋀𝜑¬𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 4587 | →→𝜑𝜓→→𝜑¬¬𝜓¬⋀𝜑¬𝜓 | Modus ponens 4583, 4586 | |
| 4588 | →→→𝜑𝜓→→𝜑¬¬𝜓¬⋀𝜑¬𝜓→→→𝜑𝜓→𝜑¬¬𝜓→→𝜑𝜓¬⋀𝜑¬𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑¬¬𝜓, 𝜒↗¬⋀𝜑¬𝜓] into ax-2 | |
| 4589 | →→→𝜑𝜓→𝜑¬¬𝜓→→𝜑𝜓¬⋀𝜑¬𝜓 | Modus ponens 4587, 4588 | |
| 4590 | →→𝜑𝜓¬⋀𝜑¬𝜓 | Modus ponens 4585, 4589 | |
| 4591 | →↔→𝜑¬¬𝜓¬⋀𝜑¬𝜓↔¬⋀𝜑¬𝜓→𝜑¬¬𝜓 | Subs [𝜑↗→𝜑¬¬𝜓, 𝜓↗¬⋀𝜑¬𝜓] into bicom1 | |
| 4592 | ↔¬⋀𝜑¬𝜓→𝜑¬¬𝜓 | Modus ponens 4581, 4591 | |
| 4593 | →↔¬⋀𝜑¬𝜓→𝜑¬¬𝜓→¬⋀𝜑¬𝜓→𝜑¬¬𝜓 | Subs [𝜑↗¬⋀𝜑¬𝜓, 𝜓↗→𝜑¬¬𝜓] into biimp | |
| 4594 | →¬⋀𝜑¬𝜓→𝜑¬¬𝜓 | Modus ponens 4592, 4593 | |
| 4595 | →↔→𝜑𝜓→𝜑¬¬𝜓↔→𝜑¬¬𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑¬¬𝜓] into bicom1 | |
| 4596 | ↔→𝜑¬¬𝜓→𝜑𝜓 | Modus ponens 4580, 4595 | |
| 4597 | →↔→𝜑¬¬𝜓→𝜑𝜓→→𝜑¬¬𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑¬¬𝜓, 𝜓↗→𝜑𝜓] into biimp | |
| 4598 | →→𝜑¬¬𝜓→𝜑𝜓 | Modus ponens 4596, 4597 | |
| 4599 | →→→𝜑¬¬𝜓→𝜑𝜓→¬⋀𝜑¬𝜓→→𝜑¬¬𝜓→𝜑𝜓 | Subs [𝜑↗→→𝜑¬¬𝜓→𝜑𝜓, 𝜓↗¬⋀𝜑¬𝜓] into ax-1 | |
| 4600 | →¬⋀𝜑¬𝜓→→𝜑¬¬𝜓→𝜑𝜓 | Modus ponens 4598, 4599 | |
| 4601 | →→¬⋀𝜑¬𝜓→→𝜑¬¬𝜓→𝜑𝜓→→¬⋀𝜑¬𝜓→𝜑¬¬𝜓→¬⋀𝜑¬𝜓→𝜑𝜓 | Subs [𝜑↗¬⋀𝜑¬𝜓, 𝜓↗→𝜑¬¬𝜓, 𝜒↗→𝜑𝜓] into ax-2 | |
| 4602 | →→¬⋀𝜑¬𝜓→𝜑¬¬𝜓→¬⋀𝜑¬𝜓→𝜑𝜓 | Modus ponens 4600, 4601 | |
| 4603 | →¬⋀𝜑¬𝜓→𝜑𝜓 | Modus ponens 4594, 4602 | |
| 4604 | →→→𝜑𝜓¬⋀𝜑¬𝜓→→¬⋀𝜑¬𝜓→𝜑𝜓↔→𝜑𝜓¬⋀𝜑¬𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗¬⋀𝜑¬𝜓] into impbi | |
| 4605 | →→¬⋀𝜑¬𝜓→𝜑𝜓↔→𝜑𝜓¬⋀𝜑¬𝜓 | Modus ponens 4590, 4604 | |
| 4606 | ↔→𝜑𝜓¬⋀𝜑¬𝜓 | Modus ponens 4603, 4605 | iman |
| 4607 | ↔→𝜑𝜑¬⋀𝜑¬𝜑 | Subs [𝜓↗𝜑] into iman | |
| 4608 | →↔→𝜑𝜑¬⋀𝜑¬𝜑→→𝜑𝜑¬⋀𝜑¬𝜑 | Subs [𝜑↗→𝜑𝜑, 𝜓↗¬⋀𝜑¬𝜑] into biimp | |
| 4609 | →→𝜑𝜑¬⋀𝜑¬𝜑 | Modus ponens 4607, 4608 | |
| 4610 | ¬⋀𝜑¬𝜑 | Modus ponens id, 4609 | pm3.24 |
| 4611 | ↔⋀𝜑¬𝜓¬¬⋀𝜑¬𝜓 | Subs [𝜑↗⋀𝜑¬𝜓] into notnotb | |
| 4612 | →↔→𝜑𝜓¬⋀𝜑¬𝜓↔¬⋀𝜑¬𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗¬⋀𝜑¬𝜓] into bicom1 | |
| 4613 | ↔¬⋀𝜑¬𝜓→𝜑𝜓 | Modus ponens iman, 4612 | |
| 4614 | ↔↔¬⋀𝜑¬𝜓→𝜑𝜓↔¬¬⋀𝜑¬𝜓¬→𝜑𝜓 | Subs [𝜑↗¬⋀𝜑¬𝜓, 𝜓↗→𝜑𝜓] into notbi | |
| 4615 | →↔↔¬⋀𝜑¬𝜓→𝜑𝜓↔¬¬⋀𝜑¬𝜓¬→𝜑𝜓→↔¬⋀𝜑¬𝜓→𝜑𝜓↔¬¬⋀𝜑¬𝜓¬→𝜑𝜓 | Subs [𝜑↗↔¬⋀𝜑¬𝜓→𝜑𝜓, 𝜓↗↔¬¬⋀𝜑¬𝜓¬→𝜑𝜓] into biimp | |
| 4616 | →↔¬⋀𝜑¬𝜓→𝜑𝜓↔¬¬⋀𝜑¬𝜓¬→𝜑𝜓 | Modus ponens 4614, 4615 | |
| 4617 | ↔¬¬⋀𝜑¬𝜓¬→𝜑𝜓 | Modus ponens 4613, 4616 | |
| 4618 | →↔¬¬⋀𝜑¬𝜓¬→𝜑𝜓→¬¬⋀𝜑¬𝜓¬→𝜑𝜓 | Subs [𝜑↗¬¬⋀𝜑¬𝜓, 𝜓↗¬→𝜑𝜓] into biimp | |
| 4619 | →¬¬⋀𝜑¬𝜓¬→𝜑𝜓 | Modus ponens 4617, 4618 | |
| 4620 | →↔⋀𝜑¬𝜓¬¬⋀𝜑¬𝜓→⋀𝜑¬𝜓¬¬⋀𝜑¬𝜓 | Subs [𝜑↗⋀𝜑¬𝜓, 𝜓↗¬¬⋀𝜑¬𝜓] into biimp | |
| 4621 | →⋀𝜑¬𝜓¬¬⋀𝜑¬𝜓 | Modus ponens 4611, 4620 | |
| 4622 | →→¬¬⋀𝜑¬𝜓¬→𝜑𝜓→⋀𝜑¬𝜓→¬¬⋀𝜑¬𝜓¬→𝜑𝜓 | Subs [𝜑↗→¬¬⋀𝜑¬𝜓¬→𝜑𝜓, 𝜓↗⋀𝜑¬𝜓] into ax-1 | |
| 4623 | →⋀𝜑¬𝜓→¬¬⋀𝜑¬𝜓¬→𝜑𝜓 | Modus ponens 4619, 4622 | |
| 4624 | →→⋀𝜑¬𝜓→¬¬⋀𝜑¬𝜓¬→𝜑𝜓→→⋀𝜑¬𝜓¬¬⋀𝜑¬𝜓→⋀𝜑¬𝜓¬→𝜑𝜓 | Subs [𝜑↗⋀𝜑¬𝜓, 𝜓↗¬¬⋀𝜑¬𝜓, 𝜒↗¬→𝜑𝜓] into ax-2 | |
| 4625 | →→⋀𝜑¬𝜓¬¬⋀𝜑¬𝜓→⋀𝜑¬𝜓¬→𝜑𝜓 | Modus ponens 4623, 4624 | |
| 4626 | →⋀𝜑¬𝜓¬→𝜑𝜓 | Modus ponens 4621, 4625 | |
| 4627 | →↔¬¬⋀𝜑¬𝜓¬→𝜑𝜓↔¬→𝜑𝜓¬¬⋀𝜑¬𝜓 | Subs [𝜑↗¬¬⋀𝜑¬𝜓, 𝜓↗¬→𝜑𝜓] into bicom1 | |
| 4628 | ↔¬→𝜑𝜓¬¬⋀𝜑¬𝜓 | Modus ponens 4617, 4627 | |
| 4629 | →↔¬→𝜑𝜓¬¬⋀𝜑¬𝜓→¬→𝜑𝜓¬¬⋀𝜑¬𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬¬⋀𝜑¬𝜓] into biimp | |
| 4630 | →¬→𝜑𝜓¬¬⋀𝜑¬𝜓 | Modus ponens 4628, 4629 | |
| 4631 | →↔⋀𝜑¬𝜓¬¬⋀𝜑¬𝜓↔¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓 | Subs [𝜑↗⋀𝜑¬𝜓, 𝜓↗¬¬⋀𝜑¬𝜓] into bicom1 | |
| 4632 | ↔¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓 | Modus ponens 4611, 4631 | |
| 4633 | →↔¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓→¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓 | Subs [𝜑↗¬¬⋀𝜑¬𝜓, 𝜓↗⋀𝜑¬𝜓] into biimp | |
| 4634 | →¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓 | Modus ponens 4632, 4633 | |
| 4635 | →→¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓→¬→𝜑𝜓→¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓 | Subs [𝜑↗→¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 4636 | →¬→𝜑𝜓→¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓 | Modus ponens 4634, 4635 | |
| 4637 | →→¬→𝜑𝜓→¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓→→¬→𝜑𝜓¬¬⋀𝜑¬𝜓→¬→𝜑𝜓⋀𝜑¬𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬¬⋀𝜑¬𝜓, 𝜒↗⋀𝜑¬𝜓] into ax-2 | |
| 4638 | →→¬→𝜑𝜓¬¬⋀𝜑¬𝜓→¬→𝜑𝜓⋀𝜑¬𝜓 | Modus ponens 4636, 4637 | |
| 4639 | →¬→𝜑𝜓⋀𝜑¬𝜓 | Modus ponens 4630, 4638 | |
| 4640 | →→⋀𝜑¬𝜓¬→𝜑𝜓→→¬→𝜑𝜓⋀𝜑¬𝜓↔⋀𝜑¬𝜓¬→𝜑𝜓 | Subs [𝜑↗⋀𝜑¬𝜓, 𝜓↗¬→𝜑𝜓] into impbi | |
| 4641 | →→¬→𝜑𝜓⋀𝜑¬𝜓↔⋀𝜑¬𝜓¬→𝜑𝜓 | Modus ponens 4626, 4640 | |
| 4642 | ↔⋀𝜑¬𝜓¬→𝜑𝜓 | Modus ponens 4639, 4641 | annim |
| 4643 | →↔⋀𝜑¬𝜓¬→𝜑𝜓↔¬→𝜑𝜓⋀𝜑¬𝜓 | Subs [𝜑↗⋀𝜑¬𝜓, 𝜓↗¬→𝜑𝜓] into bicom1 | |
| 4644 | ↔¬→𝜑𝜓⋀𝜑¬𝜓 | Modus ponens annim, 4643 | pm4.61 |
| 4645 | ↔¬→¬𝜑𝜓⋀¬𝜑¬𝜓 | Subs [𝜑↗¬𝜑] into pm4.61 | pm4.65 |
| 4646 | →→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→⋀𝜑𝜓𝜒] into id | |
| 4647 | →⋀𝜑𝜓⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓] into id | |
| 4648 | →⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→⋀𝜑𝜓𝜒] into ax-1 | |
| 4649 | →→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓→⋀𝜑𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓 | Subs [𝜑↗→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 4650 | →⋀𝜑𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓 | Modus ponens 4648, 4649 | |
| 4651 | →→⋀𝜑𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗→→⋀𝜑𝜓𝜒⋀𝜑𝜓] into ax-2 | |
| 4652 | →→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓 | Modus ponens 4650, 4651 | |
| 4653 | →→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒 | Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗⋀𝜑𝜓] into ax-2 | |
| 4654 | →→→⋀𝜑𝜓𝜒⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒 | Modus ponens 4646, 4653 | |
| 4655 | →→→→⋀𝜑𝜓𝜒⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒→⋀𝜑𝜓→→→⋀𝜑𝜓𝜒⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒 | Subs [𝜑↗→→→⋀𝜑𝜓𝜒⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 4656 | →⋀𝜑𝜓→→→⋀𝜑𝜓𝜒⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒 | Modus ponens 4654, 4655 | |
| 4657 | →→⋀𝜑𝜓→→→⋀𝜑𝜓𝜒⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→→⋀𝜑𝜓𝜒⋀𝜑𝜓, 𝜒↗→→⋀𝜑𝜓𝜒𝜒] into ax-2 | |
| 4658 | →→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒 | Modus ponens 4656, 4657 | |
| 4659 | →⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒 | Modus ponens 4648, 4658 | |
| 4660 | →↔¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓⋀𝜑𝜓 | Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗⋀𝜑𝜓] into biimp | |
| 4661 | →¬→𝜑¬𝜓⋀𝜑𝜓 | Modus ponens pm4.63, 4660 | |
| 4662 | →→⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒→¬→𝜑¬𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒 | Subs [𝜑↗→⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒, 𝜓↗¬→𝜑¬𝜓] into ax-1 | |
| 4663 | →¬→𝜑¬𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒 | Modus ponens 4659, 4662 | |
| 4664 | →→¬→𝜑¬𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒→→¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓→→⋀𝜑𝜓𝜒𝜒 | Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗→→⋀𝜑𝜓𝜒𝜒] into ax-2 | |
| 4665 | →→¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓→→⋀𝜑𝜓𝜒𝜒 | Modus ponens 4663, 4664 | |
| 4666 | →¬→𝜑¬𝜓→→⋀𝜑𝜓𝜒𝜒 | Modus ponens 4661, 4665 | |
| 4667 | →→¬→𝜑¬𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓→¬→𝜑¬𝜓→→⋀𝜑𝜓𝜒𝜒 | Subs [𝜑↗→¬→𝜑¬𝜓→→⋀𝜑𝜓𝜒𝜒] into ax-1 | |
| 4668 | →𝜓→¬→𝜑¬𝜓→→⋀𝜑𝜓𝜒𝜒 | Modus ponens 4666, 4667 | |
| 4669 | →→𝜓→¬→𝜑¬𝜓→→⋀𝜑𝜓𝜒𝜒→→𝜓¬→𝜑¬𝜓→𝜓→→⋀𝜑𝜓𝜒𝜒 | Subs [𝜑↗𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→→⋀𝜑𝜓𝜒𝜒] into ax-2 | |
| 4670 | →→𝜓¬→𝜑¬𝜓→𝜓→→⋀𝜑𝜓𝜒𝜒 | Modus ponens 4668, 4669 | |
| 4671 | →→→𝜓¬→𝜑¬𝜓→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜑→→𝜓¬→𝜑¬𝜓→𝜓→→⋀𝜑𝜓𝜒𝜒 | Subs [𝜑↗→→𝜓¬→𝜑¬𝜓→𝜓→→⋀𝜑𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1 | |
| 4672 | →𝜑→→𝜓¬→𝜑¬𝜓→𝜓→→⋀𝜑𝜓𝜒𝜒 | Modus ponens 4670, 4671 | |
| 4673 | →→𝜑→→𝜓¬→𝜑¬𝜓→𝜓→→⋀𝜑𝜓𝜒𝜒→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→𝜓→→⋀𝜑𝜓𝜒𝜒 | Subs [𝜓↗→𝜓¬→𝜑¬𝜓, 𝜒↗→𝜓→→⋀𝜑𝜓𝜒𝜒] into ax-2 | |
| 4674 | →→𝜑→𝜓¬→𝜑¬𝜓→𝜑→𝜓→→⋀𝜑𝜓𝜒𝜒 | Modus ponens 4672, 4673 | |
| 4675 | →𝜑→𝜓→→⋀𝜑𝜓𝜒𝜒 | Modus ponens pm3.2im, 4674 | |
| 4676 | →→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒 | Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗𝜒] into pm2.27 | |
| 4677 | →→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒 | Subs [𝜑↗→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒, 𝜓↗𝜑] into ax-1 | |
| 4678 | →𝜑→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒 | Modus ponens 4676, 4677 | |
| 4679 | →→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒 | Subs [𝜑↗→𝜓→→⋀𝜑𝜓𝜒𝜒, 𝜓↗→⋀𝜑𝜓𝜒] into ax-1 | |
| 4680 | →→→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜑→→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒 | Subs [𝜑↗→→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1 | |
| 4681 | →𝜑→→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒 | Modus ponens 4679, 4680 | |
| 4682 | →→𝜑→→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→𝜑→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒 | Subs [𝜓↗→𝜓→→⋀𝜑𝜓𝜒𝜒, 𝜒↗→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒] into ax-2 | |
| 4683 | →→𝜑→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒 | Modus ponens 4681, 4682 | |
| 4684 | →𝜑→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒 | Modus ponens 4675, 4683 | |
| 4685 | →→→→⋀𝜑𝜓𝜒𝜒𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒 | Subs [𝜑↗→→⋀𝜑𝜓𝜒𝜒, 𝜓↗𝜒, 𝜒↗𝜓] into imim2 | |
| 4686 | →→→→→⋀𝜑𝜓𝜒𝜒𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→⋀𝜑𝜓𝜒→→→→⋀𝜑𝜓𝜒𝜒𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒 | Subs [𝜑↗→→→→⋀𝜑𝜓𝜒𝜒𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜒] into ax-1 | |
| 4687 | →→⋀𝜑𝜓𝜒→→→→⋀𝜑𝜓𝜒𝜒𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒 | Modus ponens 4685, 4686 | |
| 4688 | →→→⋀𝜑𝜓𝜒→→→→⋀𝜑𝜓𝜒𝜒𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒 | Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→→→⋀𝜑𝜓𝜒𝜒𝜒, 𝜒↗→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒] into ax-2 | |
| 4689 | →→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒 | Modus ponens 4687, 4688 | |
| 4690 | →→→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒 | Subs [𝜑↗→→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 4691 | →𝜑→→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒 | Modus ponens 4689, 4690 | |
| 4692 | →→𝜑→→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→𝜑→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒 | Subs [𝜓↗→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒, 𝜒↗→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒] into ax-2 | |
| 4693 | →→𝜑→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒 | Modus ponens 4691, 4692 | |
| 4694 | →𝜑→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒 | Modus ponens 4678, 4693 | |
| 4695 | →→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒 | Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→𝜓→→⋀𝜑𝜓𝜒𝜒, 𝜒↗→𝜓𝜒] into ax-2 | |
| 4696 | →→→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒 | Subs [𝜑↗→→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 4697 | →𝜑→→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒 | Modus ponens 4695, 4696 | |
| 4698 | →→𝜑→→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→𝜑→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒 | Subs [𝜓↗→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒, 𝜒↗→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒] into ax-2 | |
| 4699 | →→𝜑→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒 | Modus ponens 4697, 4698 | |
| 4700 | →𝜑→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒 | Modus ponens 4694, 4699 | |
| 4701 | →→𝜑→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→𝜑→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→𝜓𝜒 | Subs [𝜓↗→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒, 𝜒↗→→⋀𝜑𝜓𝜒→𝜓𝜒] into ax-2 | |
| 4702 | →→𝜑→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→𝜓𝜒 | Modus ponens 4700, 4701 | |
| 4703 | →𝜑→→⋀𝜑𝜓𝜒→𝜓𝜒 | Modus ponens 4684, 4702 | |
| 4704 | →→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒 | Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 4705 | →→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒 | Subs [𝜑↗→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜒] into ax-1 | |
| 4706 | →→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒 | Modus ponens 4704, 4705 | |
| 4707 | →→→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒 | Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜒, 𝜒↗→𝜑→⋀𝜑𝜓𝜒] into ax-2 | |
| 4708 | →→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒 | Modus ponens 4706, 4707 | |
| 4709 | →→𝜑→→⋀𝜑𝜓𝜒→𝜓𝜒→→𝜑→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒 | Subs [𝜓↗→⋀𝜑𝜓𝜒, 𝜒↗→𝜓𝜒] into ax-2 | |
| 4710 | →→𝜑→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒 | Modus ponens 4703, 4709 | |
| 4711 | →→→𝜑→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜑→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒 | Subs [𝜑↗→→𝜑→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜒] into ax-1 | |
| 4712 | →→⋀𝜑𝜓𝜒→→𝜑→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒 | Modus ponens 4710, 4711 | |
| 4713 | →→→⋀𝜑𝜓𝜒→→𝜑→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒 | Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→𝜑→⋀𝜑𝜓𝜒, 𝜒↗→𝜑→𝜓𝜒] into ax-2 | |
| 4714 | →→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒 | Modus ponens 4712, 4713 | |
| 4715 | →→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒 | Modus ponens 4704, 4714 | pm3.3 |
| 4716 | →𝜓→→𝜑→𝜓𝜒𝜓 | Subs [𝜑↗𝜓, 𝜓↗→𝜑→𝜓𝜒] into ax-1 | |
| 4717 | →→𝜓→→𝜑→𝜓𝜒𝜓→𝜓→𝜓→→𝜑→𝜓𝜒𝜓 | Subs [𝜑↗→𝜓→→𝜑→𝜓𝜒𝜓] into ax-1 | |
| 4718 | →𝜓→𝜓→→𝜑→𝜓𝜒𝜓 | Modus ponens 4716, 4717 | |
| 4719 | →→𝜓→𝜓→→𝜑→𝜓𝜒𝜓→→𝜓𝜓→𝜓→→𝜑→𝜓𝜒𝜓 | Subs [𝜑↗𝜓, 𝜒↗→→𝜑→𝜓𝜒𝜓] into ax-2 | |
| 4720 | →→𝜓𝜓→𝜓→→𝜑→𝜓𝜒𝜓 | Modus ponens 4718, 4719 | |
| 4721 | →→→𝜑→𝜓𝜒→𝜓→𝜑𝜒→→→𝜑→𝜓𝜒𝜓→→𝜑→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜒↗→𝜑𝜒] into ax-2 | |
| 4722 | →→→𝜑→𝜓𝜒𝜓→→𝜑→𝜓𝜒→𝜑𝜒 | Modus ponens pm2.04, 4721 | |
| 4723 | →→→→𝜑→𝜓𝜒𝜓→→𝜑→𝜓𝜒→𝜑𝜒→𝜓→→→𝜑→𝜓𝜒𝜓→→𝜑→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→→→𝜑→𝜓𝜒𝜓→→𝜑→𝜓𝜒→𝜑𝜒] into ax-1 | |
| 4724 | →𝜓→→→𝜑→𝜓𝜒𝜓→→𝜑→𝜓𝜒→𝜑𝜒 | Modus ponens 4722, 4723 | |
| 4725 | →→𝜓→→→𝜑→𝜓𝜒𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→→𝜑→𝜓𝜒𝜓→𝜓→→𝜑→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗𝜓, 𝜓↗→→𝜑→𝜓𝜒𝜓, 𝜒↗→→𝜑→𝜓𝜒→𝜑𝜒] into ax-2 | |
| 4726 | →→𝜓→→𝜑→𝜓𝜒𝜓→𝜓→→𝜑→𝜓𝜒→𝜑𝜒 | Modus ponens 4724, 4725 | |
| 4727 | →𝜓→→𝜑→𝜓𝜒→𝜑𝜒 | Modus ponens 4716, 4726 | |
| 4728 | →→𝜑→→𝜑𝜒𝜒→𝜓→𝜑→→𝜑𝜒𝜒 | Subs [𝜑↗→𝜑→→𝜑𝜒𝜒] into ax-1 | |
| 4729 | →𝜓→𝜑→→𝜑𝜒𝜒 | Modus ponens 264, 4728 | |
| 4730 | →→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→→𝜑→𝜓𝜒→𝜑𝜒, 𝜓↗𝜑] into ax-1 | |
| 4731 | →→→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜓→→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒→𝜑𝜒] into ax-1 | |
| 4732 | →𝜓→→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒→𝜑𝜒 | Modus ponens 4730, 4731 | |
| 4733 | →→𝜓→→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→𝜓→𝜑→→𝜑→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗𝜓, 𝜓↗→→𝜑→𝜓𝜒→𝜑𝜒, 𝜒↗→𝜑→→𝜑→𝜓𝜒→𝜑𝜒] into ax-2 | |
| 4734 | →→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→𝜓→𝜑→→𝜑→𝜓𝜒→𝜑𝜒 | Modus ponens 4732, 4733 | |
| 4735 | →𝜓→𝜑→→𝜑→𝜓𝜒→𝜑𝜒 | Modus ponens 4727, 4734 | |
| 4736 | →→→𝜑𝜒𝜒→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗→𝜑𝜒, 𝜓↗𝜒, 𝜒↗→𝜑→𝜓𝜒] into imim2 | |
| 4737 | →→→→𝜑𝜒𝜒→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→𝜑→→→𝜑𝜒𝜒→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗→→→𝜑𝜒𝜒→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1 | |
| 4738 | →𝜑→→→𝜑𝜒𝜒→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒 | Modus ponens 4736, 4737 | |
| 4739 | →→𝜑→→→𝜑𝜒𝜒→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒 | Subs [𝜓↗→→𝜑𝜒𝜒, 𝜒↗→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒] into ax-2 | |
| 4740 | →→𝜑→→𝜑𝜒𝜒→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒 | Modus ponens 4738, 4739 | |
| 4741 | →→→𝜑→→𝜑𝜒𝜒→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→𝜓→→𝜑→→𝜑𝜒𝜒→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗→→𝜑→→𝜑𝜒𝜒→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒] into ax-1 | |
| 4742 | →𝜓→→𝜑→→𝜑𝜒𝜒→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒 | Modus ponens 4740, 4741 | |
| 4743 | →→𝜓→→𝜑→→𝜑𝜒𝜒→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→→𝜓→𝜑→→𝜑𝜒𝜒→𝜓→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗𝜓, 𝜓↗→𝜑→→𝜑𝜒𝜒, 𝜒↗→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒] into ax-2 | |
| 4744 | →→𝜓→𝜑→→𝜑𝜒𝜒→𝜓→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒 | Modus ponens 4742, 4743 | |
| 4745 | →𝜓→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒 | Modus ponens 4729, 4744 | |
| 4746 | →→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒 | Subs [𝜓↗→→𝜑→𝜓𝜒→𝜑𝜒, 𝜒↗→→𝜑→𝜓𝜒𝜒] into ax-2 | |
| 4747 | →→→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒→𝜓→→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗→→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒] into ax-1 | |
| 4748 | →𝜓→→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒 | Modus ponens 4746, 4747 | |
| 4749 | →→𝜓→→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒→→𝜓→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→𝜓→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗𝜓, 𝜓↗→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒, 𝜒↗→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒] into ax-2 | |
| 4750 | →→𝜓→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→𝜓→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒 | Modus ponens 4748, 4749 | |
| 4751 | →𝜓→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒 | Modus ponens 4745, 4750 | |
| 4752 | →→𝜓→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒→→𝜓→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜓→𝜑→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗𝜓, 𝜓↗→𝜑→→𝜑→𝜓𝜒→𝜑𝜒, 𝜒↗→𝜑→→𝜑→𝜓𝜒𝜒] into ax-2 | |
| 4753 | →→𝜓→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜓→𝜑→→𝜑→𝜓𝜒𝜒 | Modus ponens 4751, 4752 | |
| 4754 | →𝜓→𝜑→→𝜑→𝜓𝜒𝜒 | Modus ponens 4735, 4753 | |
| 4755 | →→𝜓→𝜑→→𝜑→𝜓𝜒𝜒→→𝜓𝜑→𝜓→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗𝜓, 𝜓↗𝜑, 𝜒↗→→𝜑→𝜓𝜒𝜒] into ax-2 | |
| 4756 | →→𝜓𝜑→𝜓→→𝜑→𝜓𝜒𝜒 | Modus ponens 4754, 4755 | |
| 4757 | →→→𝜓𝜑→𝜓→→𝜑→𝜓𝜒𝜒→𝜑→→𝜓𝜑→𝜓→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗→→𝜓𝜑→𝜓→→𝜑→𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1 | |
| 4758 | →𝜑→→𝜓𝜑→𝜓→→𝜑→𝜓𝜒𝜒 | Modus ponens 4756, 4757 | |
| 4759 | →→𝜑→→𝜓𝜑→𝜓→→𝜑→𝜓𝜒𝜒→→𝜑→𝜓𝜑→𝜑→𝜓→→𝜑→𝜓𝜒𝜒 | Subs [𝜓↗→𝜓𝜑, 𝜒↗→𝜓→→𝜑→𝜓𝜒𝜒] into ax-2 | |
| 4760 | →→𝜑→𝜓𝜑→𝜑→𝜓→→𝜑→𝜓𝜒𝜒 | Modus ponens 4758, 4759 | |
| 4761 | →𝜑→𝜓→→𝜑→𝜓𝜒𝜒 | Modus ponens ax-1, 4760 | |
| 4762 | →→𝜑→𝜓→→𝜑→𝜓𝜒𝜒→→𝜑𝜓→𝜑→→𝜑→𝜓𝜒𝜒 | Subs [𝜒↗→→𝜑→𝜓𝜒𝜒] into ax-2 | |
| 4763 | →→𝜑𝜓→𝜑→→𝜑→𝜓𝜒𝜒 | Modus ponens 4761, 4762 | |
| 4764 | →→→𝜑𝜓→𝜑→→𝜑→𝜓𝜒𝜒→¬¬𝜓→→𝜑𝜓→𝜑→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜑→→𝜑→𝜓𝜒𝜒, 𝜓↗¬¬𝜓] into ax-1 | |
| 4765 | →¬¬𝜓→→𝜑𝜓→𝜑→→𝜑→𝜓𝜒𝜒 | Modus ponens 4763, 4764 | |
| 4766 | →→¬¬𝜓→→𝜑𝜓→𝜑→→𝜑→𝜓𝜒𝜒→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑→→𝜑→𝜓𝜒𝜒] into ax-2 | |
| 4767 | →→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑→→𝜑→𝜓𝜒𝜒 | Modus ponens 4765, 4766 | |
| 4768 | →¬¬𝜓→𝜑→→𝜑→𝜓𝜒𝜒 | Modus ponens 575, 4767 | |
| 4769 | →→¬¬𝜓→𝜑→→𝜑→𝜓𝜒𝜒→→¬¬𝜓𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑, 𝜒↗→→𝜑→𝜓𝜒𝜒] into ax-2 | |
| 4770 | →→¬¬𝜓𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒 | Modus ponens 4768, 4769 | |
| 4771 | →→→¬¬𝜓𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒→𝜑→→¬¬𝜓𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗→→¬¬𝜓𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1 | |
| 4772 | →𝜑→→¬¬𝜓𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒 | Modus ponens 4770, 4771 | |
| 4773 | →→𝜑→→¬¬𝜓𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒 | Subs [𝜓↗→¬¬𝜓𝜑, 𝜒↗→¬¬𝜓→→𝜑→𝜓𝜒𝜒] into ax-2 | |
| 4774 | →→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒 | Modus ponens 4772, 4773 | |
| 4775 | →𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒 | Modus ponens 581, 4774 | |
| 4776 | →→→𝜑→𝜓𝜒𝜒¬¬→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗→→𝜑→𝜓𝜒𝜒] into notnot | |
| 4777 | →→→→𝜑→𝜓𝜒𝜒¬¬→→𝜑→𝜓𝜒𝜒→¬¬𝜓→→→𝜑→𝜓𝜒𝜒¬¬→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗→→→𝜑→𝜓𝜒𝜒¬¬→→𝜑→𝜓𝜒𝜒, 𝜓↗¬¬𝜓] into ax-1 | |
| 4778 | →¬¬𝜓→→→𝜑→𝜓𝜒𝜒¬¬→→𝜑→𝜓𝜒𝜒 | Modus ponens 4776, 4777 | |
| 4779 | →→¬¬𝜓→→→𝜑→𝜓𝜒𝜒¬¬→→𝜑→𝜓𝜒𝜒→→¬¬𝜓→→𝜑→𝜓𝜒𝜒→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗¬¬𝜓, 𝜓↗→→𝜑→𝜓𝜒𝜒, 𝜒↗¬¬→→𝜑→𝜓𝜒𝜒] into ax-2 | |
| 4780 | →→¬¬𝜓→→𝜑→𝜓𝜒𝜒→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒 | Modus ponens 4778, 4779 | |
| 4781 | →→→¬¬𝜓→→𝜑→𝜓𝜒𝜒→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→𝜑→→¬¬𝜓→→𝜑→𝜓𝜒𝜒→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗→→¬¬𝜓→→𝜑→𝜓𝜒𝜒→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1 | |
| 4782 | →𝜑→→¬¬𝜓→→𝜑→𝜓𝜒𝜒→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒 | Modus ponens 4780, 4781 | |
| 4783 | →→𝜑→→¬¬𝜓→→𝜑→𝜓𝜒𝜒→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→→𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒→𝜑→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒 | Subs [𝜓↗→¬¬𝜓→→𝜑→𝜓𝜒𝜒, 𝜒↗→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒] into ax-2 | |
| 4784 | →→𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒→𝜑→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒 | Modus ponens 4782, 4783 | |
| 4785 | →𝜑→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒 | Modus ponens 4775, 4784 | |
| 4786 | →→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬→→𝜑→𝜓𝜒𝜒] into ax-3 | |
| 4787 | →→→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒¬𝜓→𝜑→→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒¬𝜓 | Subs [𝜑↗→→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 4788 | →𝜑→→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒¬𝜓 | Modus ponens 4786, 4787 | |
| 4789 | →→𝜑→→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒¬𝜓→→𝜑→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→𝜑→¬→→𝜑→𝜓𝜒𝜒¬𝜓 | Subs [𝜓↗→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒, 𝜒↗→¬→→𝜑→𝜓𝜒𝜒¬𝜓] into ax-2 | |
| 4790 | →→𝜑→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→𝜑→¬→→𝜑→𝜓𝜒𝜒¬𝜓 | Modus ponens 4788, 4789 | |
| 4791 | →𝜑→¬→→𝜑→𝜓𝜒𝜒¬𝜓 | Modus ponens 4785, 4790 | |
| 4792 | →¬→→𝜑→𝜓𝜒𝜒¬→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒] into id | |
| 4793 | →¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1 | |
| 4794 | →→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒, 𝜓↗¬→→𝜑→𝜓𝜒𝜒] into ax-1 | |
| 4795 | →¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒 | Modus ponens 4793, 4794 | |
| 4796 | →→¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒→→¬→→𝜑→𝜓𝜒𝜒¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗¬→→𝜑→𝜓𝜒𝜒, 𝜒↗→𝜑¬→→𝜑→𝜓𝜒𝜒] into ax-2 | |
| 4797 | →→¬→→𝜑→𝜓𝜒𝜒¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒 | Modus ponens 4795, 4796 | |
| 4798 | →→𝜑→¬→→𝜑→𝜓𝜒𝜒¬𝜓→→𝜑¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓 | Subs [𝜓↗¬→→𝜑→𝜓𝜒𝜒, 𝜒↗¬𝜓] into ax-2 | |
| 4799 | →→𝜑¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓 | Modus ponens 4791, 4798 | |
| 4800 | →→→𝜑¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒→→𝜑¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓 | Subs [𝜑↗→→𝜑¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓, 𝜓↗¬→→𝜑→𝜓𝜒𝜒] into ax-1 | |
| 4801 | →¬→→𝜑→𝜓𝜒𝜒→→𝜑¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓 | Modus ponens 4799, 4800 | |
| 4802 | →→¬→→𝜑→𝜓𝜒𝜒→→𝜑¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓→→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓 | Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗→𝜑¬→→𝜑→𝜓𝜒𝜒, 𝜒↗→𝜑¬𝜓] into ax-2 | |
| 4803 | →→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓 | Modus ponens 4801, 4802 | |
| 4804 | →¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓 | Modus ponens 4793, 4803 | |
| 4805 | →→¬→𝜑¬𝜓¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒→¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬→→𝜑→𝜓𝜒𝜒] into ax-1 | |
| 4806 | →¬→→𝜑→𝜓𝜒𝜒→¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 619, 4805 | |
| 4807 | →¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓 | Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗¬→→𝜑→𝜓𝜒𝜒] into ax-1 | |
| 4808 | →→¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓 | Subs [𝜑↗→¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1 | |
| 4809 | →¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓 | Modus ponens 4807, 4808 | |
| 4810 | →→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓 | Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓] into ax-2 | |
| 4811 | →→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓 | Modus ponens 4809, 4810 | |
| 4812 | →¬¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓 | Modus ponens 622, 4811 | |
| 4813 | →→¬→→𝜑→𝜓𝜒𝜒→¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓 | Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗¬→𝜑¬𝜓, 𝜒↗¬→𝜑¬𝜓] into ax-2 | |
| 4814 | →→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓 | Modus ponens 4806, 4813 | |
| 4815 | →→→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓 | Subs [𝜑↗→→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1 | |
| 4816 | →¬¬¬→𝜑¬𝜓→→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓 | Modus ponens 4814, 4815 | |
| 4817 | →→¬¬¬→𝜑¬𝜓→→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓 | Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓, 𝜒↗→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓] into ax-2 | |
| 4818 | →→¬¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓 | Modus ponens 4816, 4817 | |
| 4819 | →¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1 | |
| 4820 | →→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒, 𝜓↗¬→→𝜑→𝜓𝜒𝜒] into ax-1 | |
| 4821 | →¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒 | Modus ponens 4819, 4820 | |
| 4822 | →→¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→→¬→→𝜑→𝜓𝜒𝜒¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗¬→→𝜑→𝜓𝜒𝜒, 𝜒↗→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒] into ax-2 | |
| 4823 | →→¬→→𝜑→𝜓𝜒𝜒¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒 | Modus ponens 4821, 4822 | |
| 4824 | →→¬¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬→→𝜑→𝜓𝜒𝜒, 𝜒↗¬→𝜑¬𝜓] into ax-2 | |
| 4825 | →→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 4812, 4824 | |
| 4826 | →→→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒→→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬→→𝜑→𝜓𝜒𝜒] into ax-1 | |
| 4827 | →¬→→𝜑→𝜓𝜒𝜒→→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 4825, 4826 | |
| 4828 | →→¬→→𝜑→𝜓𝜒𝜒→→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒, 𝜒↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓] into ax-2 | |
| 4829 | →→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 4827, 4828 | |
| 4830 | →¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 4819, 4829 | |
| 4831 | →→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓, 𝜓↗¬→→𝜑→𝜓𝜒𝜒] into ax-1 | |
| 4832 | →¬→→𝜑→𝜓𝜒𝜒→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Modus ponens 647, 4831 | |
| 4833 | →→¬→→𝜑→𝜓𝜒𝜒→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜒↗→→𝜑¬𝜓¬¬→𝜑¬𝜓] into ax-2 | |
| 4834 | →→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Modus ponens 4832, 4833 | |
| 4835 | →¬→→𝜑→𝜓𝜒𝜒→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Modus ponens 4830, 4834 | |
| 4836 | →→¬→→𝜑→𝜓𝜒𝜒→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬¬→𝜑¬𝜓 | Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗→𝜑¬𝜓, 𝜒↗¬¬→𝜑¬𝜓] into ax-2 | |
| 4837 | →→¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬¬→𝜑¬𝜓 | Modus ponens 4835, 4836 | |
| 4838 | →¬→→𝜑→𝜓𝜒𝜒¬¬→𝜑¬𝜓 | Modus ponens 4804, 4837 | |
| 4839 | →→¬→→𝜑→𝜓𝜒𝜒¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗→→𝜑→𝜓𝜒𝜒, 𝜓↗¬→𝜑¬𝜓] into ax-3 | |
| 4840 | →¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜒 | Modus ponens 4838, 4839 | |
| 4841 | →↔⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓¬→𝜑¬𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓] into biimp | |
| 4842 | →⋀𝜑𝜓¬→𝜑¬𝜓 | Modus ponens df-an, 4841 | |
| 4843 | →→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜒→⋀𝜑𝜓→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜒, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 4844 | →⋀𝜑𝜓→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜒 | Modus ponens 4840, 4843 | |
| 4845 | →→⋀𝜑𝜓→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜒→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓→→𝜑→𝜓𝜒𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→→𝜑→𝜓𝜒𝜒] into ax-2 | |
| 4846 | →→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓→→𝜑→𝜓𝜒𝜒 | Modus ponens 4844, 4845 | |
| 4847 | →⋀𝜑𝜓→→𝜑→𝜓𝜒𝜒 | Modus ponens 4842, 4846 | |
| 4848 | →→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 4849 | →→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒 | Subs [𝜑↗→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1 | |
| 4850 | →→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒 | Modus ponens 4848, 4849 | |
| 4851 | →→→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒→→→𝜑→𝜓𝜒→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→⋀𝜑𝜓→𝜑→𝜓𝜒] into ax-2 | |
| 4852 | →→→𝜑→𝜓𝜒→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒 | Modus ponens 4850, 4851 | |
| 4853 | →→⋀𝜑𝜓→→𝜑→𝜓𝜒𝜒→→⋀𝜑𝜓→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜑→𝜓𝜒] into ax-2 | |
| 4854 | →→⋀𝜑𝜓→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 4847, 4853 | |
| 4855 | →→→⋀𝜑𝜓→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→𝜓𝜒→→⋀𝜑𝜓→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→→⋀𝜑𝜓→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1 | |
| 4856 | →→𝜑→𝜓𝜒→→⋀𝜑𝜓→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 4854, 4855 | |
| 4857 | →→→𝜑→𝜓𝜒→→⋀𝜑𝜓→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑𝜓→𝜑→𝜓𝜒, 𝜒↗→⋀𝜑𝜓𝜒] into ax-2 | |
| 4858 | →→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 4856, 4857 | |
| 4859 | →→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 4848, 4858 | pm3.31 |
| 4860 | →→→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒→→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒↔→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒 | Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into impbi | |
| 4861 | →→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒↔→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒 | Modus ponens pm3.3, 4860 | |
| 4862 | ↔→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒 | Modus ponens pm3.31, 4861 | impexp |
| 4863 | →⋀𝜓𝜑⋀𝜓𝜑 | Subs [𝜑↗⋀𝜓𝜑] into id | |
| 4864 | ↔⋀𝜓𝜑¬→𝜓¬𝜑 | Subs [𝜑↗𝜓, 𝜓↗𝜑] into df-an | |
| 4865 | →↔⋀𝜓𝜑¬→𝜓¬𝜑↔¬→𝜓¬𝜑⋀𝜓𝜑 | Subs [𝜑↗⋀𝜓𝜑, 𝜓↗¬→𝜓¬𝜑] into bicom1 | |
| 4866 | ↔¬→𝜓¬𝜑⋀𝜓𝜑 | Modus ponens 4864, 4865 | |
| 4867 | →↔¬→𝜓¬𝜑⋀𝜓𝜑→¬→𝜓¬𝜑⋀𝜓𝜑 | Subs [𝜑↗¬→𝜓¬𝜑, 𝜓↗⋀𝜓𝜑] into biimp | |
| 4868 | →¬→𝜓¬𝜑⋀𝜓𝜑 | Modus ponens 4866, 4867 | |
| 4869 | →→⋀𝜓𝜑⋀𝜓𝜑→¬→𝜓¬𝜑→⋀𝜓𝜑⋀𝜓𝜑 | Subs [𝜑↗→⋀𝜓𝜑⋀𝜓𝜑, 𝜓↗¬→𝜓¬𝜑] into ax-1 | |
| 4870 | →¬→𝜓¬𝜑→⋀𝜓𝜑⋀𝜓𝜑 | Modus ponens 4863, 4869 | |
| 4871 | →→¬→𝜓¬𝜑→⋀𝜓𝜑⋀𝜓𝜑→→¬→𝜓¬𝜑⋀𝜓𝜑→¬→𝜓¬𝜑⋀𝜓𝜑 | Subs [𝜑↗¬→𝜓¬𝜑, 𝜓↗⋀𝜓𝜑, 𝜒↗⋀𝜓𝜑] into ax-2 | |
| 4872 | →→¬→𝜓¬𝜑⋀𝜓𝜑→¬→𝜓¬𝜑⋀𝜓𝜑 | Modus ponens 4870, 4871 | |
| 4873 | →𝜓→𝜑¬→𝜓¬𝜑 | Subs [𝜑↗𝜓, 𝜓↗𝜑] into pm3.2im | |
| 4874 | →→¬→𝜓¬𝜑⋀𝜓𝜑→𝜑→¬→𝜓¬𝜑⋀𝜓𝜑 | Subs [𝜑↗→¬→𝜓¬𝜑⋀𝜓𝜑, 𝜓↗𝜑] into ax-1 | |
| 4875 | →𝜑→¬→𝜓¬𝜑⋀𝜓𝜑 | Modus ponens 4868, 4874 | |
| 4876 | →→𝜑→¬→𝜓¬𝜑⋀𝜓𝜑→→𝜑¬→𝜓¬𝜑→𝜑⋀𝜓𝜑 | Subs [𝜓↗¬→𝜓¬𝜑, 𝜒↗⋀𝜓𝜑] into ax-2 | |
| 4877 | →→𝜑¬→𝜓¬𝜑→𝜑⋀𝜓𝜑 | Modus ponens 4875, 4876 | |
| 4878 | →→→𝜑¬→𝜓¬𝜑→𝜑⋀𝜓𝜑→𝜓→→𝜑¬→𝜓¬𝜑→𝜑⋀𝜓𝜑 | Subs [𝜑↗→→𝜑¬→𝜓¬𝜑→𝜑⋀𝜓𝜑] into ax-1 | |
| 4879 | →𝜓→→𝜑¬→𝜓¬𝜑→𝜑⋀𝜓𝜑 | Modus ponens 4877, 4878 | |
| 4880 | →→𝜓→→𝜑¬→𝜓¬𝜑→𝜑⋀𝜓𝜑→→𝜓→𝜑¬→𝜓¬𝜑→𝜓→𝜑⋀𝜓𝜑 | Subs [𝜑↗𝜓, 𝜓↗→𝜑¬→𝜓¬𝜑, 𝜒↗→𝜑⋀𝜓𝜑] into ax-2 | |
| 4881 | →→𝜓→𝜑¬→𝜓¬𝜑→𝜓→𝜑⋀𝜓𝜑 | Modus ponens 4879, 4880 | |
| 4882 | →𝜓→𝜑⋀𝜓𝜑 | Modus ponens 4873, 4881 | |
| 4883 | →→𝜓→𝜑⋀𝜓𝜑→→𝜓𝜑→𝜓⋀𝜓𝜑 | Subs [𝜑↗𝜓, 𝜓↗𝜑, 𝜒↗⋀𝜓𝜑] into ax-2 | |
| 4884 | →→𝜓𝜑→𝜓⋀𝜓𝜑 | Modus ponens 4882, 4883 | |
| 4885 | →→→𝜓𝜑→𝜓⋀𝜓𝜑→𝜑→→𝜓𝜑→𝜓⋀𝜓𝜑 | Subs [𝜑↗→→𝜓𝜑→𝜓⋀𝜓𝜑, 𝜓↗𝜑] into ax-1 | |
| 4886 | →𝜑→→𝜓𝜑→𝜓⋀𝜓𝜑 | Modus ponens 4884, 4885 | |
| 4887 | →→𝜑→→𝜓𝜑→𝜓⋀𝜓𝜑→→𝜑→𝜓𝜑→𝜑→𝜓⋀𝜓𝜑 | Subs [𝜓↗→𝜓𝜑, 𝜒↗→𝜓⋀𝜓𝜑] into ax-2 | |
| 4888 | →→𝜑→𝜓𝜑→𝜑→𝜓⋀𝜓𝜑 | Modus ponens 4886, 4887 | |
| 4889 | →𝜑→𝜓⋀𝜓𝜑 | Modus ponens ax-1, 4888 | pm3.21 |
| 4890 | →→𝜑→𝜓⋀𝜓𝜑→→𝜑𝜓→𝜑⋀𝜓𝜑 | Subs [𝜒↗⋀𝜓𝜑] into ax-2 | |
| 4891 | →→𝜑𝜓→𝜑⋀𝜓𝜑 | Modus ponens pm3.21, 4890 | ancr |
| 4892 | →→→𝜑𝜓→𝜑⋀𝜓𝜑→¬¬𝜓→→𝜑𝜓→𝜑⋀𝜓𝜑 | Subs [𝜑↗→→𝜑𝜓→𝜑⋀𝜓𝜑, 𝜓↗¬¬𝜓] into ax-1 | |
| 4893 | →¬¬𝜓→→𝜑𝜓→𝜑⋀𝜓𝜑 | Modus ponens ancr, 4892 | |
| 4894 | →→¬¬𝜓→→𝜑𝜓→𝜑⋀𝜓𝜑→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑⋀𝜓𝜑 | Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑⋀𝜓𝜑] into ax-2 | |
| 4895 | →→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑⋀𝜓𝜑 | Modus ponens 4893, 4894 | |
| 4896 | →¬¬𝜓→𝜑⋀𝜓𝜑 | Modus ponens 575, 4895 | |
| 4897 | →→¬¬𝜓→𝜑⋀𝜓𝜑→→¬¬𝜓𝜑→¬¬𝜓⋀𝜓𝜑 | Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑, 𝜒↗⋀𝜓𝜑] into ax-2 | |
| 4898 | →→¬¬𝜓𝜑→¬¬𝜓⋀𝜓𝜑 | Modus ponens 4896, 4897 | |
| 4899 | →→→¬¬𝜓𝜑→¬¬𝜓⋀𝜓𝜑→𝜑→→¬¬𝜓𝜑→¬¬𝜓⋀𝜓𝜑 | Subs [𝜑↗→→¬¬𝜓𝜑→¬¬𝜓⋀𝜓𝜑, 𝜓↗𝜑] into ax-1 | |
| 4900 | →𝜑→→¬¬𝜓𝜑→¬¬𝜓⋀𝜓𝜑 | Modus ponens 4898, 4899 | |
| 4901 | →→𝜑→→¬¬𝜓𝜑→¬¬𝜓⋀𝜓𝜑→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓⋀𝜓𝜑 | Subs [𝜓↗→¬¬𝜓𝜑, 𝜒↗→¬¬𝜓⋀𝜓𝜑] into ax-2 | |
| 4902 | →→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓⋀𝜓𝜑 | Modus ponens 4900, 4901 | |
| 4903 | →𝜑→¬¬𝜓⋀𝜓𝜑 | Modus ponens 581, 4902 | |
| 4904 | →⋀𝜓𝜑¬¬⋀𝜓𝜑 | Subs [𝜑↗⋀𝜓𝜑] into notnot | |
| 4905 | →→⋀𝜓𝜑¬¬⋀𝜓𝜑→¬¬𝜓→⋀𝜓𝜑¬¬⋀𝜓𝜑 | Subs [𝜑↗→⋀𝜓𝜑¬¬⋀𝜓𝜑, 𝜓↗¬¬𝜓] into ax-1 | |
| 4906 | →¬¬𝜓→⋀𝜓𝜑¬¬⋀𝜓𝜑 | Modus ponens 4904, 4905 | |
| 4907 | →→¬¬𝜓→⋀𝜓𝜑¬¬⋀𝜓𝜑→→¬¬𝜓⋀𝜓𝜑→¬¬𝜓¬¬⋀𝜓𝜑 | Subs [𝜑↗¬¬𝜓, 𝜓↗⋀𝜓𝜑, 𝜒↗¬¬⋀𝜓𝜑] into ax-2 | |
| 4908 | →→¬¬𝜓⋀𝜓𝜑→¬¬𝜓¬¬⋀𝜓𝜑 | Modus ponens 4906, 4907 | |
| 4909 | →→→¬¬𝜓⋀𝜓𝜑→¬¬𝜓¬¬⋀𝜓𝜑→𝜑→→¬¬𝜓⋀𝜓𝜑→¬¬𝜓¬¬⋀𝜓𝜑 | Subs [𝜑↗→→¬¬𝜓⋀𝜓𝜑→¬¬𝜓¬¬⋀𝜓𝜑, 𝜓↗𝜑] into ax-1 | |
| 4910 | →𝜑→→¬¬𝜓⋀𝜓𝜑→¬¬𝜓¬¬⋀𝜓𝜑 | Modus ponens 4908, 4909 | |
| 4911 | →→𝜑→→¬¬𝜓⋀𝜓𝜑→¬¬𝜓¬¬⋀𝜓𝜑→→𝜑→¬¬𝜓⋀𝜓𝜑→𝜑→¬¬𝜓¬¬⋀𝜓𝜑 | Subs [𝜓↗→¬¬𝜓⋀𝜓𝜑, 𝜒↗→¬¬𝜓¬¬⋀𝜓𝜑] into ax-2 | |
| 4912 | →→𝜑→¬¬𝜓⋀𝜓𝜑→𝜑→¬¬𝜓¬¬⋀𝜓𝜑 | Modus ponens 4910, 4911 | |
| 4913 | →𝜑→¬¬𝜓¬¬⋀𝜓𝜑 | Modus ponens 4903, 4912 | |
| 4914 | →→¬¬𝜓¬¬⋀𝜓𝜑→¬⋀𝜓𝜑¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬⋀𝜓𝜑] into ax-3 | |
| 4915 | →→→¬¬𝜓¬¬⋀𝜓𝜑→¬⋀𝜓𝜑¬𝜓→𝜑→→¬¬𝜓¬¬⋀𝜓𝜑→¬⋀𝜓𝜑¬𝜓 | Subs [𝜑↗→→¬¬𝜓¬¬⋀𝜓𝜑→¬⋀𝜓𝜑¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 4916 | →𝜑→→¬¬𝜓¬¬⋀𝜓𝜑→¬⋀𝜓𝜑¬𝜓 | Modus ponens 4914, 4915 | |
| 4917 | →→𝜑→→¬¬𝜓¬¬⋀𝜓𝜑→¬⋀𝜓𝜑¬𝜓→→𝜑→¬¬𝜓¬¬⋀𝜓𝜑→𝜑→¬⋀𝜓𝜑¬𝜓 | Subs [𝜓↗→¬¬𝜓¬¬⋀𝜓𝜑, 𝜒↗→¬⋀𝜓𝜑¬𝜓] into ax-2 | |
| 4918 | →→𝜑→¬¬𝜓¬¬⋀𝜓𝜑→𝜑→¬⋀𝜓𝜑¬𝜓 | Modus ponens 4916, 4917 | |
| 4919 | →𝜑→¬⋀𝜓𝜑¬𝜓 | Modus ponens 4913, 4918 | |
| 4920 | →¬⋀𝜓𝜑¬⋀𝜓𝜑 | Subs [𝜑↗¬⋀𝜓𝜑] into id | |
| 4921 | →¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑 | Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗𝜑] into ax-1 | |
| 4922 | →→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑 | Subs [𝜑↗→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑, 𝜓↗¬⋀𝜓𝜑] into ax-1 | |
| 4923 | →¬⋀𝜓𝜑→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑 | Modus ponens 4921, 4922 | |
| 4924 | →→¬⋀𝜓𝜑→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑→→¬⋀𝜓𝜑¬⋀𝜓𝜑→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑 | Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗¬⋀𝜓𝜑, 𝜒↗→𝜑¬⋀𝜓𝜑] into ax-2 | |
| 4925 | →→¬⋀𝜓𝜑¬⋀𝜓𝜑→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑 | Modus ponens 4923, 4924 | |
| 4926 | →→𝜑→¬⋀𝜓𝜑¬𝜓→→𝜑¬⋀𝜓𝜑→𝜑¬𝜓 | Subs [𝜓↗¬⋀𝜓𝜑, 𝜒↗¬𝜓] into ax-2 | |
| 4927 | →→𝜑¬⋀𝜓𝜑→𝜑¬𝜓 | Modus ponens 4919, 4926 | |
| 4928 | →→→𝜑¬⋀𝜓𝜑→𝜑¬𝜓→¬⋀𝜓𝜑→→𝜑¬⋀𝜓𝜑→𝜑¬𝜓 | Subs [𝜑↗→→𝜑¬⋀𝜓𝜑→𝜑¬𝜓, 𝜓↗¬⋀𝜓𝜑] into ax-1 | |
| 4929 | →¬⋀𝜓𝜑→→𝜑¬⋀𝜓𝜑→𝜑¬𝜓 | Modus ponens 4927, 4928 | |
| 4930 | →→¬⋀𝜓𝜑→→𝜑¬⋀𝜓𝜑→𝜑¬𝜓→→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑→¬⋀𝜓𝜑→𝜑¬𝜓 | Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗→𝜑¬⋀𝜓𝜑, 𝜒↗→𝜑¬𝜓] into ax-2 | |
| 4931 | →→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑→¬⋀𝜓𝜑→𝜑¬𝜓 | Modus ponens 4929, 4930 | |
| 4932 | →¬⋀𝜓𝜑→𝜑¬𝜓 | Modus ponens 4921, 4931 | |
| 4933 | →→¬→𝜑¬𝜓¬→𝜑¬𝜓→¬⋀𝜓𝜑→¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬⋀𝜓𝜑] into ax-1 | |
| 4934 | →¬⋀𝜓𝜑→¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 619, 4933 | |
| 4935 | →¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓 | Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗¬⋀𝜓𝜑] into ax-1 | |
| 4936 | →→¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓 | Subs [𝜑↗→¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1 | |
| 4937 | →¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓 | Modus ponens 4935, 4936 | |
| 4938 | →→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓 | Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→¬⋀𝜓𝜑¬→𝜑¬𝜓] into ax-2 | |
| 4939 | →→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓 | Modus ponens 4937, 4938 | |
| 4940 | →¬¬¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓 | Modus ponens 622, 4939 | |
| 4941 | →→¬⋀𝜓𝜑→¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓 | Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗¬→𝜑¬𝜓, 𝜒↗¬→𝜑¬𝜓] into ax-2 | |
| 4942 | →→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓 | Modus ponens 4934, 4941 | |
| 4943 | →→→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓 | Subs [𝜑↗→→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1 | |
| 4944 | →¬¬¬→𝜑¬𝜓→→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓 | Modus ponens 4942, 4943 | |
| 4945 | →→¬¬¬→𝜑¬𝜓→→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓 | Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗→¬⋀𝜓𝜑¬→𝜑¬𝜓, 𝜒↗→¬⋀𝜓𝜑¬→𝜑¬𝜓] into ax-2 | |
| 4946 | →→¬¬¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓 | Modus ponens 4944, 4945 | |
| 4947 | →¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑 | Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1 | |
| 4948 | →→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑 | Subs [𝜑↗→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑, 𝜓↗¬⋀𝜓𝜑] into ax-1 | |
| 4949 | →¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑 | Modus ponens 4947, 4948 | |
| 4950 | →→¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→→¬⋀𝜓𝜑¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑 | Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗¬⋀𝜓𝜑, 𝜒↗→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑] into ax-2 | |
| 4951 | →→¬⋀𝜓𝜑¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑 | Modus ponens 4949, 4950 | |
| 4952 | →→¬¬¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬⋀𝜓𝜑, 𝜒↗¬→𝜑¬𝜓] into ax-2 | |
| 4953 | →→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 4940, 4952 | |
| 4954 | →→→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬⋀𝜓𝜑→→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬⋀𝜓𝜑] into ax-1 | |
| 4955 | →¬⋀𝜓𝜑→→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 4953, 4954 | |
| 4956 | →→¬⋀𝜓𝜑→→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑, 𝜒↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓] into ax-2 | |
| 4957 | →→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 4955, 4956 | |
| 4958 | →¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 4947, 4957 | |
| 4959 | →→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→¬⋀𝜓𝜑→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓, 𝜓↗¬⋀𝜓𝜑] into ax-1 | |
| 4960 | →¬⋀𝜓𝜑→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Modus ponens 647, 4959 | |
| 4961 | →→¬⋀𝜓𝜑→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬⋀𝜓𝜑→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜒↗→→𝜑¬𝜓¬¬→𝜑¬𝜓] into ax-2 | |
| 4962 | →→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬⋀𝜓𝜑→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Modus ponens 4960, 4961 | |
| 4963 | →¬⋀𝜓𝜑→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Modus ponens 4958, 4962 | |
| 4964 | →→¬⋀𝜓𝜑→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬⋀𝜓𝜑→𝜑¬𝜓→¬⋀𝜓𝜑¬¬→𝜑¬𝜓 | Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗→𝜑¬𝜓, 𝜒↗¬¬→𝜑¬𝜓] into ax-2 | |
| 4965 | →→¬⋀𝜓𝜑→𝜑¬𝜓→¬⋀𝜓𝜑¬¬→𝜑¬𝜓 | Modus ponens 4963, 4964 | |
| 4966 | →¬⋀𝜓𝜑¬¬→𝜑¬𝜓 | Modus ponens 4932, 4965 | |
| 4967 | →→¬⋀𝜓𝜑¬¬→𝜑¬𝜓→¬→𝜑¬𝜓⋀𝜓𝜑 | Subs [𝜑↗⋀𝜓𝜑, 𝜓↗¬→𝜑¬𝜓] into ax-3 | |
| 4968 | →¬→𝜑¬𝜓⋀𝜓𝜑 | Modus ponens 4966, 4967 | |
| 4969 | →→¬→𝜑¬𝜓⋀𝜓𝜑→⋀𝜑𝜓→¬→𝜑¬𝜓⋀𝜓𝜑 | Subs [𝜑↗→¬→𝜑¬𝜓⋀𝜓𝜑, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 4970 | →⋀𝜑𝜓→¬→𝜑¬𝜓⋀𝜓𝜑 | Modus ponens 4968, 4969 | |
| 4971 | →→⋀𝜑𝜓→¬→𝜑¬𝜓⋀𝜓𝜑→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓⋀𝜓𝜑 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗⋀𝜓𝜑] into ax-2 | |
| 4972 | →→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓⋀𝜓𝜑 | Modus ponens 4970, 4971 | |
| 4973 | →⋀𝜑𝜓⋀𝜓𝜑 | Modus ponens 4842, 4972 | pm3.22 |
| 4974 | →⋀𝜓𝜑⋀𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜑] into pm3.22 | |
| 4975 | →→⋀𝜑𝜓⋀𝜓𝜑→→⋀𝜓𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜓𝜑] into impbi | |
| 4976 | →→⋀𝜓𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑 | Modus ponens pm3.22, 4975 | |
| 4977 | ↔⋀𝜑𝜓⋀𝜓𝜑 | Modus ponens 4974, 4976 | ancom |
| 4978 | →↔⋀𝜑𝜓⋀𝜓𝜑↔→⋀𝜑𝜓𝜒→⋀𝜓𝜑𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜓𝜑] into imbi1 | |
| 4979 | ↔→⋀𝜑𝜓𝜒→⋀𝜓𝜑𝜒 | Modus ponens ancom, 4978 | ancomst |
| 4980 | →⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒] into id | |
| 4981 | ↔⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜓↗⋀𝜓𝜒] into df-an | |
| 4982 | →↔⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒↔¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into bicom1 | |
| 4983 | ↔¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 4981, 4982 | |
| 4984 | →↔¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp | |
| 4985 | →¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 4983, 4984 | |
| 4986 | →→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into ax-1 | |
| 4987 | →¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 4980, 4986 | |
| 4988 | →→¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 4989 | →→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 4987, 4988 | |
| 4990 | →𝜑→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜓↗⋀𝜓𝜒] into pm3.2im | |
| 4991 | →→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 4992 | →⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 4985, 4991 | |
| 4993 | →→⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 4994 | →→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 4992, 4993 | |
| 4995 | →→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 4996 | →𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 4994, 4995 | |
| 4997 | →→𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→𝜑→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→𝜑→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜓↗→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜒↗→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 4998 | →→𝜑→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→𝜑→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 4996, 4997 | |
| 4999 | →𝜑→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 4990, 4998 | |
| 5000 | →⋀𝜓𝜒⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒] into id | |
| 5001 | →⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 5002 | →→⋀𝜓𝜒→𝜑⋀𝜓𝜒→⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗→⋀𝜓𝜒→𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 5003 | →⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Modus ponens 5001, 5002 | |
| 5004 | →→⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜓𝜒→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2 | |
| 5005 | →→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Modus ponens 5003, 5004 | |
| 5006 | →→𝜑→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜓↗⋀𝜓𝜒, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5007 | →→𝜑⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 4999, 5006 | |
| 5008 | →→→𝜑⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒→⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→→𝜑⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 5009 | →⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 5007, 5008 | |
| 5010 | →→⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒→→⋀𝜓𝜒→𝜑⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→𝜑⋀𝜓𝜒, 𝜒↗→𝜑⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5011 | →→⋀𝜓𝜒→𝜑⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 5009, 5010 | |
| 5012 | →⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 5001, 5011 | |
| 5013 | ↔⋀𝜓𝜒¬→𝜓¬𝜒 | Subs [𝜑↗𝜓, 𝜓↗𝜒] into df-an | |
| 5014 | →↔⋀𝜓𝜒¬→𝜓¬𝜒↔¬→𝜓¬𝜒⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒] into bicom1 | |
| 5015 | ↔¬→𝜓¬𝜒⋀𝜓𝜒 | Modus ponens 5013, 5014 | |
| 5016 | →↔¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒⋀𝜓𝜒 | Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗⋀𝜓𝜒] into biimp | |
| 5017 | →¬→𝜓¬𝜒⋀𝜓𝜒 | Modus ponens 5015, 5016 | |
| 5018 | →→⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒→¬→𝜓¬𝜒→⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒] into ax-1 | |
| 5019 | →¬→𝜓¬𝜒→⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 5012, 5018 | |
| 5020 | →→¬→𝜓¬𝜒→⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒→→¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜑⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5021 | →→¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 5019, 5020 | |
| 5022 | →¬→𝜓¬𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 5017, 5021 | |
| 5023 | →𝜓→𝜒¬→𝜓¬𝜒 | Subs [𝜑↗𝜓, 𝜓↗𝜒] into pm3.2im | |
| 5024 | →→¬→𝜓¬𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒→¬→𝜓¬𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→¬→𝜓¬𝜒→𝜑⋀𝜑⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 5025 | →𝜒→¬→𝜓¬𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 5022, 5024 | |
| 5026 | →→𝜒→¬→𝜓¬𝜒→𝜑⋀𝜑⋀𝜓𝜒→→𝜒¬→𝜓¬𝜒→𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→𝜑⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5027 | →→𝜒¬→𝜓¬𝜒→𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 5025, 5026 | |
| 5028 | →→→𝜒¬→𝜓¬𝜒→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜓→→𝜒¬→𝜓¬𝜒→𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→→𝜒¬→𝜓¬𝜒→𝜒→𝜑⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 5029 | →𝜓→→𝜒¬→𝜓¬𝜒→𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 5027, 5028 | |
| 5030 | →→𝜓→→𝜒¬→𝜓¬𝜒→𝜒→𝜑⋀𝜑⋀𝜓𝜒→→𝜓→𝜒¬→𝜓¬𝜒→𝜓→𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→𝜒¬→𝜓¬𝜒, 𝜒↗→𝜒→𝜑⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5031 | →→𝜓→𝜒¬→𝜓¬𝜒→𝜓→𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 5029, 5030 | |
| 5032 | →𝜓→𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 5023, 5031 | |
| 5033 | →𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜓↗⋀𝜑⋀𝜓𝜒] into pm2.27 | |
| 5034 | →→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜓→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 5035 | →𝜓→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5033, 5034 | |
| 5036 | →→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜒→𝜑⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 5037 | →→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜓→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 5038 | →𝜓→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 5036, 5037 | |
| 5039 | →→𝜓→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→→𝜓→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜓→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→𝜒→𝜑⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5040 | →→𝜓→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜓→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 5038, 5039 | |
| 5041 | →𝜓→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 5032, 5040 | |
| 5042 | →→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜑⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into imim2 | |
| 5043 | →→→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→𝜑→→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 5044 | →𝜑→→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5042, 5043 | |
| 5045 | →→𝜑→→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜓↗→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5046 | →→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5044, 5045 | |
| 5047 | →→→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→𝜓→→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 5048 | →𝜓→→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5046, 5047 | |
| 5049 | →→𝜓→→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→→𝜓→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜓→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5050 | →→𝜓→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜓→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5048, 5049 | |
| 5051 | →𝜓→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5035, 5050 | |
| 5052 | →→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜓↗→𝜒→𝜑⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜒⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5053 | →→→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒→𝜓→→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 5054 | →𝜓→→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5052, 5053 | |
| 5055 | →→𝜓→→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒→→𝜓→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→𝜓→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5056 | →→𝜓→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→𝜓→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5054, 5055 | |
| 5057 | →𝜓→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5051, 5056 | |
| 5058 | →→𝜓→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒→→𝜓→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜑→𝜒⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5059 | →→𝜓→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5057, 5058 | |
| 5060 | →𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5041, 5059 | |
| 5061 | →→𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒→→𝜓𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗𝜑, 𝜒↗→𝜒⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5062 | →→𝜓𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5060, 5061 | |
| 5063 | →→→𝜓𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒→𝜑→→𝜓𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→→𝜓𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 5064 | →𝜑→→𝜓𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5062, 5063 | |
| 5065 | →→𝜑→→𝜓𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→𝜓𝜑→𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜓↗→𝜓𝜑, 𝜒↗→𝜓→𝜒⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5066 | →→𝜑→𝜓𝜑→𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5064, 5065 | |
| 5067 | →𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens ax-1, 5066 | |
| 5068 | →→𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜒↗→𝜒⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5069 | →→𝜑𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5067, 5068 | |
| 5070 | →→→𝜑𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬¬𝜓] into ax-1 | |
| 5071 | →¬¬𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5069, 5070 | |
| 5072 | →→¬¬𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑→𝜒⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5073 | →→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5071, 5072 | |
| 5074 | →¬¬𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 575, 5073 | |
| 5075 | →→¬¬𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒→→¬¬𝜓𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑, 𝜒↗→𝜒⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5076 | →→¬¬𝜓𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5074, 5075 | |
| 5077 | →→→¬¬𝜓𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→𝜑→→¬¬𝜓𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→→¬¬𝜓𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 5078 | →𝜑→→¬¬𝜓𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5076, 5077 | |
| 5079 | →→𝜑→→¬¬𝜓𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜓↗→¬¬𝜓𝜑, 𝜒↗→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5080 | →→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5078, 5079 | |
| 5081 | →𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 581, 5080 | |
| 5082 | →→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜒⋀𝜑⋀𝜓𝜒] into notnot | |
| 5083 | →→→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓→→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬¬𝜓] into ax-1 | |
| 5084 | →¬¬𝜓→→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5082, 5083 | |
| 5085 | →→¬¬𝜓→→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜒⋀𝜑⋀𝜓𝜒→→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗¬¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5086 | →→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5084, 5085 | |
| 5087 | →→→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑→→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 5088 | →𝜑→→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5086, 5087 | |
| 5089 | →→𝜑→→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→𝜑→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜓↗→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5090 | →→𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→𝜑→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5088, 5089 | |
| 5091 | →𝜑→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5081, 5090 | |
| 5092 | →→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-3 | |
| 5093 | →→→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓→𝜑→→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓 | Subs [𝜑↗→→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 5094 | →𝜑→→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓 | Modus ponens 5092, 5093 | |
| 5095 | →→𝜑→→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓→→𝜑→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓 | Subs [𝜓↗→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓] into ax-2 | |
| 5096 | →→𝜑→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓 | Modus ponens 5094, 5095 | |
| 5097 | →𝜑→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓 | Modus ponens 5091, 5096 | |
| 5098 | →¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒] into id | |
| 5099 | →¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 5100 | →→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 5101 | →¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5099, 5100 | |
| 5102 | →→¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5103 | →→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5101, 5102 | |
| 5104 | →→𝜑→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓→→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓 | Subs [𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗¬𝜓] into ax-2 | |
| 5105 | →→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓 | Modus ponens 5097, 5104 | |
| 5106 | →→→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒→→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓 | Subs [𝜑↗→→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 5107 | →¬→𝜒⋀𝜑⋀𝜓𝜒→→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓 | Modus ponens 5105, 5106 | |
| 5108 | →→¬→𝜒⋀𝜑⋀𝜓𝜒→→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓→→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓 | Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜑¬𝜓] into ax-2 | |
| 5109 | →→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓 | Modus ponens 5107, 5108 | |
| 5110 | →¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓 | Modus ponens 5099, 5109 | |
| 5111 | →→¬→𝜑¬𝜓¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 5112 | →¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 619, 5111 | |
| 5113 | →¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓 | Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 5114 | →→¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓 | Subs [𝜑↗→¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1 | |
| 5115 | →¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓 | Modus ponens 5113, 5114 | |
| 5116 | →→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓 | Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓] into ax-2 | |
| 5117 | →→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓 | Modus ponens 5115, 5116 | |
| 5118 | →¬¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓 | Modus ponens 622, 5117 | |
| 5119 | →→¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓 | Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑¬𝜓, 𝜒↗¬→𝜑¬𝜓] into ax-2 | |
| 5120 | →→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓 | Modus ponens 5112, 5119 | |
| 5121 | →→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓 | Subs [𝜑↗→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1 | |
| 5122 | →¬¬¬→𝜑¬𝜓→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓 | Modus ponens 5120, 5121 | |
| 5123 | →→¬¬¬→𝜑¬𝜓→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓 | Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓, 𝜒↗→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓] into ax-2 | |
| 5124 | →→¬¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓 | Modus ponens 5122, 5123 | |
| 5125 | →¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1 | |
| 5126 | →→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 5127 | →¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5125, 5126 | |
| 5128 | →→¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5129 | →→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5127, 5128 | |
| 5130 | →→¬¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗¬→𝜑¬𝜓] into ax-2 | |
| 5131 | →→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 5118, 5130 | |
| 5132 | →→→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒→→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 5133 | →¬→𝜒⋀𝜑⋀𝜓𝜒→→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 5131, 5132 | |
| 5134 | →→¬→𝜒⋀𝜑⋀𝜓𝜒→→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓] into ax-2 | |
| 5135 | →→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 5133, 5134 | |
| 5136 | →¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 5125, 5135 | |
| 5137 | →→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 5138 | →¬→𝜒⋀𝜑⋀𝜓𝜒→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Modus ponens 647, 5137 | |
| 5139 | →→¬→𝜒⋀𝜑⋀𝜓𝜒→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜒↗→→𝜑¬𝜓¬¬→𝜑¬𝜓] into ax-2 | |
| 5140 | →→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Modus ponens 5138, 5139 | |
| 5141 | →¬→𝜒⋀𝜑⋀𝜓𝜒→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Modus ponens 5136, 5140 | |
| 5142 | →→¬→𝜒⋀𝜑⋀𝜓𝜒→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜑¬𝜓 | Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗→𝜑¬𝜓, 𝜒↗¬¬→𝜑¬𝜓] into ax-2 | |
| 5143 | →→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜑¬𝜓 | Modus ponens 5141, 5142 | |
| 5144 | →¬→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜑¬𝜓 | Modus ponens 5110, 5143 | |
| 5145 | →→¬→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑¬𝜓] into ax-3 | |
| 5146 | →¬→𝜑¬𝜓→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5144, 5145 | |
| 5147 | →→¬→𝜑¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓→¬→𝜑¬𝜓→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→¬→𝜑¬𝜓→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 5148 | →⋀𝜑𝜓→¬→𝜑¬𝜓→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5146, 5147 | |
| 5149 | →→⋀𝜑𝜓→¬→𝜑¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓→𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→𝜒⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5150 | →→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5148, 5149 | |
| 5151 | →⋀𝜑𝜓→𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 4842, 5150 | |
| 5152 | ↔⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒] into df-an | |
| 5153 | →¬¬𝜒𝜒 | Subs [𝜑↗𝜒] into notnotr | |
| 5154 | →𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 5155 | →→𝜒→⋀𝜑𝜓𝜒→¬¬𝜒→𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→𝜒→⋀𝜑𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1 | |
| 5156 | →¬¬𝜒→𝜒→⋀𝜑𝜓𝜒 | Modus ponens 5154, 5155 | |
| 5157 | →→¬¬𝜒→𝜒→⋀𝜑𝜓𝜒→→¬¬𝜒𝜒→¬¬𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗¬¬𝜒, 𝜓↗𝜒, 𝜒↗→⋀𝜑𝜓𝜒] into ax-2 | |
| 5158 | →→¬¬𝜒𝜒→¬¬𝜒→⋀𝜑𝜓𝜒 | Modus ponens 5156, 5157 | |
| 5159 | →¬¬𝜒→⋀𝜑𝜓𝜒 | Modus ponens 5153, 5158 | |
| 5160 | →→⋀𝜑𝜓→𝜒⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5161 | →→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒 | Modus ponens 5151, 5160 | |
| 5162 | →→→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒→¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1 | |
| 5163 | →¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒 | Modus ponens 5161, 5162 | |
| 5164 | →→¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒→→¬¬𝜒→⋀𝜑𝜓𝜒→¬¬𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗¬¬𝜒, 𝜓↗→⋀𝜑𝜓𝜒, 𝜒↗→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5165 | →→¬¬𝜒→⋀𝜑𝜓𝜒→¬¬𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒 | Modus ponens 5163, 5164 | |
| 5166 | →¬¬𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒 | Modus ponens 5159, 5165 | |
| 5167 | →⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬¬𝜒] into ax-1 | |
| 5168 | →→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓→⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓 | Subs [𝜑↗→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 5169 | →⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓 | Modus ponens 5167, 5168 | |
| 5170 | →→⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗→¬¬𝜒⋀𝜑𝜓] into ax-2 | |
| 5171 | →→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓 | Modus ponens 5169, 5170 | |
| 5172 | →→¬¬𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗¬¬𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5173 | →→¬¬𝜒⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5166, 5172 | |
| 5174 | →→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 5175 | →⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5173, 5174 | |
| 5176 | →→⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒⋀𝜑𝜓, 𝜒↗→¬¬𝜒⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5177 | →→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5175, 5176 | |
| 5178 | →⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5167, 5177 | |
| 5179 | →⋀𝜑⋀𝜓𝜒¬¬⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒] into notnot | |
| 5180 | →→⋀𝜑⋀𝜓𝜒¬¬⋀𝜑⋀𝜓𝜒→¬¬𝜒→⋀𝜑⋀𝜓𝜒¬¬⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→⋀𝜑⋀𝜓𝜒¬¬⋀𝜑⋀𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1 | |
| 5181 | →¬¬𝜒→⋀𝜑⋀𝜓𝜒¬¬⋀𝜑⋀𝜓𝜒 | Modus ponens 5179, 5180 | |
| 5182 | →→¬¬𝜒→⋀𝜑⋀𝜓𝜒¬¬⋀𝜑⋀𝜓𝜒→→¬¬𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗¬¬𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗¬¬⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5183 | →→¬¬𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒 | Modus ponens 5181, 5182 | |
| 5184 | →→→¬¬𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓→→¬¬𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→→¬¬𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 5185 | →⋀𝜑𝜓→→¬¬𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒 | Modus ponens 5183, 5184 | |
| 5186 | →→⋀𝜑𝜓→→¬¬𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5187 | →→⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒 | Modus ponens 5185, 5186 | |
| 5188 | →⋀𝜑𝜓→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒 | Modus ponens 5178, 5187 | |
| 5189 | →→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒] into ax-3 | |
| 5190 | →→→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒¬𝜒→⋀𝜑𝜓→→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒¬𝜒 | Subs [𝜑↗→→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒¬𝜒, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 5191 | →⋀𝜑𝜓→→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒¬𝜒 | Modus ponens 5189, 5190 | |
| 5192 | →→⋀𝜑𝜓→→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒¬𝜒→→⋀𝜑𝜓→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓→¬⋀𝜑⋀𝜓𝜒¬𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒, 𝜒↗→¬⋀𝜑⋀𝜓𝜒¬𝜒] into ax-2 | |
| 5193 | →→⋀𝜑𝜓→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓→¬⋀𝜑⋀𝜓𝜒¬𝜒 | Modus ponens 5191, 5192 | |
| 5194 | →⋀𝜑𝜓→¬⋀𝜑⋀𝜓𝜒¬𝜒 | Modus ponens 5188, 5193 | |
| 5195 | →¬⋀𝜑⋀𝜓𝜒¬⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒] into id | |
| 5196 | →¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 5197 | →→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 5198 | →¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒 | Modus ponens 5196, 5197 | |
| 5199 | →→¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→→¬⋀𝜑⋀𝜓𝜒¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒, 𝜒↗→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5200 | →→¬⋀𝜑⋀𝜓𝜒¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒 | Modus ponens 5198, 5199 | |
| 5201 | →→⋀𝜑𝜓→¬⋀𝜑⋀𝜓𝜒¬𝜒→→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬⋀𝜑⋀𝜓𝜒, 𝜒↗¬𝜒] into ax-2 | |
| 5202 | →→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒 | Modus ponens 5194, 5201 | |
| 5203 | →→→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 5204 | →¬⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒 | Modus ponens 5202, 5203 | |
| 5205 | →→¬⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒→→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒, 𝜒↗→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 5206 | →→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒 | Modus ponens 5204, 5205 | |
| 5207 | →¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒 | Modus ponens 5196, 5206 | |
| 5208 | →¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬→⋀𝜑𝜓¬𝜒] into id | |
| 5209 | →→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 5210 | →¬⋀𝜑⋀𝜓𝜒→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Modus ponens 5208, 5209 | |
| 5211 | →¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬→⋀𝜑𝜓¬𝜒] into notnotr | |
| 5212 | →¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 5213 | →→¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1 | |
| 5214 | →¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒 | Modus ponens 5212, 5213 | |
| 5215 | →→¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 5216 | →→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒 | Modus ponens 5214, 5215 | |
| 5217 | →¬¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒 | Modus ponens 5211, 5216 | |
| 5218 | →→¬⋀𝜑⋀𝜓𝜒→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗¬→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 5219 | →→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒 | Modus ponens 5210, 5218 | |
| 5220 | →→→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1 | |
| 5221 | →¬¬¬→⋀𝜑𝜓¬𝜒→→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒 | Modus ponens 5219, 5220 | |
| 5222 | →→¬¬¬→⋀𝜑𝜓¬𝜒→→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒, 𝜒↗→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 5223 | →→¬¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒 | Modus ponens 5221, 5222 | |
| 5224 | →¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1 | |
| 5225 | →→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 5226 | →¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒 | Modus ponens 5224, 5225 | |
| 5227 | →→¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→→¬⋀𝜑⋀𝜓𝜒¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5228 | →→¬⋀𝜑⋀𝜓𝜒¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒 | Modus ponens 5226, 5227 | |
| 5229 | →→¬¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒, 𝜒↗¬→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 5230 | →→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Modus ponens 5217, 5229 | |
| 5231 | →→→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 5232 | →¬⋀𝜑⋀𝜓𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Modus ponens 5230, 5231 | |
| 5233 | →→¬⋀𝜑⋀𝜓𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 5234 | →→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Modus ponens 5232, 5233 | |
| 5235 | →¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Modus ponens 5224, 5234 | |
| 5236 | →→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗→⋀𝜑𝜓¬𝜒] into ax-3 | |
| 5237 | →→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 5238 | →¬⋀𝜑⋀𝜓𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒 | Modus ponens 5236, 5237 | |
| 5239 | →→¬⋀𝜑⋀𝜓𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜒↗→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 5240 | →→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒 | Modus ponens 5238, 5239 | |
| 5241 | →¬⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒 | Modus ponens 5235, 5240 | |
| 5242 | →→¬⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗→⋀𝜑𝜓¬𝜒, 𝜒↗¬¬→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 5243 | →→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬¬→⋀𝜑𝜓¬𝜒 | Modus ponens 5241, 5242 | |
| 5244 | →¬⋀𝜑⋀𝜓𝜒¬¬→⋀𝜑𝜓¬𝜒 | Modus ponens 5207, 5243 | |
| 5245 | →→¬⋀𝜑⋀𝜓𝜒¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒] into ax-3 | |
| 5246 | →¬→⋀𝜑𝜓¬𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5244, 5245 | |
| 5247 | →↔⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒] into biimp | |
| 5248 | →⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒 | Modus ponens 5152, 5247 | |
| 5249 | →→¬→⋀𝜑𝜓¬𝜒⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 5250 | →⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5246, 5249 | |
| 5251 | →→⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒⋀𝜑⋀𝜓𝜒→→⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 5252 | →→⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5250, 5251 | |
| 5253 | →⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5248, 5252 | |
| 5254 | →⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒] into id | |
| 5255 | →↔⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒↔¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒] into bicom1 | |
| 5256 | ↔¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5152, 5255 | |
| 5257 | →↔¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗¬→⋀𝜑𝜓¬𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into biimp | |
| 5258 | →¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5256, 5257 | |
| 5259 | →→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒] into ax-1 | |
| 5260 | →¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5254, 5259 | |
| 5261 | →→¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗¬→⋀𝜑𝜓¬𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5262 | →→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5260, 5261 | |
| 5263 | →⋀𝜑𝜓→𝜒¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒] into pm3.2im | |
| 5264 | →→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒→𝜒→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 5265 | →𝜒→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5258, 5264 | |
| 5266 | →→𝜒→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒→→𝜒¬→⋀𝜑𝜓¬𝜒→𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5267 | →→𝜒¬→⋀𝜑𝜓¬𝜒→𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5265, 5266 | |
| 5268 | →→→𝜒¬→⋀𝜑𝜓¬𝜒→𝜒⋀⋀𝜑𝜓𝜒→⋀𝜑𝜓→→𝜒¬→⋀𝜑𝜓¬𝜒→𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→→𝜒¬→⋀𝜑𝜓¬𝜒→𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 5269 | →⋀𝜑𝜓→→𝜒¬→⋀𝜑𝜓¬𝜒→𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5267, 5268 | |
| 5270 | →→⋀𝜑𝜓→→𝜒¬→⋀𝜑𝜓¬𝜒→𝜒⋀⋀𝜑𝜓𝜒→→⋀𝜑𝜓→𝜒¬→⋀𝜑𝜓¬𝜒→⋀𝜑𝜓→𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜒¬→⋀𝜑𝜓¬𝜒, 𝜒↗→𝜒⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5271 | →→⋀𝜑𝜓→𝜒¬→⋀𝜑𝜓¬𝜒→⋀𝜑𝜓→𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5269, 5270 | |
| 5272 | →⋀𝜑𝜓→𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5263, 5271 | |
| 5273 | →→⋀𝜑𝜓→𝜒⋀⋀𝜑𝜓𝜒→¬→𝜑¬𝜓→⋀𝜑𝜓→𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→⋀𝜑𝜓→𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜑¬𝜓] into ax-1 | |
| 5274 | →¬→𝜑¬𝜓→⋀𝜑𝜓→𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5272, 5273 | |
| 5275 | →→¬→𝜑¬𝜓→⋀𝜑𝜓→𝜒⋀⋀𝜑𝜓𝜒→→¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓→𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗→𝜒⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5276 | →→¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓→𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5274, 5275 | |
| 5277 | →¬→𝜑¬𝜓→𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 4661, 5276 | |
| 5278 | →→¬→𝜑¬𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓→¬→𝜑¬𝜓→𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→¬→𝜑¬𝜓→𝜒⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 5279 | →𝜓→¬→𝜑¬𝜓→𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5277, 5278 | |
| 5280 | →→𝜓→¬→𝜑¬𝜓→𝜒⋀⋀𝜑𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓→𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→𝜒⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5281 | →→𝜓¬→𝜑¬𝜓→𝜓→𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5279, 5280 | |
| 5282 | →→→𝜓¬→𝜑¬𝜓→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜑→→𝜓¬→𝜑¬𝜓→𝜓→𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→→𝜓¬→𝜑¬𝜓→𝜓→𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 5283 | →𝜑→→𝜓¬→𝜑¬𝜓→𝜓→𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5281, 5282 | |
| 5284 | →→𝜑→→𝜓¬→𝜑¬𝜓→𝜓→𝜒⋀⋀𝜑𝜓𝜒→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→𝜓→𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜓↗→𝜓¬→𝜑¬𝜓, 𝜒↗→𝜓→𝜒⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5285 | →→𝜑→𝜓¬→𝜑¬𝜓→𝜑→𝜓→𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5283, 5284 | |
| 5286 | →𝜑→𝜓→𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens pm3.2im, 5285 | |
| 5287 | →𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into pm2.27 | |
| 5288 | →→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜑→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 5289 | →𝜑→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5287, 5288 | |
| 5290 | →→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→𝜓→𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 5291 | →→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜑→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 5292 | →𝜑→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5290, 5291 | |
| 5293 | →→𝜑→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→→𝜑→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜑→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜓↗→𝜓→𝜒⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5294 | →→𝜑→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜑→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5292, 5293 | |
| 5295 | →𝜑→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5286, 5294 | |
| 5296 | →→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜓] into imim2 | |
| 5297 | →→→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→𝜒→→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 5298 | →𝜒→→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒 | Modus ponens 5296, 5297 | |
| 5299 | →→𝜒→→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜒↗→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5300 | →→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒 | Modus ponens 5298, 5299 | |
| 5301 | →→→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→𝜑→→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 5302 | →𝜑→→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒 | Modus ponens 5300, 5301 | |
| 5303 | →→𝜑→→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜑→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜑→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒 | Subs [𝜓↗→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5304 | →→𝜑→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜑→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒 | Modus ponens 5302, 5303 | |
| 5305 | →𝜑→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒 | Modus ponens 5289, 5304 | |
| 5306 | →→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜓→𝜒⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜓⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5307 | →→→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒→𝜑→→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 5308 | →𝜑→→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒 | Modus ponens 5306, 5307 | |
| 5309 | →→𝜑→→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜑→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→𝜑→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒 | Subs [𝜓↗→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒, 𝜒↗→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5310 | →→𝜑→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→𝜑→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒 | Modus ponens 5308, 5309 | |
| 5311 | →𝜑→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒 | Modus ponens 5305, 5310 | |
| 5312 | →→𝜑→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜑→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜑→𝜒→𝜓⋀⋀𝜑𝜓𝜒 | Subs [𝜓↗→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜒→𝜓⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5313 | →→𝜑→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜑→𝜒→𝜓⋀⋀𝜑𝜓𝜒 | Modus ponens 5311, 5312 | |
| 5314 | →𝜑→𝜒→𝜓⋀⋀𝜑𝜓𝜒 | Modus ponens 5295, 5313 | |
| 5315 | →→𝜑→𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜑𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒 | Subs [𝜓↗𝜒, 𝜒↗→𝜓⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5316 | →→𝜑𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒 | Modus ponens 5314, 5315 | |
| 5317 | →→→𝜑𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜒→→𝜑𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→→𝜑𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 5318 | →𝜒→→𝜑𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒 | Modus ponens 5316, 5317 | |
| 5319 | →→𝜒→→𝜑𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→𝜑𝜒→𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑→𝜓⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5320 | →→𝜒→𝜑𝜒→𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒 | Modus ponens 5318, 5319 | |
| 5321 | →𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒 | Modus ponens 1834, 5320 | |
| 5322 | →𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into pm2.27 | |
| 5323 | →→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 5324 | →𝜒→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5322, 5323 | |
| 5325 | →→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→𝜑→𝜓⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 5326 | →→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 5327 | →𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒 | Modus ponens 5325, 5326 | |
| 5328 | →→𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜑→𝜓⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5329 | →→𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒 | Modus ponens 5327, 5328 | |
| 5330 | →𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒 | Modus ponens 5321, 5329 | |
| 5331 | →→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→𝜓⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜑] into imim2 | |
| 5332 | →→→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→𝜓→→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 5333 | →𝜓→→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5331, 5332 | |
| 5334 | →→𝜓→→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜒↗→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5335 | →→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5333, 5334 | |
| 5336 | →→→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 5337 | →𝜒→→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5335, 5336 | |
| 5338 | →→𝜒→→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5339 | →→𝜒→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5337, 5338 | |
| 5340 | →𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5324, 5339 | |
| 5341 | →→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→𝜑→𝜓⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜑⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5342 | →→→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 5343 | →𝜒→→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5341, 5342 | |
| 5344 | →→𝜒→→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5345 | →→𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5343, 5344 | |
| 5346 | →𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5340, 5345 | |
| 5347 | →→𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜓→𝜑⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5348 | →→𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5346, 5347 | |
| 5349 | →𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5330, 5348 | |
| 5350 | →𝜓→𝜒𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜒] into ax-1 | |
| 5351 | →→𝜓→𝜒𝜓→𝜓→𝜓→𝜒𝜓 | Subs [𝜑↗→𝜓→𝜒𝜓] into ax-1 | |
| 5352 | →𝜓→𝜓→𝜒𝜓 | Modus ponens 5350, 5351 | |
| 5353 | →→𝜓→𝜓→𝜒𝜓→→𝜓𝜓→𝜓→𝜒𝜓 | Subs [𝜑↗𝜓, 𝜒↗→𝜒𝜓] into ax-2 | |
| 5354 | →→𝜓𝜓→𝜓→𝜒𝜓 | Modus ponens 5352, 5353 | |
| 5355 | →→𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒→→𝜒𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗𝜒, 𝜒↗→𝜑⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5356 | →→𝜒𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5349, 5355 | |
| 5357 | →→→𝜒𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒→𝜓→→𝜒𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→→𝜒𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 5358 | →𝜓→→𝜒𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5356, 5357 | |
| 5359 | →→𝜓→→𝜒𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→𝜒𝜓→𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→𝜒𝜓, 𝜒↗→𝜒→𝜑⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5360 | →→𝜓→𝜒𝜓→𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5358, 5359 | |
| 5361 | →𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5350, 5360 | |
| 5362 | →𝜒→𝜓𝜒 | Subs [𝜑↗𝜒] into ax-1 | |
| 5363 | →→𝜒→𝜓𝜒→¬¬𝜒→𝜒→𝜓𝜒 | Subs [𝜑↗→𝜒→𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1 | |
| 5364 | →¬¬𝜒→𝜒→𝜓𝜒 | Modus ponens 5362, 5363 | |
| 5365 | →→¬¬𝜒→𝜒→𝜓𝜒→→¬¬𝜒𝜒→¬¬𝜒→𝜓𝜒 | Subs [𝜑↗¬¬𝜒, 𝜓↗𝜒, 𝜒↗→𝜓𝜒] into ax-2 | |
| 5366 | →→¬¬𝜒𝜒→¬¬𝜒→𝜓𝜒 | Modus ponens 5364, 5365 | |
| 5367 | →¬¬𝜒→𝜓𝜒 | Modus ponens 5153, 5366 | |
| 5368 | →→𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗→𝜑⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5369 | →→𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5361, 5368 | |
| 5370 | →→→𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒→→𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→→𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1 | |
| 5371 | →¬¬𝜒→→𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5369, 5370 | |
| 5372 | →→¬¬𝜒→→𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒→→¬¬𝜒→𝜓𝜒→¬¬𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→𝜓→𝜑⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5373 | →→¬¬𝜒→𝜓𝜒→¬¬𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5371, 5372 | |
| 5374 | →¬¬𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5367, 5373 | |
| 5375 | →𝜓→¬¬𝜒𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬¬𝜒] into ax-1 | |
| 5376 | →→𝜓→¬¬𝜒𝜓→𝜓→𝜓→¬¬𝜒𝜓 | Subs [𝜑↗→𝜓→¬¬𝜒𝜓] into ax-1 | |
| 5377 | →𝜓→𝜓→¬¬𝜒𝜓 | Modus ponens 5375, 5376 | |
| 5378 | →→𝜓→𝜓→¬¬𝜒𝜓→→𝜓𝜓→𝜓→¬¬𝜒𝜓 | Subs [𝜑↗𝜓, 𝜒↗→¬¬𝜒𝜓] into ax-2 | |
| 5379 | →→𝜓𝜓→𝜓→¬¬𝜒𝜓 | Modus ponens 5377, 5378 | |
| 5380 | →→¬¬𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒→→¬¬𝜒𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗¬¬𝜒, 𝜒↗→𝜑⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5381 | →→¬¬𝜒𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5374, 5380 | |
| 5382 | →→→¬¬𝜒𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→𝜓→→¬¬𝜒𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→→¬¬𝜒𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 5383 | →𝜓→→¬¬𝜒𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5381, 5382 | |
| 5384 | →→𝜓→→¬¬𝜒𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒𝜓, 𝜒↗→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5385 | →→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5383, 5384 | |
| 5386 | →𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5375, 5385 | |
| 5387 | →→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→𝜑⋀⋀𝜑𝜓𝜒] into notnot | |
| 5388 | →→→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒→→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1 | |
| 5389 | →¬¬𝜒→→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5387, 5388 | |
| 5390 | →→¬¬𝜒→→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗¬¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5391 | →→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5389, 5390 | |
| 5392 | →→→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓→→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 5393 | →𝜓→→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5391, 5392 | |
| 5394 | →→𝜓→→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→𝜓→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5395 | →→𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→𝜓→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5393, 5394 | |
| 5396 | →𝜓→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5386, 5395 | |
| 5397 | →→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-3 | |
| 5398 | →→→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒→𝜓→→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒 | Subs [𝜑↗→→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒] into ax-1 | |
| 5399 | →𝜓→→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒 | Modus ponens 5397, 5398 | |
| 5400 | →→𝜓→→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒→→𝜓→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒 | Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒] into ax-2 | |
| 5401 | →→𝜓→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒 | Modus ponens 5399, 5400 | |
| 5402 | →𝜓→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒 | Modus ponens 5396, 5401 | |
| 5403 | →¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒] into id | |
| 5404 | →¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 5405 | →→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 5406 | →¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5404, 5405 | |
| 5407 | →→¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5408 | →→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5406, 5407 | |
| 5409 | →→𝜓→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒→→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒 | Subs [𝜑↗𝜓, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗¬𝜒] into ax-2 | |
| 5410 | →→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒 | Modus ponens 5402, 5409 | |
| 5411 | →→→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒 | Subs [𝜑↗→→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 5412 | →¬→𝜑⋀⋀𝜑𝜓𝜒→→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒 | Modus ponens 5410, 5411 | |
| 5413 | →→¬→𝜑⋀⋀𝜑𝜓𝜒→→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒 | Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜓¬𝜒] into ax-2 | |
| 5414 | →→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒 | Modus ponens 5412, 5413 | |
| 5415 | →¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒 | Modus ponens 5404, 5414 | |
| 5416 | →¬→𝜓¬𝜒¬→𝜓¬𝜒 | Subs [𝜑↗¬→𝜓¬𝜒] into id | |
| 5417 | →→¬→𝜓¬𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒 | Subs [𝜑↗→¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 5418 | →¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒 | Modus ponens 5416, 5417 | |
| 5419 | →¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Subs [𝜑↗¬→𝜓¬𝜒] into notnotr | |
| 5420 | →¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒 | Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 5421 | →→¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒 | Subs [𝜑↗→¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1 | |
| 5422 | →¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒 | Modus ponens 5420, 5421 | |
| 5423 | →→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒 | Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒] into ax-2 | |
| 5424 | →→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒 | Modus ponens 5422, 5423 | |
| 5425 | →¬¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒 | Modus ponens 5419, 5424 | |
| 5426 | →→¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒 | Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗¬→𝜓¬𝜒] into ax-2 | |
| 5427 | →→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒 | Modus ponens 5418, 5426 | |
| 5428 | →→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒 | Subs [𝜑↗→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1 | |
| 5429 | →¬¬¬→𝜓¬𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒 | Modus ponens 5427, 5428 | |
| 5430 | →→¬¬¬→𝜓¬𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒 | Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒, 𝜒↗→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒] into ax-2 | |
| 5431 | →→¬¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒 | Modus ponens 5429, 5430 | |
| 5432 | →¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1 | |
| 5433 | →→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 5434 | →¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5432, 5433 | |
| 5435 | →→¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5436 | →→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5434, 5435 | |
| 5437 | →→¬¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗¬→𝜓¬𝜒] into ax-2 | |
| 5438 | →→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Modus ponens 5425, 5437 | |
| 5439 | →→→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Subs [𝜑↗→→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 5440 | →¬→𝜑⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Modus ponens 5438, 5439 | |
| 5441 | →→¬→𝜑⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒] into ax-2 | |
| 5442 | →→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Modus ponens 5440, 5441 | |
| 5443 | →¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Modus ponens 5432, 5442 | |
| 5444 | →→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒 | Subs [𝜑↗¬¬→𝜓¬𝜒, 𝜓↗→𝜓¬𝜒] into ax-3 | |
| 5445 | →→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒 | Subs [𝜑↗→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 5446 | →¬→𝜑⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒 | Modus ponens 5444, 5445 | |
| 5447 | →→¬→𝜑⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒 | Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜒↗→→𝜓¬𝜒¬¬→𝜓¬𝜒] into ax-2 | |
| 5448 | →→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒 | Modus ponens 5446, 5447 | |
| 5449 | →¬→𝜑⋀⋀𝜑𝜓𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒 | Modus ponens 5443, 5448 | |
| 5450 | →→¬→𝜑⋀⋀𝜑𝜓𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜓¬𝜒 | Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜓¬𝜒, 𝜒↗¬¬→𝜓¬𝜒] into ax-2 | |
| 5451 | →→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜓¬𝜒 | Modus ponens 5449, 5450 | |
| 5452 | →¬→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜓¬𝜒 | Modus ponens 5415, 5451 | |
| 5453 | →→¬→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜓¬𝜒] into ax-3 | |
| 5454 | →¬→𝜓¬𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5452, 5453 | |
| 5455 | →↔⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒¬→𝜓¬𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒] into biimp | |
| 5456 | →⋀𝜓𝜒¬→𝜓¬𝜒 | Modus ponens 5013, 5455 | |
| 5457 | →→¬→𝜓¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→⋀𝜓𝜒→¬→𝜓¬𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→¬→𝜓¬𝜒→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 5458 | →⋀𝜓𝜒→¬→𝜓¬𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5454, 5457 | |
| 5459 | →→⋀𝜓𝜒→¬→𝜓¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→→⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→𝜑⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5460 | →→⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5458, 5459 | |
| 5461 | →⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5456, 5460 | |
| 5462 | →𝜑→⋀𝜓𝜒𝜑 | Subs [𝜓↗⋀𝜓𝜒] into ax-1 | |
| 5463 | →→𝜑→⋀𝜓𝜒𝜑→𝜑→𝜑→⋀𝜓𝜒𝜑 | Subs [𝜑↗→𝜑→⋀𝜓𝜒𝜑, 𝜓↗𝜑] into ax-1 | |
| 5464 | →𝜑→𝜑→⋀𝜓𝜒𝜑 | Modus ponens 5462, 5463 | |
| 5465 | →→𝜑→𝜑→⋀𝜓𝜒𝜑→→𝜑𝜑→𝜑→⋀𝜓𝜒𝜑 | Subs [𝜓↗𝜑, 𝜒↗→⋀𝜓𝜒𝜑] into ax-2 | |
| 5466 | →→𝜑𝜑→𝜑→⋀𝜓𝜒𝜑 | Modus ponens 5464, 5465 | |
| 5467 | →→⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→⋀𝜓𝜒𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜑, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5468 | →→⋀𝜓𝜒𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5461, 5467 | |
| 5469 | →→→⋀𝜓𝜒𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→→⋀𝜓𝜒𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 5470 | →𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5468, 5469 | |
| 5471 | →→𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑→⋀𝜓𝜒𝜑→𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜓↗→⋀𝜓𝜒𝜑, 𝜒↗→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5472 | →→𝜑→⋀𝜓𝜒𝜑→𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5470, 5471 | |
| 5473 | →𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5462, 5472 | |
| 5474 | →¬¬⋀𝜓𝜒⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒] into notnotr | |
| 5475 | →→⋀𝜓𝜒→𝜑⋀𝜓𝜒→¬¬⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗→⋀𝜓𝜒→𝜑⋀𝜓𝜒, 𝜓↗¬¬⋀𝜓𝜒] into ax-1 | |
| 5476 | →¬¬⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Modus ponens 5001, 5475 | |
| 5477 | →→¬¬⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜓𝜒→→¬¬⋀𝜓𝜒⋀𝜓𝜒→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2 | |
| 5478 | →→¬¬⋀𝜓𝜒⋀𝜓𝜒→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Modus ponens 5476, 5477 | |
| 5479 | →¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Modus ponens 5474, 5478 | |
| 5480 | →→𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜓↗⋀𝜓𝜒, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5481 | →→𝜑⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5473, 5480 | |
| 5482 | →→→𝜑⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→→𝜑⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬¬⋀𝜓𝜒] into ax-1 | |
| 5483 | →¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5481, 5482 | |
| 5484 | →→¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒→¬¬⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗→𝜑⋀𝜓𝜒, 𝜒↗→𝜑⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5485 | →→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒→¬¬⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5483, 5484 | |
| 5486 | →¬¬⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 5479, 5485 | |
| 5487 | →𝜑→¬¬⋀𝜓𝜒𝜑 | Subs [𝜓↗¬¬⋀𝜓𝜒] into ax-1 | |
| 5488 | →→𝜑→¬¬⋀𝜓𝜒𝜑→𝜑→𝜑→¬¬⋀𝜓𝜒𝜑 | Subs [𝜑↗→𝜑→¬¬⋀𝜓𝜒𝜑, 𝜓↗𝜑] into ax-1 | |
| 5489 | →𝜑→𝜑→¬¬⋀𝜓𝜒𝜑 | Modus ponens 5487, 5488 | |
| 5490 | →→𝜑→𝜑→¬¬⋀𝜓𝜒𝜑→→𝜑𝜑→𝜑→¬¬⋀𝜓𝜒𝜑 | Subs [𝜓↗𝜑, 𝜒↗→¬¬⋀𝜓𝜒𝜑] into ax-2 | |
| 5491 | →→𝜑𝜑→𝜑→¬¬⋀𝜓𝜒𝜑 | Modus ponens 5489, 5490 | |
| 5492 | →→¬¬⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗𝜑, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5493 | →→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5486, 5492 | |
| 5494 | →→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 5495 | →𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5493, 5494 | |
| 5496 | →→𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑→¬¬⋀𝜓𝜒𝜑→𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜓↗→¬¬⋀𝜓𝜒𝜑, 𝜒↗→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5497 | →→𝜑→¬¬⋀𝜓𝜒𝜑→𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5495, 5496 | |
| 5498 | →𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5487, 5497 | |
| 5499 | →⋀⋀𝜑𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒] into notnot | |
| 5500 | →→⋀⋀𝜑𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒→⋀⋀𝜑𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→⋀⋀𝜑𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒, 𝜓↗¬¬⋀𝜓𝜒] into ax-1 | |
| 5501 | →¬¬⋀𝜓𝜒→⋀⋀𝜑𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒 | Modus ponens 5499, 5500 | |
| 5502 | →→¬¬⋀𝜓𝜒→⋀⋀𝜑𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗¬¬⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5503 | →→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒 | Modus ponens 5501, 5502 | |
| 5504 | →→→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→𝜑→→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 5505 | →𝜑→→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒 | Modus ponens 5503, 5504 | |
| 5506 | →→𝜑→→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→→𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜑→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒 | Subs [𝜓↗→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5507 | →→𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜑→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒 | Modus ponens 5505, 5506 | |
| 5508 | →𝜑→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒 | Modus ponens 5498, 5507 | |
| 5509 | →→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒 | Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒] into ax-3 | |
| 5510 | →→→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒→𝜑→→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒 | Subs [𝜑↗→→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 5511 | →𝜑→→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒 | Modus ponens 5509, 5510 | |
| 5512 | →→𝜑→→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒→→𝜑→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→𝜑→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒 | Subs [𝜓↗→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒, 𝜒↗→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒] into ax-2 | |
| 5513 | →→𝜑→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→𝜑→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒 | Modus ponens 5511, 5512 | |
| 5514 | →𝜑→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒 | Modus ponens 5508, 5513 | |
| 5515 | →¬⋀⋀𝜑𝜓𝜒¬⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒] into id | |
| 5516 | →¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 5517 | →→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 5518 | →¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒 | Modus ponens 5516, 5517 | |
| 5519 | →→¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜑¬⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5520 | →→¬⋀⋀𝜑𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒 | Modus ponens 5518, 5519 | |
| 5521 | →→𝜑→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒→→𝜑¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒 | Subs [𝜓↗¬⋀⋀𝜑𝜓𝜒, 𝜒↗¬⋀𝜓𝜒] into ax-2 | |
| 5522 | →→𝜑¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒 | Modus ponens 5514, 5521 | |
| 5523 | →→→𝜑¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→→𝜑¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→→𝜑¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 5524 | →¬⋀⋀𝜑𝜓𝜒→→𝜑¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒 | Modus ponens 5522, 5523 | |
| 5525 | →→¬⋀⋀𝜑𝜓𝜒→→𝜑¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜑¬⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 5526 | →→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒 | Modus ponens 5524, 5525 | |
| 5527 | →¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒 | Modus ponens 5516, 5526 | |
| 5528 | →¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒] into id | |
| 5529 | →→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 5530 | →¬⋀⋀𝜑𝜓𝜒→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 5528, 5529 | |
| 5531 | →¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒] into notnotr | |
| 5532 | →¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 5533 | →→¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1 | |
| 5534 | →¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 5532, 5533 | |
| 5535 | →→¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 5536 | →→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 5534, 5535 | |
| 5537 | →¬¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 5531, 5536 | |
| 5538 | →→¬⋀⋀𝜑𝜓𝜒→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗¬→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 5539 | →→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 5530, 5538 | |
| 5540 | →→→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1 | |
| 5541 | →¬¬¬→𝜑¬⋀𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 5539, 5540 | |
| 5542 | →→¬¬¬→𝜑¬⋀𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜒↗→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 5543 | →→¬¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 5541, 5542 | |
| 5544 | →¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1 | |
| 5545 | →→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 5546 | →¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒 | Modus ponens 5544, 5545 | |
| 5547 | →→¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5548 | →→¬⋀⋀𝜑𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒 | Modus ponens 5546, 5547 | |
| 5549 | →→¬¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒, 𝜒↗¬→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 5550 | →→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 5537, 5549 | |
| 5551 | →→→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 5552 | →¬⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 5550, 5551 | |
| 5553 | →→¬⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 5554 | →→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 5552, 5553 | |
| 5555 | →¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 5544, 5554 | |
| 5556 | →→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒] into ax-3 | |
| 5557 | →→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 5558 | →¬⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒 | Modus ponens 5556, 5557 | |
| 5559 | →→¬⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜒↗→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 5560 | →→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒 | Modus ponens 5558, 5559 | |
| 5561 | →¬⋀⋀𝜑𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒 | Modus ponens 5555, 5560 | |
| 5562 | →→¬⋀⋀𝜑𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒, 𝜒↗¬¬→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 5563 | →→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒 | Modus ponens 5561, 5562 | |
| 5564 | →¬⋀⋀𝜑𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒 | Modus ponens 5527, 5563 | |
| 5565 | →→¬⋀⋀𝜑𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into ax-3 | |
| 5566 | →¬→𝜑¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5564, 5565 | |
| 5567 | →↔⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into biimp | |
| 5568 | →⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 4981, 5567 | |
| 5569 | →→¬→𝜑¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 5570 | →⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5566, 5569 | |
| 5571 | →→⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→→⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 5572 | →→⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5570, 5571 | |
| 5573 | →⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5568, 5572 | |
| 5574 | →→⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into impbi | |
| 5575 | →→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5253, 5574 | |
| 5576 | ↔⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 5573, 5575 | anass |
| 5577 | →→⋀𝜑𝜓⋀𝜑𝜓→¬→𝜑¬𝜓→⋀𝜑𝜓⋀𝜑𝜓 | Subs [𝜑↗→⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓] into ax-1 | |
| 5578 | →¬→𝜑¬𝜓→⋀𝜑𝜓⋀𝜑𝜓 | Modus ponens 4647, 5577 | |
| 5579 | →→¬→𝜑¬𝜓→⋀𝜑𝜓⋀𝜑𝜓→→¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓⋀𝜑𝜓 | Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜑𝜓] into ax-2 | |
| 5580 | →→¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓⋀𝜑𝜓 | Modus ponens 5578, 5579 | |
| 5581 | →→¬→𝜑¬𝜓⋀𝜑𝜓→𝜓→¬→𝜑¬𝜓⋀𝜑𝜓 | Subs [𝜑↗→¬→𝜑¬𝜓⋀𝜑𝜓] into ax-1 | |
| 5582 | →𝜓→¬→𝜑¬𝜓⋀𝜑𝜓 | Modus ponens 4661, 5581 | |
| 5583 | →→𝜓→¬→𝜑¬𝜓⋀𝜑𝜓→→𝜓¬→𝜑¬𝜓→𝜓⋀𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗⋀𝜑𝜓] into ax-2 | |
| 5584 | →→𝜓¬→𝜑¬𝜓→𝜓⋀𝜑𝜓 | Modus ponens 5582, 5583 | |
| 5585 | →→→𝜓¬→𝜑¬𝜓→𝜓⋀𝜑𝜓→𝜑→→𝜓¬→𝜑¬𝜓→𝜓⋀𝜑𝜓 | Subs [𝜑↗→→𝜓¬→𝜑¬𝜓→𝜓⋀𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 5586 | →𝜑→→𝜓¬→𝜑¬𝜓→𝜓⋀𝜑𝜓 | Modus ponens 5584, 5585 | |
| 5587 | →→𝜑→→𝜓¬→𝜑¬𝜓→𝜓⋀𝜑𝜓→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→𝜓⋀𝜑𝜓 | Subs [𝜓↗→𝜓¬→𝜑¬𝜓, 𝜒↗→𝜓⋀𝜑𝜓] into ax-2 | |
| 5588 | →→𝜑→𝜓¬→𝜑¬𝜓→𝜑→𝜓⋀𝜑𝜓 | Modus ponens 5586, 5587 | |
| 5589 | →𝜑→𝜓⋀𝜑𝜓 | Modus ponens pm3.2im, 5588 | pm3.2 |
| 5590 | →𝜓→𝜒⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗𝜒] into pm3.2 | |
| 5591 | →→𝜓→𝜒⋀𝜓𝜒→𝜑→𝜓→𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜓→𝜒⋀𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 5592 | →𝜑→𝜓→𝜒⋀𝜓𝜒 | Modus ponens 5590, 5591 | |
| 5593 | →→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒 | Subs [𝜒↗→𝜒⋀𝜓𝜒] into ax-2 | |
| 5594 | →→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒 | Modus ponens 5592, 5593 | |
| 5595 | →→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒 | Subs [𝜓↗𝜒, 𝜒↗⋀𝜓𝜒] into ax-2 | |
| 5596 | →→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 5597 | →→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒 | Modus ponens 5595, 5596 | |
| 5598 | →→→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑→𝜒⋀𝜓𝜒, 𝜒↗→→𝜑𝜒→𝜑⋀𝜓𝜒] into ax-2 | |
| 5599 | →→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜓𝜒 | Modus ponens 5597, 5598 | |
| 5600 | →→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜓𝜒 | Modus ponens 5594, 5599 | pm3.43i |
| 5601 | ↔⋀→𝜑𝜓→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒] into df-an | |
| 5602 | →¬¬→𝜑𝜒→𝜑𝜒 | Subs [𝜑↗→𝜑𝜒] into notnotr | |
| 5603 | →→𝜑𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 5604 | →→→𝜑𝜒→→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗¬¬→𝜑𝜒] into ax-1 | |
| 5605 | →¬¬→𝜑𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 5603, 5604 | |
| 5606 | →→¬¬→𝜑𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→¬¬→𝜑𝜒→𝜑𝜒→¬¬→𝜑𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗¬¬→𝜑𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 5607 | →→¬¬→𝜑𝜒→𝜑𝜒→¬¬→𝜑𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 5605, 5606 | |
| 5608 | →¬¬→𝜑𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 5602, 5607 | |
| 5609 | →→→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2 | |
| 5610 | →→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Modus ponens pm3.43i, 5609 | |
| 5611 | →→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜓↗¬¬→𝜑𝜒] into ax-1 | |
| 5612 | →¬¬→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Modus ponens 5610, 5611 | |
| 5613 | →→¬¬→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→¬¬→𝜑𝜒→→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Subs [𝜑↗¬¬→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒, 𝜒↗→→𝜑𝜓→𝜑⋀𝜓𝜒] into ax-2 | |
| 5614 | →→¬¬→𝜑𝜒→→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Modus ponens 5612, 5613 | |
| 5615 | →¬¬→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Modus ponens 5608, 5614 | |
| 5616 | →→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗¬¬→𝜑𝜒] into ax-1 | |
| 5617 | →→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 5618 | →→𝜑𝜓→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓 | Modus ponens 5616, 5617 | |
| 5619 | →→→𝜑𝜓→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→¬¬→𝜑𝜒→𝜑𝜓] into ax-2 | |
| 5620 | →→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓 | Modus ponens 5618, 5619 | |
| 5621 | →→¬¬→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→¬¬→𝜑𝜒→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗¬¬→𝜑𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2 | |
| 5622 | →→¬¬→𝜑𝜒→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒 | Modus ponens 5615, 5621 | |
| 5623 | →→→¬¬→𝜑𝜒→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→→¬¬→𝜑𝜒→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗→→¬¬→𝜑𝜒→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 5624 | →→𝜑𝜓→→¬¬→𝜑𝜒→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒 | Modus ponens 5622, 5623 | |
| 5625 | →→→𝜑𝜓→→¬¬→𝜑𝜒→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓→→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜑𝜒→𝜑𝜓, 𝜒↗→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒] into ax-2 | |
| 5626 | →→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓→→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒 | Modus ponens 5624, 5625 | |
| 5627 | →→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒 | Modus ponens 5616, 5626 | |
| 5628 | →→𝜑⋀𝜓𝜒¬¬→𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜑⋀𝜓𝜒] into notnot | |
| 5629 | →→→𝜑⋀𝜓𝜒¬¬→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒→→𝜑⋀𝜓𝜒¬¬→𝜑⋀𝜓𝜒 | Subs [𝜑↗→→𝜑⋀𝜓𝜒¬¬→𝜑⋀𝜓𝜒, 𝜓↗¬¬→𝜑𝜒] into ax-1 | |
| 5630 | →¬¬→𝜑𝜒→→𝜑⋀𝜓𝜒¬¬→𝜑⋀𝜓𝜒 | Modus ponens 5628, 5629 | |
| 5631 | →→¬¬→𝜑𝜒→→𝜑⋀𝜓𝜒¬¬→𝜑⋀𝜓𝜒→→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒 | Subs [𝜑↗¬¬→𝜑𝜒, 𝜓↗→𝜑⋀𝜓𝜒, 𝜒↗¬¬→𝜑⋀𝜓𝜒] into ax-2 | |
| 5632 | →→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒 | Modus ponens 5630, 5631 | |
| 5633 | →→→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→→𝜑𝜓→→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒 | Subs [𝜑↗→→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 5634 | →→𝜑𝜓→→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒 | Modus ponens 5632, 5633 | |
| 5635 | →→→𝜑𝜓→→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→→→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜒↗→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒] into ax-2 | |
| 5636 | →→→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒 | Modus ponens 5634, 5635 | |
| 5637 | →→𝜑𝜓→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒 | Modus ponens 5627, 5636 | |
| 5638 | →→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒 | Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒] into ax-3 | |
| 5639 | →→→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒→→𝜑𝜓→→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒 | Subs [𝜑↗→→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 5640 | →→𝜑𝜓→→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒 | Modus ponens 5638, 5639 | |
| 5641 | →→→𝜑𝜓→→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒→→→𝜑𝜓→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→→𝜑𝜓→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒, 𝜒↗→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒] into ax-2 | |
| 5642 | →→→𝜑𝜓→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→→𝜑𝜓→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒 | Modus ponens 5640, 5641 | |
| 5643 | →→𝜑𝜓→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒 | Modus ponens 5637, 5642 | |
| 5644 | →¬→𝜑⋀𝜓𝜒¬→𝜑⋀𝜓𝜒 | Subs [𝜑↗¬→𝜑⋀𝜓𝜒] into id | |
| 5645 | →¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒 | Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 5646 | →→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒 | Subs [𝜑↗→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒] into ax-1 | |
| 5647 | →¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒 | Modus ponens 5645, 5646 | |
| 5648 | →→¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒→→¬→𝜑⋀𝜓𝜒¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒 | Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒, 𝜒↗→→𝜑𝜓¬→𝜑⋀𝜓𝜒] into ax-2 | |
| 5649 | →→¬→𝜑⋀𝜓𝜒¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒 | Modus ponens 5647, 5648 | |
| 5650 | →→→𝜑𝜓→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒→→→𝜑𝜓¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→𝜑⋀𝜓𝜒, 𝜒↗¬→𝜑𝜒] into ax-2 | |
| 5651 | →→→𝜑𝜓¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒 | Modus ponens 5643, 5650 | |
| 5652 | →→→→𝜑𝜓¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒→→→𝜑𝜓¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗→→→𝜑𝜓¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒] into ax-1 | |
| 5653 | →¬→𝜑⋀𝜓𝜒→→→𝜑𝜓¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒 | Modus ponens 5651, 5652 | |
| 5654 | →→¬→𝜑⋀𝜓𝜒→→→𝜑𝜓¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗→→𝜑𝜓¬→𝜑⋀𝜓𝜒, 𝜒↗→→𝜑𝜓¬→𝜑𝜒] into ax-2 | |
| 5655 | →→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒 | Modus ponens 5653, 5654 | |
| 5656 | →¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒 | Modus ponens 5645, 5655 | |
| 5657 | →¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗¬→→𝜑𝜓¬→𝜑𝜒] into id | |
| 5658 | →→¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒→¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗→¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒] into ax-1 | |
| 5659 | →¬→𝜑⋀𝜓𝜒→¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Modus ponens 5657, 5658 | |
| 5660 | →¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗¬→→𝜑𝜓¬→𝜑𝜒] into notnotr | |
| 5661 | →¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒] into ax-1 | |
| 5662 | →→¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗→¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜑𝜒] into ax-1 | |
| 5663 | →¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Modus ponens 5661, 5662 | |
| 5664 | →→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜑𝜒, 𝜒↗→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒] into ax-2 | |
| 5665 | →→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Modus ponens 5663, 5664 | |
| 5666 | →¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Modus ponens 5660, 5665 | |
| 5667 | →→¬→𝜑⋀𝜓𝜒→¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜑𝜒, 𝜒↗¬→→𝜑𝜓¬→𝜑𝜒] into ax-2 | |
| 5668 | →→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Modus ponens 5659, 5667 | |
| 5669 | →→→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗→→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜑𝜒] into ax-1 | |
| 5670 | →¬¬¬→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Modus ponens 5668, 5669 | |
| 5671 | →→¬¬¬→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒, 𝜒↗→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒] into ax-2 | |
| 5672 | →→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Modus ponens 5670, 5671 | |
| 5673 | →¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒 | Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜑𝜒] into ax-1 | |
| 5674 | →→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒 | Subs [𝜑↗→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒] into ax-1 | |
| 5675 | →¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒 | Modus ponens 5673, 5674 | |
| 5676 | →→¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→→¬→𝜑⋀𝜓𝜒¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒 | Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒, 𝜒↗→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒] into ax-2 | |
| 5677 | →→¬→𝜑⋀𝜓𝜒¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒 | Modus ponens 5675, 5676 | |
| 5678 | →→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒, 𝜒↗¬→→𝜑𝜓¬→𝜑𝜒] into ax-2 | |
| 5679 | →→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Modus ponens 5666, 5678 | |
| 5680 | →→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒] into ax-1 | |
| 5681 | →¬→𝜑⋀𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Modus ponens 5679, 5680 | |
| 5682 | →→¬→𝜑⋀𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒, 𝜒↗→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒] into ax-2 | |
| 5683 | →→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Modus ponens 5681, 5682 | |
| 5684 | →¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Modus ponens 5673, 5683 | |
| 5685 | →→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗¬¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗→→𝜑𝜓¬→𝜑𝜒] into ax-3 | |
| 5686 | →→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒] into ax-1 | |
| 5687 | →¬→𝜑⋀𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒 | Modus ponens 5685, 5686 | |
| 5688 | →→¬→𝜑⋀𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒, 𝜒↗→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒] into ax-2 | |
| 5689 | →→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒 | Modus ponens 5687, 5688 | |
| 5690 | →¬→𝜑⋀𝜓𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒 | Modus ponens 5684, 5689 | |
| 5691 | →→¬→𝜑⋀𝜓𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬¬→→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗→→𝜑𝜓¬→𝜑𝜒, 𝜒↗¬¬→→𝜑𝜓¬→𝜑𝜒] into ax-2 | |
| 5692 | →→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬¬→→𝜑𝜓¬→𝜑𝜒 | Modus ponens 5690, 5691 | |
| 5693 | →¬→𝜑⋀𝜓𝜒¬¬→→𝜑𝜓¬→𝜑𝜒 | Modus ponens 5656, 5692 | |
| 5694 | →→¬→𝜑⋀𝜓𝜒¬¬→→𝜑𝜓¬→𝜑𝜒→¬→→𝜑𝜓¬→𝜑𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜑𝜒] into ax-3 | |
| 5695 | →¬→→𝜑𝜓¬→𝜑𝜒→𝜑⋀𝜓𝜒 | Modus ponens 5693, 5694 | |
| 5696 | →↔⋀→𝜑𝜓→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→⋀→𝜑𝜓→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗⋀→𝜑𝜓→𝜑𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜑𝜒] into biimp | |
| 5697 | →⋀→𝜑𝜓→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒 | Modus ponens 5601, 5696 | |
| 5698 | →→¬→→𝜑𝜓¬→𝜑𝜒→𝜑⋀𝜓𝜒→⋀→𝜑𝜓→𝜑𝜒→¬→→𝜑𝜓¬→𝜑𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗→¬→→𝜑𝜓¬→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗⋀→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 5699 | →⋀→𝜑𝜓→𝜑𝜒→¬→→𝜑𝜓¬→𝜑𝜒→𝜑⋀𝜓𝜒 | Modus ponens 5695, 5698 | |
| 5700 | →→⋀→𝜑𝜓→𝜑𝜒→¬→→𝜑𝜓¬→𝜑𝜒→𝜑⋀𝜓𝜒→→⋀→𝜑𝜓→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀→𝜑𝜓→𝜑𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜑𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2 | |
| 5701 | →→⋀→𝜑𝜓→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒 | Modus ponens 5699, 5700 | |
| 5702 | →⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒 | Modus ponens 5697, 5701 | pm3.43 |
| 5703 | ↔⋀→𝜑𝜓→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜑] into df-an | |
| 5704 | →↔⋀→𝜑𝜓→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑↔¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗⋀→𝜑𝜓→𝜓𝜑, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑] into bicom1 | |
| 5705 | ↔¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑 | Modus ponens 5703, 5704 | |
| 5706 | →↔¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗⋀→𝜑𝜓→𝜓𝜑] into biimp | |
| 5707 | →¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑 | Modus ponens 5705, 5706 | |
| 5708 | →→¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑→↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 5709 | →↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑 | Modus ponens 5707, 5708 | |
| 5710 | →→↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗⋀→𝜑𝜓→𝜓𝜑] into ax-2 | |
| 5711 | →→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑 | Modus ponens 5709, 5710 | |
| 5712 | →↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑 | Modus ponens 1605, 5711 | |
| 5713 | →↔¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑↔⋀→𝜑𝜓→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗⋀→𝜑𝜓→𝜓𝜑] into bicom1 | |
| 5714 | →↔⋀→𝜑𝜓→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗⋀→𝜑𝜓→𝜓𝜑, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑] into biimp | |
| 5715 | →⋀→𝜑𝜓→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑 | Modus ponens 5703, 5714 | |
| 5716 | →↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑] into bicom1 | |
| 5717 | ↔¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens dfbi1, 5716 | |
| 5718 | →↔¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗↔𝜑𝜓] into biimp | |
| 5719 | →→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→⋀→𝜑𝜓→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗⋀→𝜑𝜓→𝜓𝜑] into ax-1 | |
| 5720 | →⋀→𝜑𝜓→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 1371, 5719 | |
| 5721 | →→⋀→𝜑𝜓→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→⋀→𝜑𝜓→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗⋀→𝜑𝜓→𝜓𝜑, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗↔𝜑𝜓] into ax-2 | |
| 5722 | →→⋀→𝜑𝜓→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓 | Modus ponens 5720, 5721 | |
| 5723 | →⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓 | Modus ponens 5715, 5722 | |
| 5724 | →→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀→𝜑𝜓→𝜓𝜑] into impbi | |
| 5725 | →→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑 | Modus ponens 5712, 5724 | |
| 5726 | ↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑 | Modus ponens 5723, 5725 | dfbi2 |
| 5727 | ↔↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑⋀→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀→𝜑𝜓→𝜓𝜑] into dfbi2 | |
| 5728 | →↔↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑⋀→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓→↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑⋀→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑, 𝜓↗⋀→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓] into biimp | |
| 5729 | →↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑⋀→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓 | Modus ponens 5727, 5728 | |
| 5730 | ⋀→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓 | Modus ponens dfbi2, 5729 | dfbi |
| 5731 | →→𝜑→𝜓𝜑→→𝜑𝜓→𝜑𝜑 | Subs [𝜒↗𝜑] into ax-2 | |
| 5732 | →→→𝜑𝜓→𝜑𝜑→¬¬𝜓→→𝜑𝜓→𝜑𝜑 | Subs [𝜑↗→→𝜑𝜓→𝜑𝜑, 𝜓↗¬¬𝜓] into ax-1 | |
| 5733 | →¬¬𝜓→→𝜑𝜓→𝜑𝜑 | Modus ponens 1148, 5732 | |
| 5734 | →→¬¬𝜓→→𝜑𝜓→𝜑𝜑→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑𝜑 | Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜑] into ax-2 | |
| 5735 | →→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑𝜑 | Modus ponens 5733, 5734 | |
| 5736 | →¬¬𝜓→𝜑𝜑 | Modus ponens 575, 5735 | |
| 5737 | →→¬¬𝜓→𝜑𝜑→→¬¬𝜓𝜑→¬¬𝜓𝜑 | Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑, 𝜒↗𝜑] into ax-2 | |
| 5738 | →→¬¬𝜓𝜑→¬¬𝜓𝜑 | Modus ponens 5736, 5737 | |
| 5739 | →→→¬¬𝜓𝜑→¬¬𝜓𝜑→𝜑→→¬¬𝜓𝜑→¬¬𝜓𝜑 | Subs [𝜑↗→→¬¬𝜓𝜑→¬¬𝜓𝜑, 𝜓↗𝜑] into ax-1 | |
| 5740 | →𝜑→→¬¬𝜓𝜑→¬¬𝜓𝜑 | Modus ponens 5738, 5739 | |
| 5741 | →→𝜑→→¬¬𝜓𝜑→¬¬𝜓𝜑→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓𝜑 | Subs [𝜓↗→¬¬𝜓𝜑, 𝜒↗→¬¬𝜓𝜑] into ax-2 | |
| 5742 | →→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓𝜑 | Modus ponens 5740, 5741 | |
| 5743 | →→𝜑¬¬𝜑→¬¬𝜓→𝜑¬¬𝜑 | Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜓] into ax-1 | |
| 5744 | →¬¬𝜓→𝜑¬¬𝜑 | Modus ponens notnot, 5743 | |
| 5745 | →→¬¬𝜓→𝜑¬¬𝜑→→¬¬𝜓𝜑→¬¬𝜓¬¬𝜑 | Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2 | |
| 5746 | →→¬¬𝜓𝜑→¬¬𝜓¬¬𝜑 | Modus ponens 5744, 5745 | |
| 5747 | →→→¬¬𝜓𝜑→¬¬𝜓¬¬𝜑→𝜑→→¬¬𝜓𝜑→¬¬𝜓¬¬𝜑 | Subs [𝜑↗→→¬¬𝜓𝜑→¬¬𝜓¬¬𝜑, 𝜓↗𝜑] into ax-1 | |
| 5748 | →𝜑→→¬¬𝜓𝜑→¬¬𝜓¬¬𝜑 | Modus ponens 5746, 5747 | |
| 5749 | →→𝜑→→¬¬𝜓𝜑→¬¬𝜓¬¬𝜑→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓¬¬𝜑 | Subs [𝜓↗→¬¬𝜓𝜑, 𝜒↗→¬¬𝜓¬¬𝜑] into ax-2 | |
| 5750 | →→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓¬¬𝜑 | Modus ponens 5748, 5749 | |
| 5751 | →𝜑→¬¬𝜓¬¬𝜑 | Modus ponens 581, 5750 | |
| 5752 | →→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓→𝜑→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓 | Subs [𝜑↗→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 5753 | →𝜑→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓 | Modus ponens 2033, 5752 | |
| 5754 | →→𝜑→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓→→𝜑→¬¬𝜓¬¬𝜑→𝜑→¬𝜑¬𝜓 | Subs [𝜓↗→¬¬𝜓¬¬𝜑, 𝜒↗→¬𝜑¬𝜓] into ax-2 | |
| 5755 | →→𝜑→¬¬𝜓¬¬𝜑→𝜑→¬𝜑¬𝜓 | Modus ponens 5753, 5754 | |
| 5756 | →𝜑→¬𝜑¬𝜓 | Modus ponens 5751, 5755 | |
| 5757 | →→¬𝜑→𝜑¬𝜑→¬𝜑→¬𝜑→𝜑¬𝜑 | Subs [𝜑↗→¬𝜑→𝜑¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 5758 | →¬𝜑→¬𝜑→𝜑¬𝜑 | Modus ponens 414, 5757 | |
| 5759 | →→¬𝜑→¬𝜑→𝜑¬𝜑→→¬𝜑¬𝜑→¬𝜑→𝜑¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→𝜑¬𝜑] into ax-2 | |
| 5760 | →→¬𝜑¬𝜑→¬𝜑→𝜑¬𝜑 | Modus ponens 5758, 5759 | |
| 5761 | →→𝜑→¬𝜑¬𝜓→→𝜑¬𝜑→𝜑¬𝜓 | Subs [𝜓↗¬𝜑, 𝜒↗¬𝜓] into ax-2 | |
| 5762 | →→𝜑¬𝜑→𝜑¬𝜓 | Modus ponens 5756, 5761 | |
| 5763 | →→→𝜑¬𝜑→𝜑¬𝜓→¬𝜑→→𝜑¬𝜑→𝜑¬𝜓 | Subs [𝜑↗→→𝜑¬𝜑→𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 5764 | →¬𝜑→→𝜑¬𝜑→𝜑¬𝜓 | Modus ponens 5762, 5763 | |
| 5765 | →→¬𝜑→→𝜑¬𝜑→𝜑¬𝜓→→¬𝜑→𝜑¬𝜑→¬𝜑→𝜑¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗→𝜑¬𝜑, 𝜒↗→𝜑¬𝜓] into ax-2 | |
| 5766 | →→¬𝜑→𝜑¬𝜑→¬𝜑→𝜑¬𝜓 | Modus ponens 5764, 5765 | |
| 5767 | →¬𝜑→𝜑¬𝜓 | Modus ponens 414, 5766 | |
| 5768 | →→¬→𝜑¬𝜓¬→𝜑¬𝜓→¬𝜑→¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 5769 | →¬𝜑→¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 619, 5768 | |
| 5770 | →¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓 | Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 5771 | →→¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓 | Subs [𝜑↗→¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1 | |
| 5772 | →¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓 | Modus ponens 5770, 5771 | |
| 5773 | →→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓 | Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→¬𝜑¬→𝜑¬𝜓] into ax-2 | |
| 5774 | →→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓 | Modus ponens 5772, 5773 | |
| 5775 | →¬¬¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓 | Modus ponens 622, 5774 | |
| 5776 | →→¬𝜑→¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬𝜑¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗¬→𝜑¬𝜓, 𝜒↗¬→𝜑¬𝜓] into ax-2 | |
| 5777 | →→¬𝜑¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓 | Modus ponens 5769, 5776 | |
| 5778 | →→→¬𝜑¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→→¬𝜑¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓 | Subs [𝜑↗→→¬𝜑¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1 | |
| 5779 | →¬¬¬→𝜑¬𝜓→→¬𝜑¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓 | Modus ponens 5777, 5778 | |
| 5780 | →→¬¬¬→𝜑¬𝜓→→¬𝜑¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓 | Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗→¬𝜑¬→𝜑¬𝜓, 𝜒↗→¬𝜑¬→𝜑¬𝜓] into ax-2 | |
| 5781 | →→¬¬¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓 | Modus ponens 5779, 5780 | |
| 5782 | →¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1 | |
| 5783 | →→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑→¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 5784 | →¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑 | Modus ponens 5782, 5783 | |
| 5785 | →→¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→𝜑¬𝜓¬𝜑] into ax-2 | |
| 5786 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑 | Modus ponens 5784, 5785 | |
| 5787 | →→¬¬¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬𝜑, 𝜒↗¬→𝜑¬𝜓] into ax-2 | |
| 5788 | →→¬¬¬→𝜑¬𝜓¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 5775, 5787 | |
| 5789 | →→→¬¬¬→𝜑¬𝜓¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬𝜑→→¬¬¬→𝜑¬𝜓¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 5790 | →¬𝜑→→¬¬¬→𝜑¬𝜓¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 5788, 5789 | |
| 5791 | →→¬𝜑→→¬¬¬→𝜑¬𝜓¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→𝜑¬𝜓¬𝜑, 𝜒↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓] into ax-2 | |
| 5792 | →→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 5790, 5791 | |
| 5793 | →¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 5782, 5792 | |
| 5794 | →→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→¬𝜑→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 5795 | →¬𝜑→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Modus ponens 647, 5794 | |
| 5796 | →→¬𝜑→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬𝜑→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜒↗→→𝜑¬𝜓¬¬→𝜑¬𝜓] into ax-2 | |
| 5797 | →→¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬𝜑→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Modus ponens 5795, 5796 | |
| 5798 | →¬𝜑→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Modus ponens 5793, 5797 | |
| 5799 | →→¬𝜑→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬𝜑→𝜑¬𝜓→¬𝜑¬¬→𝜑¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗→𝜑¬𝜓, 𝜒↗¬¬→𝜑¬𝜓] into ax-2 | |
| 5800 | →→¬𝜑→𝜑¬𝜓→¬𝜑¬¬→𝜑¬𝜓 | Modus ponens 5798, 5799 | |
| 5801 | →¬𝜑¬¬→𝜑¬𝜓 | Modus ponens 5767, 5800 | |
| 5802 | →→¬𝜑¬¬→𝜑¬𝜓→¬→𝜑¬𝜓𝜑 | Subs [𝜓↗¬→𝜑¬𝜓] into ax-3 | |
| 5803 | →→¬→𝜑¬𝜓𝜑→⋀𝜑𝜓→¬→𝜑¬𝜓𝜑 | Subs [𝜑↗→¬→𝜑¬𝜓𝜑, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 5804 | →⋀𝜑𝜓→¬→𝜑¬𝜓𝜑 | Modus ponens 866, 5803 | |
| 5805 | →→⋀𝜑𝜓→¬→𝜑¬𝜓𝜑→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓𝜑 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗𝜑] into ax-2 | |
| 5806 | →→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓𝜑 | Modus ponens 5804, 5805 | |
| 5807 | →⋀𝜑𝜓𝜑 | Modus ponens 4842, 5806 | simpl |
| 5808 | →→𝜓→𝜑𝜓→𝜓→𝜓→𝜑𝜓 | Subs [𝜑↗→𝜓→𝜑𝜓] into ax-1 | |
| 5809 | →𝜓→𝜓→𝜑𝜓 | Modus ponens 208, 5808 | |
| 5810 | →→𝜓→𝜓→𝜑𝜓→→𝜓𝜓→𝜓→𝜑𝜓 | Subs [𝜑↗𝜓, 𝜒↗→𝜑𝜓] into ax-2 | |
| 5811 | →→𝜓𝜓→𝜓→𝜑𝜓 | Modus ponens 5809, 5810 | |
| 5812 | →→𝜑→𝜓𝜑→¬¬𝜑→𝜑→𝜓𝜑 | Subs [𝜑↗→𝜑→𝜓𝜑, 𝜓↗¬¬𝜑] into ax-1 | |
| 5813 | →¬¬𝜑→𝜑→𝜓𝜑 | Modus ponens ax-1, 5812 | |
| 5814 | →→¬¬𝜑→𝜑→𝜓𝜑→→¬¬𝜑𝜑→¬¬𝜑→𝜓𝜑 | Subs [𝜑↗¬¬𝜑, 𝜓↗𝜑, 𝜒↗→𝜓𝜑] into ax-2 | |
| 5815 | →→¬¬𝜑𝜑→¬¬𝜑→𝜓𝜑 | Modus ponens 5813, 5814 | |
| 5816 | →¬¬𝜑→𝜓𝜑 | Modus ponens notnotr, 5815 | |
| 5817 | →→𝜓→𝜑𝜓→→𝜓𝜑→𝜓𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2 | |
| 5818 | →→𝜓𝜑→𝜓𝜓 | Modus ponens 208, 5817 | |
| 5819 | →→→𝜓𝜑→𝜓𝜓→¬¬𝜑→→𝜓𝜑→𝜓𝜓 | Subs [𝜑↗→→𝜓𝜑→𝜓𝜓, 𝜓↗¬¬𝜑] into ax-1 | |
| 5820 | →¬¬𝜑→→𝜓𝜑→𝜓𝜓 | Modus ponens 5818, 5819 | |
| 5821 | →→¬¬𝜑→→𝜓𝜑→𝜓𝜓→→¬¬𝜑→𝜓𝜑→¬¬𝜑→𝜓𝜓 | Subs [𝜑↗¬¬𝜑, 𝜓↗→𝜓𝜑, 𝜒↗→𝜓𝜓] into ax-2 | |
| 5822 | →→¬¬𝜑→𝜓𝜑→¬¬𝜑→𝜓𝜓 | Modus ponens 5820, 5821 | |
| 5823 | →¬¬𝜑→𝜓𝜓 | Modus ponens 5816, 5822 | |
| 5824 | →𝜓→¬¬𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬¬𝜑] into ax-1 | |
| 5825 | →→𝜓→¬¬𝜑𝜓→𝜓→𝜓→¬¬𝜑𝜓 | Subs [𝜑↗→𝜓→¬¬𝜑𝜓] into ax-1 | |
| 5826 | →𝜓→𝜓→¬¬𝜑𝜓 | Modus ponens 5824, 5825 | |
| 5827 | →→𝜓→𝜓→¬¬𝜑𝜓→→𝜓𝜓→𝜓→¬¬𝜑𝜓 | Subs [𝜑↗𝜓, 𝜒↗→¬¬𝜑𝜓] into ax-2 | |
| 5828 | →→𝜓𝜓→𝜓→¬¬𝜑𝜓 | Modus ponens 5826, 5827 | |
| 5829 | →→¬¬𝜑→𝜓𝜓→→¬¬𝜑𝜓→¬¬𝜑𝜓 | Subs [𝜑↗¬¬𝜑, 𝜒↗𝜓] into ax-2 | |
| 5830 | →→¬¬𝜑𝜓→¬¬𝜑𝜓 | Modus ponens 5823, 5829 | |
| 5831 | →→→¬¬𝜑𝜓→¬¬𝜑𝜓→𝜓→→¬¬𝜑𝜓→¬¬𝜑𝜓 | Subs [𝜑↗→→¬¬𝜑𝜓→¬¬𝜑𝜓] into ax-1 | |
| 5832 | →𝜓→→¬¬𝜑𝜓→¬¬𝜑𝜓 | Modus ponens 5830, 5831 | |
| 5833 | →→𝜓→→¬¬𝜑𝜓→¬¬𝜑𝜓→→𝜓→¬¬𝜑𝜓→𝜓→¬¬𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜑𝜓, 𝜒↗→¬¬𝜑𝜓] into ax-2 | |
| 5834 | →→𝜓→¬¬𝜑𝜓→𝜓→¬¬𝜑𝜓 | Modus ponens 5832, 5833 | |
| 5835 | →→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓→𝜓→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓 | Subs [𝜑↗→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓] into ax-1 | |
| 5836 | →𝜓→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓 | Modus ponens 488, 5835 | |
| 5837 | →→𝜓→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓→→𝜓→¬¬𝜑𝜓→𝜓→¬¬𝜑¬¬𝜓 | Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜑𝜓, 𝜒↗→¬¬𝜑¬¬𝜓] into ax-2 | |
| 5838 | →→𝜓→¬¬𝜑𝜓→𝜓→¬¬𝜑¬¬𝜓 | Modus ponens 5836, 5837 | |
| 5839 | →𝜓→¬¬𝜑¬¬𝜓 | Modus ponens 5824, 5838 | |
| 5840 | →→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑→𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑 | Subs [𝜑↗→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑] into ax-1 | |
| 5841 | →𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑 | Modus ponens 494, 5840 | |
| 5842 | →→𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑→→𝜓→¬¬𝜑¬¬𝜓→𝜓→¬𝜓¬𝜑 | Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜑¬¬𝜓, 𝜒↗→¬𝜓¬𝜑] into ax-2 | |
| 5843 | →→𝜓→¬¬𝜑¬¬𝜓→𝜓→¬𝜓¬𝜑 | Modus ponens 5841, 5842 | |
| 5844 | →𝜓→¬𝜓¬𝜑 | Modus ponens 5839, 5843 | |
| 5845 | →¬𝜓→𝜓¬𝜓 | Subs [𝜑↗¬𝜓] into ax-1 | |
| 5846 | →→¬𝜓→𝜓¬𝜓→¬𝜓→¬𝜓→𝜓¬𝜓 | Subs [𝜑↗→¬𝜓→𝜓¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 5847 | →¬𝜓→¬𝜓→𝜓¬𝜓 | Modus ponens 5845, 5846 | |
| 5848 | →→¬𝜓→¬𝜓→𝜓¬𝜓→→¬𝜓¬𝜓→¬𝜓→𝜓¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→𝜓¬𝜓] into ax-2 | |
| 5849 | →→¬𝜓¬𝜓→¬𝜓→𝜓¬𝜓 | Modus ponens 5847, 5848 | |
| 5850 | →→𝜓→¬𝜓¬𝜑→→𝜓¬𝜓→𝜓¬𝜑 | Subs [𝜑↗𝜓, 𝜓↗¬𝜓, 𝜒↗¬𝜑] into ax-2 | |
| 5851 | →→𝜓¬𝜓→𝜓¬𝜑 | Modus ponens 5844, 5850 | |
| 5852 | →→→𝜓¬𝜓→𝜓¬𝜑→¬𝜓→→𝜓¬𝜓→𝜓¬𝜑 | Subs [𝜑↗→→𝜓¬𝜓→𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1 | |
| 5853 | →¬𝜓→→𝜓¬𝜓→𝜓¬𝜑 | Modus ponens 5851, 5852 | |
| 5854 | →→¬𝜓→→𝜓¬𝜓→𝜓¬𝜑→→¬𝜓→𝜓¬𝜓→¬𝜓→𝜓¬𝜑 | Subs [𝜑↗¬𝜓, 𝜓↗→𝜓¬𝜓, 𝜒↗→𝜓¬𝜑] into ax-2 | |
| 5855 | →→¬𝜓→𝜓¬𝜓→¬𝜓→𝜓¬𝜑 | Modus ponens 5853, 5854 | |
| 5856 | →¬𝜓→𝜓¬𝜑 | Modus ponens 5845, 5855 | |
| 5857 | →¬→𝜓¬𝜑¬→𝜓¬𝜑 | Subs [𝜑↗¬→𝜓¬𝜑] into id | |
| 5858 | →→¬→𝜓¬𝜑¬→𝜓¬𝜑→¬𝜓→¬→𝜓¬𝜑¬→𝜓¬𝜑 | Subs [𝜑↗→¬→𝜓¬𝜑¬→𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1 | |
| 5859 | →¬𝜓→¬→𝜓¬𝜑¬→𝜓¬𝜑 | Modus ponens 5857, 5858 | |
| 5860 | →¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑 | Subs [𝜑↗¬→𝜓¬𝜑] into notnotr | |
| 5861 | →¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑 | Subs [𝜑↗¬→𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1 | |
| 5862 | →→¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑→¬¬¬→𝜓¬𝜑→¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑 | Subs [𝜑↗→¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑, 𝜓↗¬¬¬→𝜓¬𝜑] into ax-1 | |
| 5863 | →¬¬¬→𝜓¬𝜑→¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑 | Modus ponens 5861, 5862 | |
| 5864 | →→¬¬¬→𝜓¬𝜑→¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑→→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→¬¬¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑 | Subs [𝜑↗¬¬¬→𝜓¬𝜑, 𝜓↗¬→𝜓¬𝜑, 𝜒↗→¬𝜓¬→𝜓¬𝜑] into ax-2 | |
| 5865 | →→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→¬¬¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑 | Modus ponens 5863, 5864 | |
| 5866 | →¬¬¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑 | Modus ponens 5860, 5865 | |
| 5867 | →→¬𝜓→¬→𝜓¬𝜑¬→𝜓¬𝜑→→¬𝜓¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑 | Subs [𝜑↗¬𝜓, 𝜓↗¬→𝜓¬𝜑, 𝜒↗¬→𝜓¬𝜑] into ax-2 | |
| 5868 | →→¬𝜓¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑 | Modus ponens 5859, 5867 | |
| 5869 | →→→¬𝜓¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑→¬¬¬→𝜓¬𝜑→→¬𝜓¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑 | Subs [𝜑↗→→¬𝜓¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑, 𝜓↗¬¬¬→𝜓¬𝜑] into ax-1 | |
| 5870 | →¬¬¬→𝜓¬𝜑→→¬𝜓¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑 | Modus ponens 5868, 5869 | |
| 5871 | →→¬¬¬→𝜓¬𝜑→→¬𝜓¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑→→¬¬¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑→¬¬¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑 | Subs [𝜑↗¬¬¬→𝜓¬𝜑, 𝜓↗→¬𝜓¬→𝜓¬𝜑, 𝜒↗→¬𝜓¬→𝜓¬𝜑] into ax-2 | |
| 5872 | →→¬¬¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑→¬¬¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑 | Modus ponens 5870, 5871 | |
| 5873 | →¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→𝜓¬𝜑] into ax-1 | |
| 5874 | →→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓→¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 5875 | →¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓 | Modus ponens 5873, 5874 | |
| 5876 | →→¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→𝜓¬𝜑¬𝜓] into ax-2 | |
| 5877 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓 | Modus ponens 5875, 5876 | |
| 5878 | →→¬¬¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑→→¬¬¬→𝜓¬𝜑¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑 | Subs [𝜑↗¬¬¬→𝜓¬𝜑, 𝜓↗¬𝜓, 𝜒↗¬→𝜓¬𝜑] into ax-2 | |
| 5879 | →→¬¬¬→𝜓¬𝜑¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑 | Modus ponens 5866, 5878 | |
| 5880 | →→→¬¬¬→𝜓¬𝜑¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→¬𝜓→→¬¬¬→𝜓¬𝜑¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑 | Subs [𝜑↗→→¬¬¬→𝜓¬𝜑¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1 | |
| 5881 | →¬𝜓→→¬¬¬→𝜓¬𝜑¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑 | Modus ponens 5879, 5880 | |
| 5882 | →→¬𝜓→→¬¬¬→𝜓¬𝜑¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜓¬𝜑¬𝜓, 𝜒↗→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑] into ax-2 | |
| 5883 | →→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑 | Modus ponens 5881, 5882 | |
| 5884 | →¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑 | Modus ponens 5873, 5883 | |
| 5885 | →→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→→𝜓¬𝜑¬¬→𝜓¬𝜑 | Subs [𝜑↗¬¬→𝜓¬𝜑, 𝜓↗→𝜓¬𝜑] into ax-3 | |
| 5886 | →→→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→→𝜓¬𝜑¬¬→𝜓¬𝜑→¬𝜓→→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→→𝜓¬𝜑¬¬→𝜓¬𝜑 | Subs [𝜑↗→→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→→𝜓¬𝜑¬¬→𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1 | |
| 5887 | →¬𝜓→→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→→𝜓¬𝜑¬¬→𝜓¬𝜑 | Modus ponens 5885, 5886 | |
| 5888 | →→¬𝜓→→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→→𝜓¬𝜑¬¬→𝜓¬𝜑→→¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→¬𝜓→→𝜓¬𝜑¬¬→𝜓¬𝜑 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑, 𝜒↗→→𝜓¬𝜑¬¬→𝜓¬𝜑] into ax-2 | |
| 5889 | →→¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→¬𝜓→→𝜓¬𝜑¬¬→𝜓¬𝜑 | Modus ponens 5887, 5888 | |
| 5890 | →¬𝜓→→𝜓¬𝜑¬¬→𝜓¬𝜑 | Modus ponens 5884, 5889 | |
| 5891 | →→¬𝜓→→𝜓¬𝜑¬¬→𝜓¬𝜑→→¬𝜓→𝜓¬𝜑→¬𝜓¬¬→𝜓¬𝜑 | Subs [𝜑↗¬𝜓, 𝜓↗→𝜓¬𝜑, 𝜒↗¬¬→𝜓¬𝜑] into ax-2 | |
| 5892 | →→¬𝜓→𝜓¬𝜑→¬𝜓¬¬→𝜓¬𝜑 | Modus ponens 5890, 5891 | |
| 5893 | →¬𝜓¬¬→𝜓¬𝜑 | Modus ponens 5856, 5892 | |
| 5894 | →→¬𝜓¬¬→𝜓¬𝜑→¬→𝜓¬𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→𝜓¬𝜑] into ax-3 | |
| 5895 | →¬→𝜓¬𝜑𝜓 | Modus ponens 5893, 5894 | |
| 5896 | →↔⋀𝜓𝜑¬→𝜓¬𝜑→⋀𝜓𝜑¬→𝜓¬𝜑 | Subs [𝜑↗⋀𝜓𝜑, 𝜓↗¬→𝜓¬𝜑] into biimp | |
| 5897 | →⋀𝜓𝜑¬→𝜓¬𝜑 | Modus ponens 4864, 5896 | |
| 5898 | →→¬→𝜓¬𝜑𝜓→⋀𝜓𝜑→¬→𝜓¬𝜑𝜓 | Subs [𝜑↗→¬→𝜓¬𝜑𝜓, 𝜓↗⋀𝜓𝜑] into ax-1 | |
| 5899 | →⋀𝜓𝜑→¬→𝜓¬𝜑𝜓 | Modus ponens 5895, 5898 | |
| 5900 | →→⋀𝜓𝜑→¬→𝜓¬𝜑𝜓→→⋀𝜓𝜑¬→𝜓¬𝜑→⋀𝜓𝜑𝜓 | Subs [𝜑↗⋀𝜓𝜑, 𝜓↗¬→𝜓¬𝜑, 𝜒↗𝜓] into ax-2 | |
| 5901 | →→⋀𝜓𝜑¬→𝜓¬𝜑→⋀𝜓𝜑𝜓 | Modus ponens 5899, 5900 | |
| 5902 | →⋀𝜓𝜑𝜓 | Modus ponens 5897, 5901 | |
| 5903 | →→⋀𝜓𝜑𝜓→¬→𝜓¬𝜑→⋀𝜓𝜑𝜓 | Subs [𝜑↗→⋀𝜓𝜑𝜓, 𝜓↗¬→𝜓¬𝜑] into ax-1 | |
| 5904 | →¬→𝜓¬𝜑→⋀𝜓𝜑𝜓 | Modus ponens 5902, 5903 | |
| 5905 | →→¬→𝜓¬𝜑→⋀𝜓𝜑𝜓→→¬→𝜓¬𝜑⋀𝜓𝜑→¬→𝜓¬𝜑𝜓 | Subs [𝜑↗¬→𝜓¬𝜑, 𝜓↗⋀𝜓𝜑, 𝜒↗𝜓] into ax-2 | |
| 5906 | →→¬→𝜓¬𝜑⋀𝜓𝜑→¬→𝜓¬𝜑𝜓 | Modus ponens 5904, 5905 | |
| 5907 | →→¬→𝜓¬𝜑𝜓→𝜑→¬→𝜓¬𝜑𝜓 | Subs [𝜑↗→¬→𝜓¬𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 5908 | →𝜑→¬→𝜓¬𝜑𝜓 | Modus ponens 5895, 5907 | |
| 5909 | →→𝜑→¬→𝜓¬𝜑𝜓→→𝜑¬→𝜓¬𝜑→𝜑𝜓 | Subs [𝜓↗¬→𝜓¬𝜑, 𝜒↗𝜓] into ax-2 | |
| 5910 | →→𝜑¬→𝜓¬𝜑→𝜑𝜓 | Modus ponens 5908, 5909 | |
| 5911 | →→→𝜑¬→𝜓¬𝜑→𝜑𝜓→𝜓→→𝜑¬→𝜓¬𝜑→𝜑𝜓 | Subs [𝜑↗→→𝜑¬→𝜓¬𝜑→𝜑𝜓] into ax-1 | |
| 5912 | →𝜓→→𝜑¬→𝜓¬𝜑→𝜑𝜓 | Modus ponens 5910, 5911 | |
| 5913 | →→𝜓→→𝜑¬→𝜓¬𝜑→𝜑𝜓→→𝜓→𝜑¬→𝜓¬𝜑→𝜓→𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗→𝜑¬→𝜓¬𝜑, 𝜒↗→𝜑𝜓] into ax-2 | |
| 5914 | →→𝜓→𝜑¬→𝜓¬𝜑→𝜓→𝜑𝜓 | Modus ponens 5912, 5913 | |
| 5915 | →→→𝜓𝜑→𝜓𝜓→𝜑→→𝜓𝜑→𝜓𝜓 | Subs [𝜑↗→→𝜓𝜑→𝜓𝜓, 𝜓↗𝜑] into ax-1 | |
| 5916 | →𝜑→→𝜓𝜑→𝜓𝜓 | Modus ponens 5818, 5915 | |
| 5917 | →→𝜑→→𝜓𝜑→𝜓𝜓→→𝜑→𝜓𝜑→𝜑→𝜓𝜓 | Subs [𝜓↗→𝜓𝜑, 𝜒↗→𝜓𝜓] into ax-2 | |
| 5918 | →→𝜑→𝜓𝜑→𝜑→𝜓𝜓 | Modus ponens 5916, 5917 | |
| 5919 | →→¬→𝜑¬𝜓𝜓→⋀𝜑𝜓→¬→𝜑¬𝜓𝜓 | Subs [𝜑↗→¬→𝜑¬𝜓𝜓, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 5920 | →⋀𝜑𝜓→¬→𝜑¬𝜓𝜓 | Modus ponens simprim, 5919 | |
| 5921 | →→⋀𝜑𝜓→¬→𝜑¬𝜓𝜓→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗𝜓] into ax-2 | |
| 5922 | →→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓𝜓 | Modus ponens 5920, 5921 | |
| 5923 | →⋀𝜑𝜓𝜓 | Modus ponens 4842, 5922 | simpr |
| 5924 | →→𝜑𝜒→𝜑𝜒 | Modus ponens 815, 2228 | |
| 5925 | →𝜑→→𝜑𝜒𝜑 | Subs [𝜓↗→𝜑𝜒] into ax-1 | |
| 5926 | →→𝜑→→𝜑𝜒𝜑→⋀𝜑𝜓→𝜑→→𝜑𝜒𝜑 | Subs [𝜑↗→𝜑→→𝜑𝜒𝜑, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 5927 | →⋀𝜑𝜓→𝜑→→𝜑𝜒𝜑 | Modus ponens 5925, 5926 | |
| 5928 | →→⋀𝜑𝜓→𝜑→→𝜑𝜒𝜑→→⋀𝜑𝜓𝜑→⋀𝜑𝜓→→𝜑𝜒𝜑 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜑, 𝜒↗→→𝜑𝜒𝜑] into ax-2 | |
| 5929 | →→⋀𝜑𝜓𝜑→⋀𝜑𝜓→→𝜑𝜒𝜑 | Modus ponens 5927, 5928 | |
| 5930 | →⋀𝜑𝜓→→𝜑𝜒𝜑 | Modus ponens simpl, 5929 | |
| 5931 | →→→𝜑𝜒→𝜑𝜒→→→𝜑𝜒𝜑→→𝜑𝜒𝜒 | Subs [𝜑↗→𝜑𝜒, 𝜓↗𝜑] into ax-2 | |
| 5932 | →→→𝜑𝜒𝜑→→𝜑𝜒𝜒 | Modus ponens 5924, 5931 | |
| 5933 | →→→→𝜑𝜒𝜑→→𝜑𝜒𝜒→⋀𝜑𝜓→→→𝜑𝜒𝜑→→𝜑𝜒𝜒 | Subs [𝜑↗→→→𝜑𝜒𝜑→→𝜑𝜒𝜒, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 5934 | →⋀𝜑𝜓→→→𝜑𝜒𝜑→→𝜑𝜒𝜒 | Modus ponens 5932, 5933 | |
| 5935 | →→⋀𝜑𝜓→→→𝜑𝜒𝜑→→𝜑𝜒𝜒→→⋀𝜑𝜓→→𝜑𝜒𝜑→⋀𝜑𝜓→→𝜑𝜒𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→→𝜑𝜒𝜑, 𝜒↗→→𝜑𝜒𝜒] into ax-2 | |
| 5936 | →→⋀𝜑𝜓→→𝜑𝜒𝜑→⋀𝜑𝜓→→𝜑𝜒𝜒 | Modus ponens 5934, 5935 | |
| 5937 | →⋀𝜑𝜓→→𝜑𝜒𝜒 | Modus ponens 5930, 5936 | |
| 5938 | →→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑𝜒, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 5939 | →→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒→→𝜑𝜒→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑𝜒] into ax-1 | |
| 5940 | →→𝜑𝜒→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒 | Modus ponens 5938, 5939 | |
| 5941 | →→→𝜑𝜒→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→⋀𝜑𝜓→𝜑𝜒] into ax-2 | |
| 5942 | →→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒 | Modus ponens 5940, 5941 | |
| 5943 | →→⋀𝜑𝜓→→𝜑𝜒𝜒→→⋀𝜑𝜓→𝜑𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜑𝜒] into ax-2 | |
| 5944 | →→⋀𝜑𝜓→𝜑𝜒→⋀𝜑𝜓𝜒 | Modus ponens 5937, 5943 | |
| 5945 | →→→⋀𝜑𝜓→𝜑𝜒→⋀𝜑𝜓𝜒→→𝜑𝜒→→⋀𝜑𝜓→𝜑𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→→⋀𝜑𝜓→𝜑𝜒→⋀𝜑𝜓𝜒, 𝜓↗→𝜑𝜒] into ax-1 | |
| 5946 | →→𝜑𝜒→→⋀𝜑𝜓→𝜑𝜒→⋀𝜑𝜓𝜒 | Modus ponens 5944, 5945 | |
| 5947 | →→→𝜑𝜒→→⋀𝜑𝜓→𝜑𝜒→⋀𝜑𝜓𝜒→→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒→→𝜑𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→𝜑𝜒, 𝜓↗→⋀𝜑𝜓→𝜑𝜒, 𝜒↗→⋀𝜑𝜓𝜒] into ax-2 | |
| 5948 | →→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒→→𝜑𝜒→⋀𝜑𝜓𝜒 | Modus ponens 5946, 5947 | |
| 5949 | →→𝜑𝜒→⋀𝜑𝜓𝜒 | Modus ponens 5938, 5948 | pm3.41 |
| 5950 | →𝜓→𝜒𝜒 | Modus ponens 209, 51 | |
| 5951 | →𝜓→→𝜓𝜒𝜓 | Subs [𝜑↗𝜓, 𝜓↗→𝜓𝜒] into ax-1 | |
| 5952 | →→𝜓→→𝜓𝜒𝜓→⋀𝜑𝜓→𝜓→→𝜓𝜒𝜓 | Subs [𝜑↗→𝜓→→𝜓𝜒𝜓, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 5953 | →⋀𝜑𝜓→𝜓→→𝜓𝜒𝜓 | Modus ponens 5951, 5952 | |
| 5954 | →→⋀𝜑𝜓→𝜓→→𝜓𝜒𝜓→→⋀𝜑𝜓𝜓→⋀𝜑𝜓→→𝜓𝜒𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜒↗→→𝜓𝜒𝜓] into ax-2 | |
| 5955 | →→⋀𝜑𝜓𝜓→⋀𝜑𝜓→→𝜓𝜒𝜓 | Modus ponens 5953, 5954 | |
| 5956 | →⋀𝜑𝜓→→𝜓𝜒𝜓 | Modus ponens simpr, 5955 | |
| 5957 | →→→𝜓𝜒→𝜓𝜒→→→𝜓𝜒𝜓→→𝜓𝜒𝜒 | Subs [𝜑↗→𝜓𝜒] into ax-2 | |
| 5958 | →→→𝜓𝜒𝜓→→𝜓𝜒𝜒 | Modus ponens 867, 5957 | |
| 5959 | →→→→𝜓𝜒𝜓→→𝜓𝜒𝜒→⋀𝜑𝜓→→→𝜓𝜒𝜓→→𝜓𝜒𝜒 | Subs [𝜑↗→→→𝜓𝜒𝜓→→𝜓𝜒𝜒, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 5960 | →⋀𝜑𝜓→→→𝜓𝜒𝜓→→𝜓𝜒𝜒 | Modus ponens 5958, 5959 | |
| 5961 | →→⋀𝜑𝜓→→→𝜓𝜒𝜓→→𝜓𝜒𝜒→→⋀𝜑𝜓→→𝜓𝜒𝜓→⋀𝜑𝜓→→𝜓𝜒𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→→𝜓𝜒𝜓, 𝜒↗→→𝜓𝜒𝜒] into ax-2 | |
| 5962 | →→⋀𝜑𝜓→→𝜓𝜒𝜓→⋀𝜑𝜓→→𝜓𝜒𝜒 | Modus ponens 5960, 5961 | |
| 5963 | →⋀𝜑𝜓→→𝜓𝜒𝜒 | Modus ponens 5956, 5962 | |
| 5964 | →→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒 | Subs [𝜑↗→𝜓𝜒, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 5965 | →→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒→→𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒 | Subs [𝜑↗→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒, 𝜓↗→𝜓𝜒] into ax-1 | |
| 5966 | →→𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒 | Modus ponens 5964, 5965 | |
| 5967 | →→→𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒 | Subs [𝜑↗→𝜓𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→⋀𝜑𝜓→𝜓𝜒] into ax-2 | |
| 5968 | →→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒 | Modus ponens 5966, 5967 | |
| 5969 | →→⋀𝜑𝜓→→𝜓𝜒𝜒→→⋀𝜑𝜓→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜓𝜒] into ax-2 | |
| 5970 | →→⋀𝜑𝜓→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 5963, 5969 | |
| 5971 | →→→⋀𝜑𝜓→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→→⋀𝜑𝜓→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗→𝜓𝜒] into ax-1 | |
| 5972 | →→𝜓𝜒→→⋀𝜑𝜓→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 5970, 5971 | |
| 5973 | →→→𝜓𝜒→→⋀𝜑𝜓→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→𝜓𝜒, 𝜓↗→⋀𝜑𝜓→𝜓𝜒, 𝜒↗→⋀𝜑𝜓𝜒] into ax-2 | |
| 5974 | →→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 5972, 5973 | |
| 5975 | →→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 5964, 5974 | pm3.42 |
| 5976 | →↔𝜑⋀𝜓𝜒→⋀𝜓𝜒𝜑 | Subs [𝜓↗⋀𝜓𝜒] into biimpr | |
| 5977 | →⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1 | |
| 5978 | →→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒 | Subs [𝜑↗→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 5979 | →⋀𝜓𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒 | Modus ponens 5977, 5978 | |
| 5980 | →→⋀𝜓𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→↔𝜑⋀𝜓𝜒⋀𝜓𝜒] into ax-2 | |
| 5981 | →→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒 | Modus ponens 5979, 5980 | |
| 5982 | →→↔𝜑⋀𝜓𝜒→⋀𝜓𝜒𝜑→→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑 | Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗𝜑] into ax-2 | |
| 5983 | →→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑 | Modus ponens 5976, 5982 | |
| 5984 | →→→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑→⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑 | Subs [𝜑↗→→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 5985 | →⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑 | Modus ponens 5983, 5984 | |
| 5986 | →→⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑→→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→↔𝜑⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→↔𝜑⋀𝜓𝜒𝜑] into ax-2 | |
| 5987 | →→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑 | Modus ponens 5985, 5986 | |
| 5988 | →⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑 | Modus ponens 5977, 5987 | |
| 5989 | →→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑→¬→𝜓¬𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑 | Subs [𝜑↗→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑, 𝜓↗¬→𝜓¬𝜒] into ax-1 | |
| 5990 | →¬→𝜓¬𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑 | Modus ponens 5988, 5989 | |
| 5991 | →→¬→𝜓¬𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑→→¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒→↔𝜑⋀𝜓𝜒𝜑 | Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→↔𝜑⋀𝜓𝜒𝜑] into ax-2 | |
| 5992 | →→¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒→↔𝜑⋀𝜓𝜒𝜑 | Modus ponens 5990, 5991 | |
| 5993 | →¬→𝜓¬𝜒→↔𝜑⋀𝜓𝜒𝜑 | Modus ponens 5017, 5992 | |
| 5994 | →→¬→𝜓¬𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒→¬→𝜓¬𝜒→↔𝜑⋀𝜓𝜒𝜑 | Subs [𝜑↗→¬→𝜓¬𝜒→↔𝜑⋀𝜓𝜒𝜑, 𝜓↗𝜒] into ax-1 | |
| 5995 | →𝜒→¬→𝜓¬𝜒→↔𝜑⋀𝜓𝜒𝜑 | Modus ponens 5993, 5994 | |
| 5996 | →→𝜒→¬→𝜓¬𝜒→↔𝜑⋀𝜓𝜒𝜑→→𝜒¬→𝜓¬𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑 | Subs [𝜑↗𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→↔𝜑⋀𝜓𝜒𝜑] into ax-2 | |
| 5997 | →→𝜒¬→𝜓¬𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑 | Modus ponens 5995, 5996 | |
| 5998 | →→→𝜒¬→𝜓¬𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜓→→𝜒¬→𝜓¬𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑 | Subs [𝜑↗→→𝜒¬→𝜓¬𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑] into ax-1 | |
| 5999 | →𝜓→→𝜒¬→𝜓¬𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑 | Modus ponens 5997, 5998 | |
| 6000 | →→𝜓→→𝜒¬→𝜓¬𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→→𝜓→𝜒¬→𝜓¬𝜒→𝜓→𝜒→↔𝜑⋀𝜓𝜒𝜑 | Subs [𝜑↗𝜓, 𝜓↗→𝜒¬→𝜓¬𝜒, 𝜒↗→𝜒→↔𝜑⋀𝜓𝜒𝜑] into ax-2 | |
| 6001 | →→𝜓→𝜒¬→𝜓¬𝜒→𝜓→𝜒→↔𝜑⋀𝜓𝜒𝜑 | Modus ponens 5999, 6000 | |
| 6002 | →𝜓→𝜒→↔𝜑⋀𝜓𝜒𝜑 | Modus ponens 5023, 6001 | |
| 6003 | →↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑 | Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗𝜑] into pm2.27 | |
| 6004 | →→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→𝜓→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑 | Subs [𝜑↗→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑] into ax-1 | |
| 6005 | →𝜓→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑 | Modus ponens 6003, 6004 | |
| 6006 | →→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑 | Subs [𝜑↗→𝜒→↔𝜑⋀𝜓𝜒𝜑, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1 | |
| 6007 | →→→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜓→→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑 | Subs [𝜑↗→→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑] into ax-1 | |
| 6008 | →𝜓→→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑 | Modus ponens 6006, 6007 | |
| 6009 | →→𝜓→→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→→𝜓→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜓→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑 | Subs [𝜑↗𝜓, 𝜓↗→𝜒→↔𝜑⋀𝜓𝜒𝜑, 𝜒↗→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑] into ax-2 | |
| 6010 | →→𝜓→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜓→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑 | Modus ponens 6008, 6009 | |
| 6011 | →𝜓→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑 | Modus ponens 6002, 6010 | |
| 6012 | →→→↔𝜑⋀𝜓𝜒𝜑𝜑→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑 | Subs [𝜑↗→↔𝜑⋀𝜓𝜒𝜑, 𝜓↗𝜑] into imim2 | |
| 6013 | →→→→↔𝜑⋀𝜓𝜒𝜑𝜑→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→↔𝜑⋀𝜓𝜒→→→↔𝜑⋀𝜓𝜒𝜑𝜑→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑 | Subs [𝜑↗→→→↔𝜑⋀𝜓𝜒𝜑𝜑→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1 | |
| 6014 | →↔𝜑⋀𝜓𝜒→→→↔𝜑⋀𝜓𝜒𝜑𝜑→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑 | Modus ponens 6012, 6013 | |
| 6015 | →→↔𝜑⋀𝜓𝜒→→→↔𝜑⋀𝜓𝜒𝜑𝜑→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑 | Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗→→↔𝜑⋀𝜓𝜒𝜑𝜑, 𝜒↗→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑] into ax-2 | |
| 6016 | →→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑 | Modus ponens 6014, 6015 | |
| 6017 | →→→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→𝜓→→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑 | Subs [𝜑↗→→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑] into ax-1 | |
| 6018 | →𝜓→→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑 | Modus ponens 6016, 6017 | |
| 6019 | →→𝜓→→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→→𝜓→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→𝜓→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑 | Subs [𝜑↗𝜓, 𝜓↗→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑, 𝜒↗→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑] into ax-2 | |
| 6020 | →→𝜓→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→𝜓→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑 | Modus ponens 6018, 6019 | |
| 6021 | →𝜓→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑 | Modus ponens 6005, 6020 | |
| 6022 | →→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑 | Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗→𝜒→↔𝜑⋀𝜓𝜒𝜑, 𝜒↗→𝜒𝜑] into ax-2 | |
| 6023 | →→→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑→𝜓→→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑 | Subs [𝜑↗→→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑] into ax-1 | |
| 6024 | →𝜓→→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑 | Modus ponens 6022, 6023 | |
| 6025 | →→𝜓→→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑→→𝜓→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→𝜓→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑 | Subs [𝜑↗𝜓, 𝜓↗→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑, 𝜒↗→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑] into ax-2 | |
| 6026 | →→𝜓→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→𝜓→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑 | Modus ponens 6024, 6025 | |
| 6027 | →𝜓→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑 | Modus ponens 6021, 6026 | |
| 6028 | →→𝜓→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑→→𝜓→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜓→↔𝜑⋀𝜓𝜒→𝜒𝜑 | Subs [𝜑↗𝜓, 𝜓↗→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑, 𝜒↗→↔𝜑⋀𝜓𝜒→𝜒𝜑] into ax-2 | |
| 6029 | →→𝜓→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜓→↔𝜑⋀𝜓𝜒→𝜒𝜑 | Modus ponens 6027, 6028 | |
| 6030 | →𝜓→↔𝜑⋀𝜓𝜒→𝜒𝜑 | Modus ponens 6011, 6029 | |
| 6031 | →↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔𝜑⋀𝜓𝜒] into id | |
| 6032 | →↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔𝜑⋀𝜓𝜒] into ax-1 | |
| 6033 | →→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1 | |
| 6034 | →↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒 | Modus ponens 6032, 6033 | |
| 6035 | →→↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜒, 𝜒↗→𝜓↔𝜑⋀𝜓𝜒] into ax-2 | |
| 6036 | →→↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒 | Modus ponens 6034, 6035 | |
| 6037 | →→𝜓→↔𝜑⋀𝜓𝜒→𝜒𝜑→→𝜓↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑 | Subs [𝜑↗𝜓, 𝜓↗↔𝜑⋀𝜓𝜒, 𝜒↗→𝜒𝜑] into ax-2 | |
| 6038 | →→𝜓↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑 | Modus ponens 6030, 6037 | |
| 6039 | →→→𝜓↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑→↔𝜑⋀𝜓𝜒→→𝜓↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑 | Subs [𝜑↗→→𝜓↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1 | |
| 6040 | →↔𝜑⋀𝜓𝜒→→𝜓↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑 | Modus ponens 6038, 6039 | |
| 6041 | →→↔𝜑⋀𝜓𝜒→→𝜓↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑→→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑 | Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗→𝜓↔𝜑⋀𝜓𝜒, 𝜒↗→𝜓→𝜒𝜑] into ax-2 | |
| 6042 | →→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑 | Modus ponens 6040, 6041 | |
| 6043 | →↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑 | Modus ponens 6032, 6042 | |
| 6044 | →𝜒→→𝜒𝜑𝜑 | Subs [𝜑↗𝜒, 𝜓↗𝜑] into pm2.27 | |
| 6045 | →→𝜒→→𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→𝜒→→𝜒𝜑𝜑 | Subs [𝜑↗→𝜒→→𝜒𝜑𝜑, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1 | |
| 6046 | →↔𝜑⋀𝜓𝜒→𝜒→→𝜒𝜑𝜑 | Modus ponens 6044, 6045 | |
| 6047 | →→𝜓→𝜒𝜑→𝜒→𝜓→𝜒𝜑 | Subs [𝜑↗→𝜓→𝜒𝜑, 𝜓↗𝜒] into ax-1 | |
| 6048 | →→→𝜓→𝜒𝜑→𝜒→𝜓→𝜒𝜑→↔𝜑⋀𝜓𝜒→→𝜓→𝜒𝜑→𝜒→𝜓→𝜒𝜑 | Subs [𝜑↗→→𝜓→𝜒𝜑→𝜒→𝜓→𝜒𝜑, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1 | |
| 6049 | →↔𝜑⋀𝜓𝜒→→𝜓→𝜒𝜑→𝜒→𝜓→𝜒𝜑 | Modus ponens 6047, 6048 | |
| 6050 | →→↔𝜑⋀𝜓𝜒→→𝜓→𝜒𝜑→𝜒→𝜓→𝜒𝜑→→↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→𝜓→𝜒𝜑 | Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗→𝜓→𝜒𝜑, 𝜒↗→𝜒→𝜓→𝜒𝜑] into ax-2 | |
| 6051 | →→↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→𝜓→𝜒𝜑 | Modus ponens 6049, 6050 | |
| 6052 | →↔𝜑⋀𝜓𝜒→𝜒→𝜓→𝜒𝜑 | Modus ponens 6043, 6051 | |
| 6053 | →→→𝜒𝜑𝜑→→𝜓→𝜒𝜑→𝜓𝜑 | Subs [𝜑↗→𝜒𝜑, 𝜓↗𝜑, 𝜒↗𝜓] into imim2 | |
| 6054 | →→→→𝜒𝜑𝜑→→𝜓→𝜒𝜑→𝜓𝜑→𝜒→→→𝜒𝜑𝜑→→𝜓→𝜒𝜑→𝜓𝜑 | Subs [𝜑↗→→→𝜒𝜑𝜑→→𝜓→𝜒𝜑→𝜓𝜑, 𝜓↗𝜒] into ax-1 | |
| 6055 | →𝜒→→→𝜒𝜑𝜑→→𝜓→𝜒𝜑→𝜓𝜑 | Modus ponens 6053, 6054 | |
| 6056 | →→𝜒→→→𝜒𝜑𝜑→→𝜓→𝜒𝜑→𝜓𝜑→→𝜒→→𝜒𝜑𝜑→𝜒→→𝜓→𝜒𝜑→𝜓𝜑 | Subs [𝜑↗𝜒, 𝜓↗→→𝜒𝜑𝜑, 𝜒↗→→𝜓→𝜒𝜑→𝜓𝜑] into ax-2 | |
| 6057 | →→𝜒→→𝜒𝜑𝜑→𝜒→→𝜓→𝜒𝜑→𝜓𝜑 | Modus ponens 6055, 6056 | |
| 6058 | →→→𝜒→→𝜒𝜑𝜑→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→↔𝜑⋀𝜓𝜒→→𝜒→→𝜒𝜑𝜑→𝜒→→𝜓→𝜒𝜑→𝜓𝜑 | Subs [𝜑↗→→𝜒→→𝜒𝜑𝜑→𝜒→→𝜓→𝜒𝜑→𝜓𝜑, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1 | |
| 6059 | →↔𝜑⋀𝜓𝜒→→𝜒→→𝜒𝜑𝜑→𝜒→→𝜓→𝜒𝜑→𝜓𝜑 | Modus ponens 6057, 6058 | |
| 6060 | →→↔𝜑⋀𝜓𝜒→→𝜒→→𝜒𝜑𝜑→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→→↔𝜑⋀𝜓𝜒→𝜒→→𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→𝜒→→𝜓→𝜒𝜑→𝜓𝜑 | Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗→𝜒→→𝜒𝜑𝜑, 𝜒↗→𝜒→→𝜓→𝜒𝜑→𝜓𝜑] into ax-2 | |
| 6061 | →→↔𝜑⋀𝜓𝜒→𝜒→→𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→𝜒→→𝜓→𝜒𝜑→𝜓𝜑 | Modus ponens 6059, 6060 | |
| 6062 | →↔𝜑⋀𝜓𝜒→𝜒→→𝜓→𝜒𝜑→𝜓𝜑 | Modus ponens 6046, 6061 | |
| 6063 | →→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑 | Subs [𝜑↗𝜒, 𝜓↗→𝜓→𝜒𝜑, 𝜒↗→𝜓𝜑] into ax-2 | |
| 6064 | →→→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑→↔𝜑⋀𝜓𝜒→→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑 | Subs [𝜑↗→→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1 | |
| 6065 | →↔𝜑⋀𝜓𝜒→→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑 | Modus ponens 6063, 6064 | |
| 6066 | →→↔𝜑⋀𝜓𝜒→→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑→→↔𝜑⋀𝜓𝜒→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→↔𝜑⋀𝜓𝜒→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑 | Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗→𝜒→→𝜓→𝜒𝜑→𝜓𝜑, 𝜒↗→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑] into ax-2 | |
| 6067 | →→↔𝜑⋀𝜓𝜒→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→↔𝜑⋀𝜓𝜒→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑 | Modus ponens 6065, 6066 | |
| 6068 | →↔𝜑⋀𝜓𝜒→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑 | Modus ponens 6062, 6067 | |
| 6069 | →→↔𝜑⋀𝜓𝜒→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑→→↔𝜑⋀𝜓𝜒→𝜒→𝜓→𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→𝜓𝜑 | Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗→𝜒→𝜓→𝜒𝜑, 𝜒↗→𝜒→𝜓𝜑] into ax-2 | |
| 6070 | →→↔𝜑⋀𝜓𝜒→𝜒→𝜓→𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→𝜓𝜑 | Modus ponens 6068, 6069 | |
| 6071 | →↔𝜑⋀𝜓𝜒→𝜒→𝜓𝜑 | Modus ponens 6052, 6070 | simplbi2comt |
| 6072 | →⋀𝜓𝜒𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜒] into simpl | |
| 6073 | →→⋀𝜓𝜒𝜓→𝜑→⋀𝜓𝜒𝜓 | Subs [𝜑↗→⋀𝜓𝜒𝜓, 𝜓↗𝜑] into ax-1 | |
| 6074 | →𝜑→⋀𝜓𝜒𝜓 | Modus ponens 6072, 6073 | |
| 6075 | →→𝜑→⋀𝜓𝜒𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓 | Subs [𝜓↗⋀𝜓𝜒, 𝜒↗𝜓] into ax-2 | |
| 6076 | →→𝜑⋀𝜓𝜒→𝜑𝜓 | Modus ponens 6074, 6075 | |
| 6077 | →⋀𝜓𝜒𝜒 | Subs [𝜑↗𝜓, 𝜓↗𝜒] into simpr | |
| 6078 | →→⋀𝜓𝜒𝜒→𝜑→⋀𝜓𝜒𝜒 | Subs [𝜑↗→⋀𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1 | |
| 6079 | →𝜑→⋀𝜓𝜒𝜒 | Modus ponens 6077, 6078 | |
| 6080 | →→𝜑→⋀𝜓𝜒𝜒→→𝜑⋀𝜓𝜒→𝜑𝜒 | Subs [𝜓↗⋀𝜓𝜒] into ax-2 | |
| 6081 | →→𝜑⋀𝜓𝜒→𝜑𝜒 | Modus ponens 6079, 6080 | |
| 6082 | →→𝜑𝜓→→𝜑𝜒⋀→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒] into pm3.2 | |
| 6083 | →→→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→𝜑⋀𝜓𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑⋀𝜓𝜒] into ax-1 | |
| 6084 | →→𝜑⋀𝜓𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 5603, 6083 | |
| 6085 | →→→𝜑⋀𝜓𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑⋀𝜓𝜒→𝜑𝜒→→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 6086 | →→→𝜑⋀𝜓𝜒→𝜑𝜒→→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 6084, 6085 | |
| 6087 | →→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 6081, 6086 | |
| 6088 | →→→𝜑𝜓→→𝜑𝜒⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗⋀→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 6089 | →→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒 | Modus ponens 6082, 6088 | |
| 6090 | →→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑⋀𝜓𝜒] into ax-1 | |
| 6091 | →→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒 | Modus ponens 6089, 6090 | |
| 6092 | →→→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒, 𝜒↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 6093 | →→→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒 | Modus ponens 6091, 6092 | |
| 6094 | →→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒 | Modus ponens 6087, 6093 | |
| 6095 | →→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜓𝜒] into ax-1 | |
| 6096 | →→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 6097 | →→𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓 | Modus ponens 6095, 6096 | |
| 6098 | →→→𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜑⋀𝜓𝜒→𝜑𝜓] into ax-2 | |
| 6099 | →→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓 | Modus ponens 6097, 6098 | |
| 6100 | →→→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓, 𝜒↗⋀→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 6101 | →→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒 | Modus ponens 6094, 6100 | |
| 6102 | →→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 6103 | →→𝜑𝜓→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒 | Modus ponens 6101, 6102 | |
| 6104 | →→→𝜑𝜓→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜑⋀𝜓𝜒→𝜑𝜓, 𝜒↗→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 6105 | →→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒 | Modus ponens 6103, 6104 | |
| 6106 | →→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒 | Modus ponens 6095, 6105 | |
| 6107 | →→→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒→→𝜑⋀𝜓𝜒→→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑⋀𝜓𝜒] into ax-1 | |
| 6108 | →→𝜑⋀𝜓𝜒→→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒 | Modus ponens 6106, 6107 | |
| 6109 | →→→𝜑⋀𝜓𝜒→→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 6110 | →→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒 | Modus ponens 6108, 6109 | |
| 6111 | →→𝜑⋀𝜓𝜒→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒 | Modus ponens 6076, 6110 | |
| 6112 | →→𝜑⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜑⋀𝜓𝜒] into id | |
| 6113 | →→→𝜑⋀𝜓𝜒→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒→→→𝜑⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗→𝜑⋀𝜓𝜒, 𝜒↗⋀→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 6114 | →→→𝜑⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒 | Modus ponens 6111, 6113 | |
| 6115 | →→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒 | Modus ponens 6112, 6114 | |
| 6116 | →→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒→→⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗⋀→𝜑𝜓→𝜑𝜒] into impbi | |
| 6117 | →→⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒 | Modus ponens 6115, 6116 | |
| 6118 | ↔→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒 | Modus ponens pm3.43, 6117 | jcab |
| 6119 | →↔→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗⋀→𝜑𝜓→𝜑𝜒] into bicom1 | |
| 6120 | ↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒 | Modus ponens jcab, 6119 | pm4.76 |
| 6121 | →→⋀𝜓𝜑𝜓→𝜑→⋀𝜓𝜑𝜓 | Subs [𝜑↗→⋀𝜓𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 6122 | →𝜑→⋀𝜓𝜑𝜓 | Modus ponens 5902, 6121 | |
| 6123 | →→𝜓⋀𝜓𝜑→→⋀𝜓𝜑𝜓↔𝜓⋀𝜓𝜑 | Subs [𝜑↗𝜓, 𝜓↗⋀𝜓𝜑] into impbi | |
| 6124 | →→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓 | Subs [𝜑↗→⋀𝜓𝜑𝜓, 𝜓↗→𝜓⋀𝜓𝜑] into ax-1 | |
| 6125 | →→→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→𝜑→→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓 | Subs [𝜑↗→→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 6126 | →𝜑→→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓 | Modus ponens 6124, 6125 | |
| 6127 | →→𝜑→→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→→𝜑→⋀𝜓𝜑𝜓→𝜑→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓 | Subs [𝜓↗→⋀𝜓𝜑𝜓, 𝜒↗→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓] into ax-2 | |
| 6128 | →→𝜑→⋀𝜓𝜑𝜓→𝜑→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓 | Modus ponens 6126, 6127 | |
| 6129 | →𝜑→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓 | Modus ponens 6122, 6128 | |
| 6130 | →→→𝜓⋀𝜓𝜑→→⋀𝜓𝜑𝜓↔𝜓⋀𝜓𝜑→→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑 | Subs [𝜑↗→𝜓⋀𝜓𝜑, 𝜓↗→⋀𝜓𝜑𝜓, 𝜒↗↔𝜓⋀𝜓𝜑] into ax-2 | |
| 6131 | →→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑 | Modus ponens 6123, 6130 | |
| 6132 | →→→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑→𝜑→→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑 | Subs [𝜑↗→→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑, 𝜓↗𝜑] into ax-1 | |
| 6133 | →𝜑→→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑 | Modus ponens 6131, 6132 | |
| 6134 | →→𝜑→→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑→→𝜑→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→𝜑→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑 | Subs [𝜓↗→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓, 𝜒↗→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑] into ax-2 | |
| 6135 | →→𝜑→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→𝜑→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑 | Modus ponens 6133, 6134 | |
| 6136 | →𝜑→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑 | Modus ponens 6129, 6135 | |
| 6137 | →→𝜓⋀𝜓𝜑→𝜓⋀𝜓𝜑 | Subs [𝜑↗→𝜓⋀𝜓𝜑] into id | |
| 6138 | →→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑 | Subs [𝜑↗→𝜓⋀𝜓𝜑, 𝜓↗𝜑] into ax-1 | |
| 6139 | →→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑 | Subs [𝜑↗→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑, 𝜓↗→𝜓⋀𝜓𝜑] into ax-1 | |
| 6140 | →→𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑 | Modus ponens 6138, 6139 | |
| 6141 | →→→𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑→→→𝜓⋀𝜓𝜑→𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑 | Subs [𝜑↗→𝜓⋀𝜓𝜑, 𝜓↗→𝜓⋀𝜓𝜑, 𝜒↗→𝜑→𝜓⋀𝜓𝜑] into ax-2 | |
| 6142 | →→→𝜓⋀𝜓𝜑→𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑 | Modus ponens 6140, 6141 | |
| 6143 | →→𝜑→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑→→𝜑→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑 | Subs [𝜓↗→𝜓⋀𝜓𝜑, 𝜒↗↔𝜓⋀𝜓𝜑] into ax-2 | |
| 6144 | →→𝜑→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑 | Modus ponens 6136, 6143 | |
| 6145 | →→→𝜑→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→→𝜑→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑 | Subs [𝜑↗→→𝜑→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑, 𝜓↗→𝜓⋀𝜓𝜑] into ax-1 | |
| 6146 | →→𝜓⋀𝜓𝜑→→𝜑→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑 | Modus ponens 6144, 6145 | |
| 6147 | →→→𝜓⋀𝜓𝜑→→𝜑→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑→→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑 | Subs [𝜑↗→𝜓⋀𝜓𝜑, 𝜓↗→𝜑→𝜓⋀𝜓𝜑, 𝜒↗→𝜑↔𝜓⋀𝜓𝜑] into ax-2 | |
| 6148 | →→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑 | Modus ponens 6146, 6147 | |
| 6149 | →→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑 | Modus ponens 6138, 6148 | |
| 6150 | →→→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑→𝜑→→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑 | Subs [𝜑↗→→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑, 𝜓↗𝜑] into ax-1 | |
| 6151 | →𝜑→→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑 | Modus ponens 6149, 6150 | |
| 6152 | →→𝜑→→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑→→𝜑→𝜓⋀𝜓𝜑→𝜑→𝜑↔𝜓⋀𝜓𝜑 | Subs [𝜓↗→𝜓⋀𝜓𝜑, 𝜒↗→𝜑↔𝜓⋀𝜓𝜑] into ax-2 | |
| 6153 | →→𝜑→𝜓⋀𝜓𝜑→𝜑→𝜑↔𝜓⋀𝜓𝜑 | Modus ponens 6151, 6152 | |
| 6154 | →𝜑→𝜑↔𝜓⋀𝜓𝜑 | Modus ponens pm3.21, 6153 | |
| 6155 | →→𝜑→𝜑↔𝜓⋀𝜓𝜑→→𝜑𝜑→𝜑↔𝜓⋀𝜓𝜑 | Subs [𝜓↗𝜑, 𝜒↗↔𝜓⋀𝜓𝜑] into ax-2 | |
| 6156 | →→𝜑𝜑→𝜑↔𝜓⋀𝜓𝜑 | Modus ponens 6154, 6155 | |
| 6157 | →→→𝜑𝜑→𝜑↔𝜓⋀𝜓𝜑→𝜑→→𝜑𝜑→𝜑↔𝜓⋀𝜓𝜑 | Subs [𝜑↗→→𝜑𝜑→𝜑↔𝜓⋀𝜓𝜑, 𝜓↗𝜑] into ax-1 | |
| 6158 | →𝜑→→𝜑𝜑→𝜑↔𝜓⋀𝜓𝜑 | Modus ponens 6156, 6157 | |
| 6159 | →→𝜑→→𝜑𝜑→𝜑↔𝜓⋀𝜓𝜑→→𝜑→𝜑𝜑→𝜑→𝜑↔𝜓⋀𝜓𝜑 | Subs [𝜓↗→𝜑𝜑, 𝜒↗→𝜑↔𝜓⋀𝜓𝜑] into ax-2 | |
| 6160 | →→𝜑→𝜑𝜑→𝜑→𝜑↔𝜓⋀𝜓𝜑 | Modus ponens 6158, 6159 | |
| 6161 | →𝜑↔𝜓⋀𝜓𝜑 | Modus ponens id, 6156 | iba |
| 6162 | ↔⋀𝜓𝜑⋀𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜑] into ancom | |
| 6163 | →↔⋀𝜓𝜑⋀𝜑𝜓→𝜑↔⋀𝜓𝜑⋀𝜑𝜓 | Subs [𝜑↗↔⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 6164 | →𝜑↔⋀𝜓𝜑⋀𝜑𝜓 | Modus ponens 6162, 6163 | |
| 6165 | ↔→𝜑↔𝜓⋀𝜓𝜑↔→𝜑𝜓→𝜑⋀𝜓𝜑 | Subs [𝜒↗⋀𝜓𝜑] into pm5.74 | |
| 6166 | →↔→𝜑↔𝜓⋀𝜓𝜑↔→𝜑𝜓→𝜑⋀𝜓𝜑→→𝜑↔𝜓⋀𝜓𝜑↔→𝜑𝜓→𝜑⋀𝜓𝜑 | Subs [𝜑↗→𝜑↔𝜓⋀𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜑⋀𝜓𝜑] into biimp | |
| 6167 | →→𝜑↔𝜓⋀𝜓𝜑↔→𝜑𝜓→𝜑⋀𝜓𝜑 | Modus ponens 6165, 6166 | |
| 6168 | ↔→𝜑𝜓→𝜑⋀𝜓𝜑 | Modus ponens iba, 6167 | ancrb |
| 6169 | ↔→𝜑↔⋀𝜓𝜑⋀𝜑𝜓↔→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓 | Subs [𝜓↗⋀𝜓𝜑, 𝜒↗⋀𝜑𝜓] into pm5.74 | |
| 6170 | →↔→𝜑↔⋀𝜓𝜑⋀𝜑𝜓↔→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓→→𝜑↔⋀𝜓𝜑⋀𝜑𝜓↔→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓 | Subs [𝜑↗→𝜑↔⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗↔→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓] into biimp | |
| 6171 | →→𝜑↔⋀𝜓𝜑⋀𝜑𝜓↔→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓 | Modus ponens 6169, 6170 | |
| 6172 | ↔→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓 | Modus ponens 6164, 6171 | |
| 6173 | →↔→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓→→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓 | Subs [𝜑↗→𝜑⋀𝜓𝜑, 𝜓↗→𝜑⋀𝜑𝜓] into biimp | |
| 6174 | →→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓 | Modus ponens 6172, 6173 | |
| 6175 | →↔→𝜑𝜓→𝜑⋀𝜓𝜑→→𝜑𝜓→𝜑⋀𝜓𝜑 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜓𝜑] into biimp | |
| 6176 | →→→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓 | Subs [𝜑↗→→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 6177 | →→𝜑𝜓→→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓 | Modus ponens 6174, 6176 | |
| 6178 | →→→𝜑𝜓→→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓→→→𝜑𝜓→𝜑⋀𝜓𝜑→→𝜑𝜓→𝜑⋀𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜓𝜑, 𝜒↗→𝜑⋀𝜑𝜓] into ax-2 | |
| 6179 | →→→𝜑𝜓→𝜑⋀𝜓𝜑→→𝜑𝜓→𝜑⋀𝜑𝜓 | Modus ponens 6177, 6178 | |
| 6180 | →→𝜑𝜓→𝜑⋀𝜑𝜓 | Modus ponens ancr, 6179 | ancl |
| 6181 | →↔→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓↔→𝜑⋀𝜑𝜓→𝜑⋀𝜓𝜑 | Subs [𝜑↗→𝜑⋀𝜓𝜑, 𝜓↗→𝜑⋀𝜑𝜓] into bicom1 | |
| 6182 | ↔→𝜑⋀𝜑𝜓→𝜑⋀𝜓𝜑 | Modus ponens 6172, 6181 | |
| 6183 | →↔→𝜑⋀𝜑𝜓→𝜑⋀𝜓𝜑→→𝜑⋀𝜑𝜓→𝜑⋀𝜓𝜑 | Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜓𝜑] into biimp | |
| 6184 | →→𝜑⋀𝜑𝜓→𝜑⋀𝜓𝜑 | Modus ponens 6182, 6183 | |
| 6185 | →↔→𝜑𝜓→𝜑⋀𝜓𝜑↔→𝜑⋀𝜓𝜑→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜓𝜑] into bicom1 | |
| 6186 | ↔→𝜑⋀𝜓𝜑→𝜑𝜓 | Modus ponens ancrb, 6185 | |
| 6187 | →↔→𝜑⋀𝜓𝜑→𝜑𝜓→→𝜑⋀𝜓𝜑→𝜑𝜓 | Subs [𝜑↗→𝜑⋀𝜓𝜑, 𝜓↗→𝜑𝜓] into biimp | |
| 6188 | →→𝜑⋀𝜓𝜑→𝜑𝜓 | Modus ponens 6186, 6187 | |
| 6189 | →→→𝜑⋀𝜓𝜑→𝜑𝜓→→𝜑⋀𝜑𝜓→→𝜑⋀𝜓𝜑→𝜑𝜓 | Subs [𝜑↗→→𝜑⋀𝜓𝜑→𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓] into ax-1 | |
| 6190 | →→𝜑⋀𝜑𝜓→→𝜑⋀𝜓𝜑→𝜑𝜓 | Modus ponens 6188, 6189 | |
| 6191 | →→→𝜑⋀𝜑𝜓→→𝜑⋀𝜓𝜑→𝜑𝜓→→→𝜑⋀𝜑𝜓→𝜑⋀𝜓𝜑→→𝜑⋀𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜓𝜑, 𝜒↗→𝜑𝜓] into ax-2 | |
| 6192 | →→→𝜑⋀𝜑𝜓→𝜑⋀𝜓𝜑→→𝜑⋀𝜑𝜓→𝜑𝜓 | Modus ponens 6190, 6191 | |
| 6193 | →→𝜑⋀𝜑𝜓→𝜑𝜓 | Modus ponens 6184, 6192 | |
| 6194 | →→→𝜑𝜓→𝜑⋀𝜑𝜓→→→𝜑⋀𝜑𝜓→𝜑𝜓↔→𝜑𝜓→𝜑⋀𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓] into impbi | |
| 6195 | →→→𝜑⋀𝜑𝜓→𝜑𝜓↔→𝜑𝜓→𝜑⋀𝜑𝜓 | Modus ponens ancl, 6194 | |
| 6196 | ↔→𝜑𝜓→𝜑⋀𝜑𝜓 | Modus ponens 6193, 6195 | anclb |
| 6197 | ↔→𝜑↔𝜓⋀𝜑𝜓↔→𝜑𝜓→𝜑⋀𝜑𝜓 | Subs [𝜒↗⋀𝜑𝜓] into pm5.74 | |
| 6198 | →↔→𝜑↔𝜓⋀𝜑𝜓↔→𝜑𝜓→𝜑⋀𝜑𝜓↔↔→𝜑𝜓→𝜑⋀𝜑𝜓→𝜑↔𝜓⋀𝜑𝜓 | Subs [𝜑↗→𝜑↔𝜓⋀𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜑⋀𝜑𝜓] into bicom1 | |
| 6199 | ↔↔→𝜑𝜓→𝜑⋀𝜑𝜓→𝜑↔𝜓⋀𝜑𝜓 | Modus ponens 6197, 6198 | |
| 6200 | →↔↔→𝜑𝜓→𝜑⋀𝜑𝜓→𝜑↔𝜓⋀𝜑𝜓→↔→𝜑𝜓→𝜑⋀𝜑𝜓→𝜑↔𝜓⋀𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜓→𝜑⋀𝜑𝜓, 𝜓↗→𝜑↔𝜓⋀𝜑𝜓] into biimp | |
| 6201 | →↔→𝜑𝜓→𝜑⋀𝜑𝜓→𝜑↔𝜓⋀𝜑𝜓 | Modus ponens 6199, 6200 | |
| 6202 | →𝜑↔𝜓⋀𝜑𝜓 | Modus ponens anclb, 6201 | ibar |
| 6203 | →→𝜑𝜓↔→𝜑𝜒⋀→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒] into ibar | |
| 6204 | →↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 6205 | →→𝜑𝜓↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒 | Modus ponens pm4.76, 6204 | |
| 6206 | ↔→→𝜑𝜓↔→𝜑𝜒⋀→𝜑𝜓→𝜑𝜒↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗⋀→𝜑𝜓→𝜑𝜒] into pm5.74 | |
| 6207 | →↔→→𝜑𝜓↔→𝜑𝜒⋀→𝜑𝜓→𝜑𝜒↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓↔→𝜑𝜒⋀→𝜑𝜓→𝜑𝜒↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜓↔→𝜑𝜒⋀→𝜑𝜓→𝜑𝜒, 𝜓↗↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒] into biimp | |
| 6208 | →→→𝜑𝜓↔→𝜑𝜒⋀→𝜑𝜓→𝜑𝜒↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒 | Modus ponens 6206, 6207 | |
| 6209 | ↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒 | Modus ponens 6203, 6208 | |
| 6210 | ↔→→𝜑𝜓↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into pm5.74 | |
| 6211 | →↔→→𝜑𝜓↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→→𝜑𝜓↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒] into biimp | |
| 6212 | →→→𝜑𝜓↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Modus ponens 6210, 6211 | |
| 6213 | ↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Modus ponens 6205, 6212 | |
| 6214 | →↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑⋀𝜓𝜒] into biimp | |
| 6215 | →→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Modus ponens 6213, 6214 | |
| 6216 | →↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒] into biimp | |
| 6217 | →→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 6218 | →→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Modus ponens 6215, 6217 | |
| 6219 | →→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒, 𝜒↗→→𝜑𝜓→𝜑⋀𝜓𝜒] into ax-2 | |
| 6220 | →→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Modus ponens 6218, 6219 | |
| 6221 | →↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒↔→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑⋀𝜓𝜒] into bicom1 | |
| 6222 | ↔→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒 | Modus ponens 6213, 6221 | |
| 6223 | →↔→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜓↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒] into biimp | |
| 6224 | →→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒 | Modus ponens 6222, 6223 | |
| 6225 | →↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒] into bicom1 | |
| 6226 | ↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 6209, 6225 | |
| 6227 | →↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into biimp | |
| 6228 | →→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 6226, 6227 | |
| 6229 | →→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑⋀𝜓𝜒] into ax-1 | |
| 6230 | →→→𝜑𝜓→𝜑⋀𝜓𝜒→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 6228, 6229 | |
| 6231 | →→→→𝜑𝜓→𝜑⋀𝜓𝜒→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜓↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 6232 | →→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 6230, 6231 | |
| 6233 | →→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 6224, 6232 | |
| 6234 | →→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑⋀𝜓𝜒] into impbi | |
| 6235 | →→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Modus ponens 5610, 6234 | |
| 6236 | ↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Modus ponens 6233, 6235 | |
| 6237 | ↔→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into pm5.74 | |
| 6238 | →↔→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒↔↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒] into bicom1 | |
| 6239 | ↔↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒 | Modus ponens 6237, 6238 | |
| 6240 | →↔↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒→↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜓↗→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒] into biimp | |
| 6241 | →↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒 | Modus ponens 6239, 6240 | |
| 6242 | →→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒 | Modus ponens 6236, 6241 | pm5.44 |
| 6243 | ↔↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜑⋀𝜓𝜒] into bicom | |
| 6244 | →↔↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒→↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒 | Subs [𝜑↗↔→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗↔→𝜑⋀𝜓𝜒→𝜑𝜒] into biimp | |
| 6245 | →↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒 | Modus ponens 6243, 6244 | |
| 6246 | →→↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒→→𝜑𝜓→↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 6247 | →→𝜑𝜓→↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒 | Modus ponens 6245, 6246 | |
| 6248 | →→→𝜑𝜓→↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒→→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓↔→𝜑⋀𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜒↗↔→𝜑⋀𝜓𝜒→𝜑𝜒] into ax-2 | |
| 6249 | →→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓↔→𝜑⋀𝜓𝜒→𝜑𝜒 | Modus ponens 6247, 6248 | |
| 6250 | →→𝜑𝜓↔→𝜑⋀𝜓𝜒→𝜑𝜒 | Modus ponens pm5.44, 6249 | |
| 6251 | ↔↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜒] into bicom | |
| 6252 | →↔↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒→↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗↔→𝜑⋀𝜓𝜒→𝜑𝜒, 𝜓↗↔→𝜑𝜒→𝜑⋀𝜓𝜒] into biimp | |
| 6253 | →↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒 | Modus ponens 6251, 6252 | |
| 6254 | →→↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 6255 | →→𝜑𝜓→↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒 | Modus ponens 6253, 6254 | |
| 6256 | →→→𝜑𝜓→↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒→→→𝜑𝜓↔→𝜑⋀𝜓𝜒→𝜑𝜒→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗↔→𝜑⋀𝜓𝜒→𝜑𝜒, 𝜒↗↔→𝜑𝜒→𝜑⋀𝜓𝜒] into ax-2 | |
| 6257 | →→→𝜑𝜓↔→𝜑⋀𝜓𝜒→𝜑𝜒→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒 | Modus ponens 6255, 6256 | |
| 6258 | →𝜑↔𝜒⋀𝜑𝜒 | Subs [𝜓↗𝜒] into ibar | |
| 6259 | →↔𝜒⋀𝜑𝜒→𝜓↔𝜒⋀𝜑𝜒 | Subs [𝜑↗↔𝜒⋀𝜑𝜒] into ax-1 | |
| 6260 | →→↔𝜒⋀𝜑𝜒→𝜓↔𝜒⋀𝜑𝜒→𝜑→↔𝜒⋀𝜑𝜒→𝜓↔𝜒⋀𝜑𝜒 | Subs [𝜑↗→↔𝜒⋀𝜑𝜒→𝜓↔𝜒⋀𝜑𝜒, 𝜓↗𝜑] into ax-1 | |
| 6261 | →𝜑→↔𝜒⋀𝜑𝜒→𝜓↔𝜒⋀𝜑𝜒 | Modus ponens 6259, 6260 | |
| 6262 | →→𝜑→↔𝜒⋀𝜑𝜒→𝜓↔𝜒⋀𝜑𝜒→→𝜑↔𝜒⋀𝜑𝜒→𝜑→𝜓↔𝜒⋀𝜑𝜒 | Subs [𝜓↗↔𝜒⋀𝜑𝜒, 𝜒↗→𝜓↔𝜒⋀𝜑𝜒] into ax-2 | |
| 6263 | →→𝜑↔𝜒⋀𝜑𝜒→𝜑→𝜓↔𝜒⋀𝜑𝜒 | Modus ponens 6261, 6262 | |
| 6264 | →𝜑→𝜓↔𝜒⋀𝜑𝜒 | Modus ponens 6258, 6263 | |
| 6265 | ↔→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒 | Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗⋀𝜑𝜒] into pm5.74 | |
| 6266 | →↔→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒→→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒 | Subs [𝜑↗→𝜓↔𝜒⋀𝜑𝜒, 𝜓↗↔→𝜓𝜒→𝜓⋀𝜑𝜒] into biimp | |
| 6267 | →→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒 | Modus ponens 6265, 6266 | |
| 6268 | →→→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒→𝜑→→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒 | Subs [𝜑↗→→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒, 𝜓↗𝜑] into ax-1 | |
| 6269 | →𝜑→→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒 | Modus ponens 6267, 6268 | |
| 6270 | →→𝜑→→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒→→𝜑→𝜓↔𝜒⋀𝜑𝜒→𝜑↔→𝜓𝜒→𝜓⋀𝜑𝜒 | Subs [𝜓↗→𝜓↔𝜒⋀𝜑𝜒, 𝜒↗↔→𝜓𝜒→𝜓⋀𝜑𝜒] into ax-2 | |
| 6271 | →→𝜑→𝜓↔𝜒⋀𝜑𝜒→𝜑↔→𝜓𝜒→𝜓⋀𝜑𝜒 | Modus ponens 6269, 6270 | |
| 6272 | →𝜑↔→𝜓𝜒→𝜓⋀𝜑𝜒 | Modus ponens 6264, 6271 | |
| 6273 | ↔→𝜑↔→𝜓𝜒→𝜓⋀𝜑𝜒↔→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒 | Subs [𝜓↗→𝜓𝜒, 𝜒↗→𝜓⋀𝜑𝜒] into pm5.74 | |
| 6274 | →↔→𝜑↔→𝜓𝜒→𝜓⋀𝜑𝜒↔→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒→→𝜑↔→𝜓𝜒→𝜓⋀𝜑𝜒↔→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒 | Subs [𝜑↗→𝜑↔→𝜓𝜒→𝜓⋀𝜑𝜒, 𝜓↗↔→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒] into biimp | |
| 6275 | →→𝜑↔→𝜓𝜒→𝜓⋀𝜑𝜒↔→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒 | Modus ponens 6273, 6274 | |
| 6276 | ↔→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒 | Modus ponens 6272, 6275 | pm5.42 |
| 6277 | →→𝜑→𝜓⋀𝜑𝜓→→𝜑𝜓→𝜑⋀𝜑𝜓 | Subs [𝜒↗⋀𝜑𝜓] into ax-2 | |
| 6278 | →↔→𝜑↔𝜓⋀𝜑𝜓↔→𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑↔𝜓⋀𝜑𝜓↔→𝜑𝜓→𝜑⋀𝜑𝜓 | Subs [𝜑↗→𝜑↔𝜓⋀𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜑⋀𝜑𝜓] into biimp | |
| 6279 | →→𝜑↔𝜓⋀𝜑𝜓↔→𝜑𝜓→𝜑⋀𝜑𝜓 | Modus ponens 6197, 6278 | |
| 6280 | →↔→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒→→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓⋀𝜑𝜒] into biimp | |
| 6281 | →→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒 | Modus ponens pm5.42, 6280 | anc2l |
| 6282 | →𝜑→𝜒⋀𝜒𝜑 | Subs [𝜓↗𝜒] into pm3.21 | |
| 6283 | →→𝜒⋀𝜒𝜑→𝜓→𝜒⋀𝜒𝜑 | Subs [𝜑↗→𝜒⋀𝜒𝜑] into ax-1 | |
| 6284 | →→→𝜒⋀𝜒𝜑→𝜓→𝜒⋀𝜒𝜑→𝜑→→𝜒⋀𝜒𝜑→𝜓→𝜒⋀𝜒𝜑 | Subs [𝜑↗→→𝜒⋀𝜒𝜑→𝜓→𝜒⋀𝜒𝜑, 𝜓↗𝜑] into ax-1 | |
| 6285 | →𝜑→→𝜒⋀𝜒𝜑→𝜓→𝜒⋀𝜒𝜑 | Modus ponens 6283, 6284 | |
| 6286 | →→𝜑→→𝜒⋀𝜒𝜑→𝜓→𝜒⋀𝜒𝜑→→𝜑→𝜒⋀𝜒𝜑→𝜑→𝜓→𝜒⋀𝜒𝜑 | Subs [𝜓↗→𝜒⋀𝜒𝜑, 𝜒↗→𝜓→𝜒⋀𝜒𝜑] into ax-2 | |
| 6287 | →→𝜑→𝜒⋀𝜒𝜑→𝜑→𝜓→𝜒⋀𝜒𝜑 | Modus ponens 6285, 6286 | |
| 6288 | →𝜑→𝜓→𝜒⋀𝜒𝜑 | Modus ponens 6282, 6287 | |
| 6289 | →→𝜓→𝜒⋀𝜒𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑 | Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗⋀𝜒𝜑] into ax-2 | |
| 6290 | →→→𝜓→𝜒⋀𝜒𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑→𝜑→→𝜓→𝜒⋀𝜒𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑 | Subs [𝜑↗→→𝜓→𝜒⋀𝜒𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑, 𝜓↗𝜑] into ax-1 | |
| 6291 | →𝜑→→𝜓→𝜒⋀𝜒𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑 | Modus ponens 6289, 6290 | |
| 6292 | →→𝜑→→𝜓→𝜒⋀𝜒𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑→→𝜑→𝜓→𝜒⋀𝜒𝜑→𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑 | Subs [𝜓↗→𝜓→𝜒⋀𝜒𝜑, 𝜒↗→→𝜓𝜒→𝜓⋀𝜒𝜑] into ax-2 | |
| 6293 | →→𝜑→𝜓→𝜒⋀𝜒𝜑→𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑 | Modus ponens 6291, 6292 | |
| 6294 | →𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑 | Modus ponens 6288, 6293 | |
| 6295 | →→𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑→→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜒𝜑 | Subs [𝜓↗→𝜓𝜒, 𝜒↗→𝜓⋀𝜒𝜑] into ax-2 | |
| 6296 | →→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜒𝜑 | Modus ponens 6294, 6295 | anc2r |
| 6297 | →→⋀𝜑𝜓𝜑↔→𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑 | Subs [𝜑↗→⋀𝜑𝜓𝜑, 𝜓↗→𝜑⋀𝜑𝜓] into iba | |
| 6298 | ↔→𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑 | Modus ponens simpl, 6297 | |
| 6299 | ↔↔𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑 | Subs [𝜓↗⋀𝜑𝜓] into dfbi2 | |
| 6300 | →↔↔𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓 | Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑] into bicom1 | |
| 6301 | ↔⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓 | Modus ponens 6299, 6300 | |
| 6302 | →↔⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓 | Subs [𝜑↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑, 𝜓↗↔𝜑⋀𝜑𝜓] into biimp | |
| 6303 | →⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓 | Modus ponens 6301, 6302 | |
| 6304 | →↔→𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→→𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑 | Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑] into biimp | |
| 6305 | →→𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑 | Modus ponens 6298, 6304 | |
| 6306 | →→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓→→𝜑⋀𝜑𝜓→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓 | Subs [𝜑↗→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓] into ax-1 | |
| 6307 | →→𝜑⋀𝜑𝜓→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓 | Modus ponens 6303, 6306 | |
| 6308 | →→→𝜑⋀𝜑𝜓→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓→→→𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓 | Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑, 𝜒↗↔𝜑⋀𝜑𝜓] into ax-2 | |
| 6309 | →→→𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓 | Modus ponens 6307, 6308 | |
| 6310 | →→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓 | Modus ponens 6305, 6309 | |
| 6311 | →↔⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓↔↔𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑 | Subs [𝜑↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑, 𝜓↗↔𝜑⋀𝜑𝜓] into bicom1 | |
| 6312 | →↔↔𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑 | Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑] into biimp | |
| 6313 | →↔𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑 | Modus ponens 6299, 6312 | |
| 6314 | →↔→𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓 | Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑] into bicom1 | |
| 6315 | ↔⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓 | Modus ponens 6298, 6314 | |
| 6316 | →↔⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓 | Subs [𝜑↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑, 𝜓↗→𝜑⋀𝜑𝜓] into biimp | |
| 6317 | →⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓 | Modus ponens 6315, 6316 | |
| 6318 | →→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓→↔𝜑⋀𝜑𝜓→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓 | Subs [𝜑↗→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓] into ax-1 | |
| 6319 | →↔𝜑⋀𝜑𝜓→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓 | Modus ponens 6317, 6318 | |
| 6320 | →→↔𝜑⋀𝜑𝜓→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓 | Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑, 𝜒↗→𝜑⋀𝜑𝜓] into ax-2 | |
| 6321 | →→↔𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓 | Modus ponens 6319, 6320 | |
| 6322 | →↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓 | Modus ponens 6313, 6321 | |
| 6323 | →→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓↔→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓 | Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓] into impbi | |
| 6324 | →→↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓↔→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓 | Modus ponens 6310, 6323 | |
| 6325 | ↔→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓 | Modus ponens 6322, 6324 | |
| 6326 | →↔→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓 | Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓] into biimp | |
| 6327 | →↔→𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑𝜓→𝜑⋀𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓] into biimp | |
| 6328 | →→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓 | Subs [𝜑↗→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 6329 | →→𝜑𝜓→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓 | Modus ponens 6310, 6328 | |
| 6330 | →→→𝜑𝜓→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓→→→𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑𝜓↔𝜑⋀𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓, 𝜒↗↔𝜑⋀𝜑𝜓] into ax-2 | |
| 6331 | →→→𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑𝜓↔𝜑⋀𝜑𝜓 | Modus ponens 6329, 6330 | |
| 6332 | →→𝜑𝜓↔𝜑⋀𝜑𝜓 | Modus ponens ancl, 6331 | |
| 6333 | →↔→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓↔↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓 | Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓] into bicom1 | |
| 6334 | ↔↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓 | Modus ponens 6325, 6333 | |
| 6335 | →↔↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓→↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓 | Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓] into biimp | |
| 6336 | →↔→𝜑𝜓→𝜑⋀𝜑𝜓↔→𝜑⋀𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓] into bicom1 | |
| 6337 | ↔→𝜑⋀𝜑𝜓→𝜑𝜓 | Modus ponens anclb, 6336 | |
| 6338 | →↔→𝜑⋀𝜑𝜓→𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into biimp | |
| 6339 | →→→𝜑⋀𝜑𝜓→𝜑𝜓→↔𝜑⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→→𝜑⋀𝜑𝜓→𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓] into ax-1 | |
| 6340 | →↔𝜑⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓 | Modus ponens 6193, 6339 | |
| 6341 | →→↔𝜑⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓→→↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓→↔𝜑⋀𝜑𝜓→𝜑𝜓 | Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2 | |
| 6342 | →→↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓→↔𝜑⋀𝜑𝜓→𝜑𝜓 | Modus ponens 6340, 6341 | |
| 6343 | →↔𝜑⋀𝜑𝜓→𝜑𝜓 | Modus ponens 6322, 6342 | |
| 6344 | →→→𝜑𝜓↔𝜑⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓→𝜑𝜓↔→𝜑𝜓↔𝜑⋀𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓] into impbi | |
| 6345 | →→↔𝜑⋀𝜑𝜓→𝜑𝜓↔→𝜑𝜓↔𝜑⋀𝜑𝜓 | Modus ponens 6332, 6344 | |
| 6346 | ↔→𝜑𝜓↔𝜑⋀𝜑𝜓 | Modus ponens 6343, 6345 | pm4.71 |
| 6347 | →↔𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓 | Subs [𝜑↗↔𝜑⋀𝜑𝜓] into id | |
| 6348 | →↔⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑 | Subs [𝜑↗↔⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗↔𝜑⋀𝜑𝜓] into ax-1 | |
| 6349 | →↔𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑 | Modus ponens ancom, 6348 | |
| 6350 | ↔→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓 | Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗𝜑, 𝜒↗⋀𝜑𝜓] into pm5.74 | |
| 6351 | →↔→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓 | Subs [𝜑↗→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓, 𝜓↗↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓] into biimp | |
| 6352 | →→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓 | Modus ponens 6350, 6351 | |
| 6353 | ↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓 | Modus ponens 6347, 6352 | |
| 6354 | ↔→↔𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑 | Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜓𝜑] into pm5.74 | |
| 6355 | →↔→↔𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→→↔𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑 | Subs [𝜑↗→↔𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑] into biimp | |
| 6356 | →→↔𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑 | Modus ponens 6354, 6355 | |
| 6357 | ↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑 | Modus ponens 6349, 6356 | |
| 6358 | →↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑 | Subs [𝜑↗→↔𝜑⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜓𝜑] into biimp | |
| 6359 | →→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑 | Modus ponens 6357, 6358 | |
| 6360 | →↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓 | Subs [𝜑↗→↔𝜑⋀𝜑𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜑𝜓] into biimp | |
| 6361 | →→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓 | Modus ponens 6353, 6360 | |
| 6362 | →→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→→↔𝜑⋀𝜑𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑 | Subs [𝜑↗→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓𝜑] into ax-1 | |
| 6363 | →→↔𝜑⋀𝜑𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑 | Modus ponens 6359, 6362 | |
| 6364 | →→→↔𝜑⋀𝜑𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→→→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑 | Subs [𝜑↗→↔𝜑⋀𝜑𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜑𝜓, 𝜒↗→↔𝜑⋀𝜑𝜓⋀𝜓𝜑] into ax-2 | |
| 6365 | →→→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑 | Modus ponens 6363, 6364 | |
| 6366 | →→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑 | Modus ponens 6361, 6365 | |
| 6367 | →↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑↔→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓 | Subs [𝜑↗→↔𝜑⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜓𝜑] into bicom1 | |
| 6368 | ↔→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓 | Modus ponens 6357, 6367 | |
| 6369 | →↔→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓 | Subs [𝜑↗→↔𝜑⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜑𝜓] into biimp | |
| 6370 | →→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓 | Modus ponens 6368, 6369 | |
| 6371 | →↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑 | Subs [𝜑↗→↔𝜑⋀𝜑𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜑𝜓] into bicom1 | |
| 6372 | ↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑 | Modus ponens 6353, 6371 | |
| 6373 | →↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑 | Subs [𝜑↗→↔𝜑⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗→↔𝜑⋀𝜑𝜓𝜑] into biimp | |
| 6374 | →→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑 | Modus ponens 6372, 6373 | |
| 6375 | →→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑 | Subs [𝜑↗→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜓𝜑] into ax-1 | |
| 6376 | →→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑 | Modus ponens 6374, 6375 | |
| 6377 | →→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑→→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓𝜑 | Subs [𝜑↗→↔𝜑⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜑𝜓, 𝜒↗→↔𝜑⋀𝜑𝜓𝜑] into ax-2 | |
| 6378 | →→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓𝜑 | Modus ponens 6376, 6377 | |
| 6379 | →→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓𝜑 | Modus ponens 6370, 6378 | |
| 6380 | →→→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓𝜑↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑 | Subs [𝜑↗→↔𝜑⋀𝜑𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜓𝜑] into impbi | |
| 6381 | →→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓𝜑↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑 | Modus ponens 6366, 6380 | |
| 6382 | ↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑 | Modus ponens 6379, 6381 | |
| 6383 | ↔→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑 | Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗𝜑, 𝜒↗⋀𝜓𝜑] into pm5.74 | |
| 6384 | →↔→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑↔↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑 | Subs [𝜑↗→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑, 𝜓↗↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑] into bicom1 | |
| 6385 | ↔↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑 | Modus ponens 6383, 6384 | |
| 6386 | →↔↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑→↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑 | Subs [𝜑↗↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑] into biimp | |
| 6387 | →↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑 | Modus ponens 6385, 6386 | |
| 6388 | →↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑 | Modus ponens 6382, 6387 | |
| 6389 | →↔𝜑⋀𝜓𝜑↔𝜑⋀𝜓𝜑 | Subs [𝜑↗↔𝜑⋀𝜓𝜑] into id | |
| 6390 | →↔⋀𝜑𝜓⋀𝜓𝜑↔⋀𝜓𝜑⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜓𝜑] into bicom1 | |
| 6391 | →↔⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑⋀𝜑𝜓 | Subs [𝜑↗↔⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑] into ax-1 | |
| 6392 | →↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑⋀𝜑𝜓 | Modus ponens 6162, 6391 | |
| 6393 | ↔→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜓𝜑↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑 | Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗𝜑, 𝜒↗⋀𝜓𝜑] into pm5.74 | |
| 6394 | →↔→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜓𝜑↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜓𝜑↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑 | Subs [𝜑↗→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜓𝜑, 𝜓↗↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑] into biimp | |
| 6395 | →→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜓𝜑↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑 | Modus ponens 6393, 6394 | |
| 6396 | ↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑 | Modus ponens 6389, 6395 | |
| 6397 | ↔→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓 | Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗⋀𝜓𝜑, 𝜒↗⋀𝜑𝜓] into pm5.74 | |
| 6398 | →↔→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓 | Subs [𝜑↗→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓] into biimp | |
| 6399 | →→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓 | Modus ponens 6397, 6398 | |
| 6400 | ↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓 | Modus ponens 6392, 6399 | |
| 6401 | →↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓 | Subs [𝜑↗→↔𝜑⋀𝜓𝜑⋀𝜓𝜑, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜑𝜓] into biimp | |
| 6402 | →→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓 | Modus ponens 6400, 6401 | |
| 6403 | →↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑 | Subs [𝜑↗→↔𝜑⋀𝜓𝜑𝜑, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜓𝜑] into biimp | |
| 6404 | →→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑 | Modus ponens 6396, 6403 | |
| 6405 | →→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→→↔𝜑⋀𝜓𝜑𝜑→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓 | Subs [𝜑↗→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗→↔𝜑⋀𝜓𝜑𝜑] into ax-1 | |
| 6406 | →→↔𝜑⋀𝜓𝜑𝜑→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓 | Modus ponens 6402, 6405 | |
| 6407 | →→→↔𝜑⋀𝜓𝜑𝜑→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→→→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓 | Subs [𝜑↗→↔𝜑⋀𝜓𝜑𝜑, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜓𝜑, 𝜒↗→↔𝜑⋀𝜓𝜑⋀𝜑𝜓] into ax-2 | |
| 6408 | →→→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓 | Modus ponens 6406, 6407 | |
| 6409 | →→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓 | Modus ponens 6404, 6408 | |
| 6410 | →↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑⋀𝜓𝜑 | Subs [𝜑↗→↔𝜑⋀𝜓𝜑⋀𝜓𝜑, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜑𝜓] into bicom1 | |
| 6411 | ↔→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑⋀𝜓𝜑 | Modus ponens 6400, 6410 | |
| 6412 | →↔→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑⋀𝜓𝜑 | Subs [𝜑↗→↔𝜑⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜓𝜑] into biimp | |
| 6413 | →→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑⋀𝜓𝜑 | Modus ponens 6411, 6412 | |
| 6414 | →↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑 | Subs [𝜑↗→↔𝜑⋀𝜓𝜑𝜑, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜓𝜑] into bicom1 | |
| 6415 | ↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑 | Modus ponens 6396, 6414 | |
| 6416 | →↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑 | Subs [𝜑↗→↔𝜑⋀𝜓𝜑⋀𝜓𝜑, 𝜓↗→↔𝜑⋀𝜓𝜑𝜑] into biimp | |
| 6417 | →→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑 | Modus ponens 6415, 6416 | |
| 6418 | →→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑 | Subs [𝜑↗→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜑𝜓] into ax-1 | |
| 6419 | →→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑 | Modus ponens 6417, 6418 | |
| 6420 | →→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑→→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑𝜑 | Subs [𝜑↗→↔𝜑⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜓𝜑, 𝜒↗→↔𝜑⋀𝜓𝜑𝜑] into ax-2 | |
| 6421 | →→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑𝜑 | Modus ponens 6419, 6420 | |
| 6422 | →→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑𝜑 | Modus ponens 6413, 6421 | |
| 6423 | →→→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑𝜑↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓 | Subs [𝜑↗→↔𝜑⋀𝜓𝜑𝜑, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜑𝜓] into impbi | |
| 6424 | →→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑𝜑↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓 | Modus ponens 6409, 6423 | |
| 6425 | ↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓 | Modus ponens 6422, 6424 | |
| 6426 | ↔→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓 | Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗𝜑, 𝜒↗⋀𝜑𝜓] into pm5.74 | |
| 6427 | →↔→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓↔↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓 | Subs [𝜑↗→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓, 𝜓↗↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓] into bicom1 | |
| 6428 | ↔↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓 | Modus ponens 6426, 6427 | |
| 6429 | →↔↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓→↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓 | Subs [𝜑↗↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓] into biimp | |
| 6430 | →↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓 | Modus ponens 6428, 6429 | |
| 6431 | →↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓 | Modus ponens 6425, 6430 | |
| 6432 | →→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓↔↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑 | Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑] into impbi | |
| 6433 | →→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓↔↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑 | Modus ponens 6388, 6432 | |
| 6434 | ↔↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑 | Modus ponens 6431, 6433 | |
| 6435 | →↔↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑 | Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑] into biimp | |
| 6436 | →↔→𝜑𝜓↔𝜑⋀𝜑𝜓→→𝜑𝜓↔𝜑⋀𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓] into biimp | |
| 6437 | →→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑→→𝜑𝜓→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑 | Subs [𝜑↗→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑, 𝜓↗→𝜑𝜓] into ax-1 | |
| 6438 | →→𝜑𝜓→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑 | Modus ponens 6388, 6437 | |
| 6439 | →→→𝜑𝜓→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑→→→𝜑𝜓↔𝜑⋀𝜑𝜓→→𝜑𝜓↔𝜑⋀𝜓𝜑 | Subs [𝜑↗→𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓, 𝜒↗↔𝜑⋀𝜓𝜑] into ax-2 | |
| 6440 | →→→𝜑𝜓↔𝜑⋀𝜑𝜓→→𝜑𝜓↔𝜑⋀𝜓𝜑 | Modus ponens 6438, 6439 | |
| 6441 | →→𝜑𝜓↔𝜑⋀𝜓𝜑 | Modus ponens 6332, 6440 | |
| 6442 | →↔↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑↔↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓 | Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑] into bicom1 | |
| 6443 | ↔↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓 | Modus ponens 6434, 6442 | |
| 6444 | →↔↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓 | Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗↔𝜑⋀𝜑𝜓] into biimp | |
| 6445 | →↔→𝜑𝜓↔𝜑⋀𝜑𝜓↔↔𝜑⋀𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓] into bicom1 | |
| 6446 | ↔↔𝜑⋀𝜑𝜓→𝜑𝜓 | Modus ponens pm4.71, 6445 | |
| 6447 | →↔↔𝜑⋀𝜑𝜓→𝜑𝜓→↔𝜑⋀𝜑𝜓→𝜑𝜓 | Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into biimp | |
| 6448 | →→↔𝜑⋀𝜑𝜓→𝜑𝜓→↔𝜑⋀𝜓𝜑→↔𝜑⋀𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→↔𝜑⋀𝜑𝜓→𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑] into ax-1 | |
| 6449 | →↔𝜑⋀𝜓𝜑→↔𝜑⋀𝜑𝜓→𝜑𝜓 | Modus ponens 6343, 6448 | |
| 6450 | →→↔𝜑⋀𝜓𝜑→↔𝜑⋀𝜑𝜓→𝜑𝜓→→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑→𝜑𝜓 | Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗↔𝜑⋀𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2 | |
| 6451 | →→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑→𝜑𝜓 | Modus ponens 6449, 6450 | |
| 6452 | →↔𝜑⋀𝜓𝜑→𝜑𝜓 | Modus ponens 6431, 6451 | |
| 6453 | →→→𝜑𝜓↔𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑→𝜑𝜓↔→𝜑𝜓↔𝜑⋀𝜓𝜑 | Subs [𝜑↗→𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑] into impbi | |
| 6454 | →→↔𝜑⋀𝜓𝜑→𝜑𝜓↔→𝜑𝜓↔𝜑⋀𝜓𝜑 | Modus ponens 6441, 6453 | |
| 6455 | ↔→𝜑𝜓↔𝜑⋀𝜓𝜑 | Modus ponens 6452, 6454 | pm4.71r |
| 6456 | ↔→𝜑𝜑↔𝜑⋀𝜑𝜑 | Subs [𝜓↗𝜑] into pm4.71 | |
| 6457 | →↔→𝜑𝜑↔𝜑⋀𝜑𝜑→→𝜑𝜑↔𝜑⋀𝜑𝜑 | Subs [𝜑↗→𝜑𝜑, 𝜓↗↔𝜑⋀𝜑𝜑] into biimp | |
| 6458 | →→𝜑𝜑↔𝜑⋀𝜑𝜑 | Modus ponens 6456, 6457 | |
| 6459 | ↔𝜑⋀𝜑𝜑 | Modus ponens id, 6458 | pm4.24 |
| 6460 | →↔𝜑⋀𝜑𝜑↔⋀𝜑𝜑𝜑 | Subs [𝜓↗⋀𝜑𝜑] into bicom1 | |
| 6461 | ↔⋀𝜑𝜑𝜑 | Modus ponens pm4.24, 6460 | anidm |
| 6462 | ↔⋀𝜓𝜓𝜓 | Subs [𝜑↗𝜓] into anidm | |
| 6463 | →↔⋀𝜓𝜓𝜓→𝜑↔⋀𝜓𝜓𝜓 | Subs [𝜑↗↔⋀𝜓𝜓𝜓, 𝜓↗𝜑] into ax-1 | |
| 6464 | →𝜑↔⋀𝜓𝜓𝜓 | Modus ponens 6462, 6463 | |
| 6465 | ↔→𝜑↔⋀𝜓𝜓𝜓↔→𝜑⋀𝜓𝜓→𝜑𝜓 | Subs [𝜓↗⋀𝜓𝜓, 𝜒↗𝜓] into pm5.74 | |
| 6466 | →↔→𝜑↔⋀𝜓𝜓𝜓↔→𝜑⋀𝜓𝜓→𝜑𝜓→→𝜑↔⋀𝜓𝜓𝜓↔→𝜑⋀𝜓𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑↔⋀𝜓𝜓𝜓, 𝜓↗↔→𝜑⋀𝜓𝜓→𝜑𝜓] into biimp | |
| 6467 | →→𝜑↔⋀𝜓𝜓𝜓↔→𝜑⋀𝜓𝜓→𝜑𝜓 | Modus ponens 6465, 6466 | |
| 6468 | ↔→𝜑⋀𝜓𝜓→𝜑𝜓 | Modus ponens 6464, 6467 | anidmdbi |
| 6469 | ↔→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓⋀𝜑𝜒 | Subs [𝜒↗⋀𝜑𝜒] into impexp | |
| 6470 | →↔→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓⋀𝜑𝜒↔→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗→⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗→𝜑→𝜓⋀𝜑𝜒] into bicom1 | |
| 6471 | ↔→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 6469, 6470 | |
| 6472 | →↔→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒→→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗→𝜑→𝜓⋀𝜑𝜒, 𝜓↗→⋀𝜑𝜓⋀𝜑𝜒] into biimp | |
| 6473 | →→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 6471, 6472 | |
| 6474 | →→→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒→→𝜑→𝜓𝜒→→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗→→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1 | |
| 6475 | →→𝜑→𝜓𝜒→→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 6473, 6474 | |
| 6476 | →→→𝜑→𝜓𝜒→→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒→→→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓⋀𝜑𝜒, 𝜒↗→⋀𝜑𝜓⋀𝜑𝜒] into ax-2 | |
| 6477 | →→→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 6475, 6476 | |
| 6478 | →→𝜑→𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens anc2l, 6477 | |
| 6479 | →↔→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒↔→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓⋀𝜑𝜒 | Subs [𝜑↗→𝜑→𝜓⋀𝜑𝜒, 𝜓↗→⋀𝜑𝜓⋀𝜑𝜒] into bicom1 | |
| 6480 | →↔→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓⋀𝜑𝜒→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓⋀𝜑𝜒 | Subs [𝜑↗→⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗→𝜑→𝜓⋀𝜑𝜒] into biimp | |
| 6481 | →→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓⋀𝜑𝜒 | Modus ponens 6469, 6480 | |
| 6482 | →↔→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒↔→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓⋀𝜑𝜒] into bicom1 | |
| 6483 | ↔→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒 | Modus ponens pm5.42, 6482 | |
| 6484 | →↔→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒→→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒 | Subs [𝜑↗→𝜑→𝜓⋀𝜑𝜒, 𝜓↗→𝜑→𝜓𝜒] into biimp | |
| 6485 | →→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒 | Modus ponens 6483, 6484 | |
| 6486 | →→→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒→→⋀𝜑𝜓⋀𝜑𝜒→→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒 | Subs [𝜑↗→→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑𝜓⋀𝜑𝜒] into ax-1 | |
| 6487 | →→⋀𝜑𝜓⋀𝜑𝜒→→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒 | Modus ponens 6485, 6486 | |
| 6488 | →→→⋀𝜑𝜓⋀𝜑𝜒→→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒→→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓⋀𝜑𝜒→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓𝜒 | Subs [𝜑↗→⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗→𝜑→𝜓⋀𝜑𝜒, 𝜒↗→𝜑→𝜓𝜒] into ax-2 | |
| 6489 | →→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓⋀𝜑𝜒→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓𝜒 | Modus ponens 6487, 6488 | |
| 6490 | →→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓𝜒 | Modus ponens 6481, 6489 | |
| 6491 | →→→𝜑→𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒→→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑𝜓⋀𝜑𝜒] into impbi | |
| 6492 | →→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 6478, 6491 | |
| 6493 | ↔→𝜑→𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 6490, 6492 | imdistan |
| 6494 | →→𝜑↔𝜒⋀𝜑𝜒→⋀𝜑𝜓→𝜑↔𝜒⋀𝜑𝜒 | Subs [𝜑↗→𝜑↔𝜒⋀𝜑𝜒, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 6495 | →⋀𝜑𝜓→𝜑↔𝜒⋀𝜑𝜒 | Modus ponens 6258, 6494 | |
| 6496 | →→⋀𝜑𝜓→𝜑↔𝜒⋀𝜑𝜒→→⋀𝜑𝜓𝜑→⋀𝜑𝜓↔𝜒⋀𝜑𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜑, 𝜒↗↔𝜒⋀𝜑𝜒] into ax-2 | |
| 6497 | →→⋀𝜑𝜓𝜑→⋀𝜑𝜓↔𝜒⋀𝜑𝜒 | Modus ponens 6495, 6496 | |
| 6498 | →⋀𝜑𝜓↔𝜒⋀𝜑𝜒 | Modus ponens simpl, 6497 | |
| 6499 | ↔→⋀𝜑𝜓↔𝜒⋀𝜑𝜒↔→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒, 𝜒↗⋀𝜑𝜒] into pm5.74 | |
| 6500 | →↔→⋀𝜑𝜓↔𝜒⋀𝜑𝜒↔→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒→→⋀𝜑𝜓↔𝜒⋀𝜑𝜒↔→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗→⋀𝜑𝜓↔𝜒⋀𝜑𝜒, 𝜓↗↔→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒] into biimp | |
| 6501 | →→⋀𝜑𝜓↔𝜒⋀𝜑𝜒↔→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 6499, 6500 | |
| 6502 | ↔→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 6498, 6501 | pm5.3 |
| 6503 | ↔↔𝜓𝜒↔¬𝜓¬𝜒 | Subs [𝜑↗𝜓, 𝜓↗𝜒] into notbi | |
| 6504 | →↔↔𝜓𝜒↔¬𝜓¬𝜒→𝜑↔↔𝜓𝜒↔¬𝜓¬𝜒 | Subs [𝜑↗↔↔𝜓𝜒↔¬𝜓¬𝜒, 𝜓↗𝜑] into ax-1 | |
| 6505 | →𝜑↔↔𝜓𝜒↔¬𝜓¬𝜒 | Modus ponens 6503, 6504 | |
| 6506 | ↔→𝜑↔↔𝜓𝜒↔¬𝜓¬𝜒↔→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒 | Subs [𝜓↗↔𝜓𝜒, 𝜒↗↔¬𝜓¬𝜒] into pm5.74 | |
| 6507 | →↔→𝜑↔↔𝜓𝜒↔¬𝜓¬𝜒↔→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒→→𝜑↔↔𝜓𝜒↔¬𝜓¬𝜒↔→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒 | Subs [𝜑↗→𝜑↔↔𝜓𝜒↔¬𝜓¬𝜒, 𝜓↗↔→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒] into biimp | |
| 6508 | →→𝜑↔↔𝜓𝜒↔¬𝜓¬𝜒↔→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒 | Modus ponens 6506, 6507 | |
| 6509 | ↔→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒 | Modus ponens 6505, 6508 | |
| 6510 | ↔→𝜑↔¬𝜓¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒 | Subs [𝜓↗¬𝜓, 𝜒↗¬𝜒] into pm5.74 | |
| 6511 | ↔↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→𝜑¬𝜒] into notbi | |
| 6512 | →↔↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗↔→𝜑¬𝜓→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into biimp | |
| 6513 | →↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6511, 6512 | |
| 6514 | →↔→𝜑↔¬𝜓¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒→→𝜑↔¬𝜓¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒 | Subs [𝜑↗→𝜑↔¬𝜓¬𝜒, 𝜓↗↔→𝜑¬𝜓→𝜑¬𝜒] into biimp | |
| 6515 | →→𝜑↔¬𝜓¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒 | Modus ponens 6510, 6514 | |
| 6516 | →→↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔¬𝜓¬𝜒→↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗→↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→𝜑↔¬𝜓¬𝜒] into ax-1 | |
| 6517 | →→𝜑↔¬𝜓¬𝜒→↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6513, 6516 | |
| 6518 | →→→𝜑↔¬𝜓¬𝜒→↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→→𝜑↔¬𝜓¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗→𝜑↔¬𝜓¬𝜒, 𝜓↗↔→𝜑¬𝜓→𝜑¬𝜒, 𝜒↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-2 | |
| 6519 | →→→𝜑↔¬𝜓¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6517, 6518 | |
| 6520 | →→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6515, 6519 | |
| 6521 | →↔↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒 | Subs [𝜑↗↔→𝜑¬𝜓→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into bicom1 | |
| 6522 | ↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒 | Modus ponens 6511, 6521 | |
| 6523 | →↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒 | Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔→𝜑¬𝜓→𝜑¬𝜒] into biimp | |
| 6524 | →↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒 | Modus ponens 6522, 6523 | |
| 6525 | →↔→𝜑↔¬𝜓¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒↔↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒 | Subs [𝜑↗→𝜑↔¬𝜓¬𝜒, 𝜓↗↔→𝜑¬𝜓→𝜑¬𝜒] into bicom1 | |
| 6526 | ↔↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒 | Modus ponens 6510, 6525 | |
| 6527 | →↔↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒→↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒 | Subs [𝜑↗↔→𝜑¬𝜓→𝜑¬𝜒, 𝜓↗→𝜑↔¬𝜓¬𝜒] into biimp | |
| 6528 | →↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒 | Modus ponens 6526, 6527 | |
| 6529 | →→↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒 | Subs [𝜑↗→↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-1 | |
| 6530 | →↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒 | Modus ponens 6528, 6529 | |
| 6531 | →→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒 | Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔→𝜑¬𝜓→𝜑¬𝜒, 𝜒↗→𝜑↔¬𝜓¬𝜒] into ax-2 | |
| 6532 | →→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒 | Modus ponens 6530, 6531 | |
| 6533 | →↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒 | Modus ponens 6524, 6532 | |
| 6534 | →→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒↔→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗→𝜑↔¬𝜓¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into impbi | |
| 6535 | →→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒↔→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6520, 6534 | |
| 6536 | ↔→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6533, 6535 | |
| 6537 | →↔→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗→𝜑↔¬𝜓¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into biimp | |
| 6538 | →↔→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒→→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔¬𝜓¬𝜒] into biimp | |
| 6539 | →→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒 | Modus ponens 6509, 6538 | |
| 6540 | →→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔𝜓𝜒→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1 | |
| 6541 | →→𝜑↔𝜓𝜒→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6520, 6540 | |
| 6542 | →→→𝜑↔𝜓𝜒→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒→→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔¬𝜓¬𝜒, 𝜒↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-2 | |
| 6543 | →→→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒→→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6541, 6542 | |
| 6544 | →→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6539, 6543 | |
| 6545 | →↔→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒 | Subs [𝜑↗→𝜑↔¬𝜓¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into bicom1 | |
| 6546 | ↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒 | Modus ponens 6536, 6545 | |
| 6547 | →↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒 | Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→𝜑↔¬𝜓¬𝜒] into biimp | |
| 6548 | →↔→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒↔→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔¬𝜓¬𝜒] into bicom1 | |
| 6549 | ↔→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒 | Modus ponens 6509, 6548 | |
| 6550 | →↔→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒→→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒 | Subs [𝜑↗→𝜑↔¬𝜓¬𝜒, 𝜓↗→𝜑↔𝜓𝜒] into biimp | |
| 6551 | →→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒 | Modus ponens 6549, 6550 | |
| 6552 | →→→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒 | Subs [𝜑↗→→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-1 | |
| 6553 | →↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒 | Modus ponens 6551, 6552 | |
| 6554 | →→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒 | Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→𝜑↔¬𝜓¬𝜒, 𝜒↗→𝜑↔𝜓𝜒] into ax-2 | |
| 6555 | →→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒 | Modus ponens 6553, 6554 | |
| 6556 | →↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒 | Modus ponens 6533, 6555 | |
| 6557 | →→→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into impbi | |
| 6558 | →→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6544, 6557 | |
| 6559 | ↔→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6556, 6558 | |
| 6560 | ↔⋀𝜑𝜒¬→𝜑¬𝜒 | Subs [𝜓↗𝜒] into df-an | |
| 6561 | →↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒] into id | |
| 6562 | →↔⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜒¬→𝜑¬𝜒 | Subs [𝜑↗↔⋀𝜑𝜒¬→𝜑¬𝜒, 𝜓↗↔⋀𝜑𝜓⋀𝜑𝜒] into ax-1 | |
| 6563 | →↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜒¬→𝜑¬𝜒 | Modus ponens 6560, 6562 | |
| 6564 | ↔→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒 | Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜑𝜒] into pm5.74 | |
| 6565 | →↔→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒 | Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒] into biimp | |
| 6566 | →→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒 | Modus ponens 6564, 6565 | |
| 6567 | ↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒 | Modus ponens 6561, 6566 | |
| 6568 | ↔→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜒¬→𝜑¬𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒 | Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗⋀𝜑𝜒, 𝜒↗¬→𝜑¬𝜒] into pm5.74 | |
| 6569 | →↔→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜒¬→𝜑¬𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜒¬→𝜑¬𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒 | Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜒¬→𝜑¬𝜒, 𝜓↗↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒] into biimp | |
| 6570 | →→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜒¬→𝜑¬𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒 | Modus ponens 6568, 6569 | |
| 6571 | ↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒 | Modus ponens 6563, 6570 | |
| 6572 | →↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒 | Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒] into biimp | |
| 6573 | →→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒 | Modus ponens 6571, 6572 | |
| 6574 | →↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒 | Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒] into biimp | |
| 6575 | →→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒 | Modus ponens 6567, 6574 | |
| 6576 | →→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒 | Subs [𝜑↗→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓] into ax-1 | |
| 6577 | →→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒 | Modus ponens 6573, 6576 | |
| 6578 | →→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒 | Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒, 𝜒↗→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒] into ax-2 | |
| 6579 | →→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒 | Modus ponens 6577, 6578 | |
| 6580 | →→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒 | Modus ponens 6575, 6579 | |
| 6581 | →↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒 | Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒] into bicom1 | |
| 6582 | ↔→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒 | Modus ponens 6571, 6581 | |
| 6583 | →↔→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒 | Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒] into biimp | |
| 6584 | →→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒 | Modus ponens 6582, 6583 | |
| 6585 | →↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓 | Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒] into bicom1 | |
| 6586 | ↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓 | Modus ponens 6567, 6585 | |
| 6587 | →↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓 | Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓] into biimp | |
| 6588 | →→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓 | Modus ponens 6586, 6587 | |
| 6589 | →→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓 | Subs [𝜑↗→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒] into ax-1 | |
| 6590 | →→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓 | Modus ponens 6588, 6589 | |
| 6591 | →→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓 | Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒, 𝜒↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓] into ax-2 | |
| 6592 | →→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓 | Modus ponens 6590, 6591 | |
| 6593 | →→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓 | Modus ponens 6584, 6592 | |
| 6594 | →→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒 | Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒] into impbi | |
| 6595 | →→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒 | Modus ponens 6580, 6594 | |
| 6596 | ↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒 | Modus ponens 6593, 6595 | |
| 6597 | ↔→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒 | Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗¬→𝜑¬𝜒] into pm5.74 | |
| 6598 | →↔→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒↔↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒 | Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒] into bicom1 | |
| 6599 | ↔↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒 | Modus ponens 6597, 6598 | |
| 6600 | →↔↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒→↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒 | Subs [𝜑↗↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒] into biimp | |
| 6601 | →↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒 | Modus ponens 6599, 6600 | |
| 6602 | →↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒 | Modus ponens 6596, 6601 | |
| 6603 | →↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒 | Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into id | |
| 6604 | →↔⋀𝜑𝜒¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜒 | Subs [𝜑↗⋀𝜑𝜒, 𝜓↗¬→𝜑¬𝜒] into bicom1 | |
| 6605 | ↔¬→𝜑¬𝜒⋀𝜑𝜒 | Modus ponens 6560, 6604 | |
| 6606 | →↔¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜒 | Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜒, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into ax-1 | |
| 6607 | →↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜒 | Modus ponens 6605, 6606 | |
| 6608 | ↔→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒 | Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗¬→𝜑¬𝜒] into pm5.74 | |
| 6609 | →↔→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒 | Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒] into biimp | |
| 6610 | →→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒 | Modus ponens 6608, 6609 | |
| 6611 | ↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒 | Modus ponens 6603, 6610 | |
| 6612 | ↔→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒 | Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗¬→𝜑¬𝜒, 𝜒↗⋀𝜑𝜒] into pm5.74 | |
| 6613 | →↔→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒 | Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜒, 𝜓↗↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒] into biimp | |
| 6614 | →→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒 | Modus ponens 6612, 6613 | |
| 6615 | ↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒 | Modus ponens 6607, 6614 | |
| 6616 | →↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒 | Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒] into biimp | |
| 6617 | →→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒 | Modus ponens 6615, 6616 | |
| 6618 | →↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒 | Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒] into biimp | |
| 6619 | →→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒 | Modus ponens 6611, 6618 | |
| 6620 | →→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒 | Subs [𝜑↗→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓] into ax-1 | |
| 6621 | →→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒 | Modus ponens 6617, 6620 | |
| 6622 | →→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒 | Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜒↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒] into ax-2 | |
| 6623 | →→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒 | Modus ponens 6621, 6622 | |
| 6624 | →→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒 | Modus ponens 6619, 6623 | |
| 6625 | →↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒 | Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒] into bicom1 | |
| 6626 | ↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒 | Modus ponens 6615, 6625 | |
| 6627 | →↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒 | Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒] into biimp | |
| 6628 | →→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒 | Modus ponens 6626, 6627 | |
| 6629 | →↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓 | Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒] into bicom1 | |
| 6630 | ↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓 | Modus ponens 6611, 6629 | |
| 6631 | →↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓 | Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓] into biimp | |
| 6632 | →→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓 | Modus ponens 6630, 6631 | |
| 6633 | →→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓 | Subs [𝜑↗→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒] into ax-1 | |
| 6634 | →→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓 | Modus ponens 6632, 6633 | |
| 6635 | →→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓 | Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜒↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓] into ax-2 | |
| 6636 | →→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓 | Modus ponens 6634, 6635 | |
| 6637 | →→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓 | Modus ponens 6628, 6636 | |
| 6638 | →→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒 | Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒] into impbi | |
| 6639 | →→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒 | Modus ponens 6624, 6638 | |
| 6640 | ↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒 | Modus ponens 6637, 6639 | |
| 6641 | ↔→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒 | Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜑𝜒] into pm5.74 | |
| 6642 | →↔→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒↔↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒] into bicom1 | |
| 6643 | ↔↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 6641, 6642 | |
| 6644 | →↔↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒→↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒] into biimp | |
| 6645 | →↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 6643, 6644 | |
| 6646 | →↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 6640, 6645 | |
| 6647 | →→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒 | Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into impbi | |
| 6648 | →→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒 | Modus ponens 6602, 6647 | |
| 6649 | ↔↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒 | Modus ponens 6646, 6648 | |
| 6650 | ↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜒] into bicom | |
| 6651 | →↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓 | Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓] into id | |
| 6652 | →↔⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜓 | Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜓, 𝜓↗↔¬→𝜑¬𝜒⋀𝜑𝜓] into ax-1 | |
| 6653 | →↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜓 | Modus ponens df-an, 6652 | |
| 6654 | ↔→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓 | Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜒, 𝜒↗⋀𝜑𝜓] into pm5.74 | |
| 6655 | →↔→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓 | Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓] into biimp | |
| 6656 | →→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓 | Modus ponens 6654, 6655 | |
| 6657 | ↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓 | Modus ponens 6651, 6656 | |
| 6658 | ↔→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓 | Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗¬→𝜑¬𝜓] into pm5.74 | |
| 6659 | →↔→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜓, 𝜓↗↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓] into biimp | |
| 6660 | →→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓 | Modus ponens 6658, 6659 | |
| 6661 | ↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓 | Modus ponens 6653, 6660 | |
| 6662 | →↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓] into biimp | |
| 6663 | →→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓 | Modus ponens 6661, 6662 | |
| 6664 | →↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓 | Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓] into biimp | |
| 6665 | →→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓 | Modus ponens 6657, 6664 | |
| 6666 | →→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒] into ax-1 | |
| 6667 | →→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓 | Modus ponens 6663, 6666 | |
| 6668 | →→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓, 𝜒↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓] into ax-2 | |
| 6669 | →→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓 | Modus ponens 6667, 6668 | |
| 6670 | →→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓 | Modus ponens 6665, 6669 | |
| 6671 | →↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓 | Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓] into bicom1 | |
| 6672 | ↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓 | Modus ponens 6661, 6671 | |
| 6673 | →↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓 | Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓] into biimp | |
| 6674 | →→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓 | Modus ponens 6672, 6673 | |
| 6675 | →↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒 | Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓] into bicom1 | |
| 6676 | ↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒 | Modus ponens 6657, 6675 | |
| 6677 | →↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒 | Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒] into biimp | |
| 6678 | →→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒 | Modus ponens 6676, 6677 | |
| 6679 | →→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒 | Subs [𝜑↗→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓] into ax-1 | |
| 6680 | →→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒 | Modus ponens 6678, 6679 | |
| 6681 | →→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒 | Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓, 𝜒↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒] into ax-2 | |
| 6682 | →→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒 | Modus ponens 6680, 6681 | |
| 6683 | →→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒 | Modus ponens 6674, 6682 | |
| 6684 | →→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓] into impbi | |
| 6685 | →→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓 | Modus ponens 6670, 6684 | |
| 6686 | ↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓 | Modus ponens 6683, 6685 | |
| 6687 | ↔→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓 | Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜒, 𝜒↗¬→𝜑¬𝜓] into pm5.74 | |
| 6688 | →↔→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓↔↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓 | Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜓↗↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓] into bicom1 | |
| 6689 | ↔↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓 | Modus ponens 6687, 6688 | |
| 6690 | →↔↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓→↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓 | Subs [𝜑↗↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓] into biimp | |
| 6691 | →↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓 | Modus ponens 6689, 6690 | |
| 6692 | →↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓 | Modus ponens 6686, 6691 | |
| 6693 | →↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓 | Subs [𝜑↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓] into id | |
| 6694 | →↔¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓⋀𝜑𝜓 | Subs [𝜑↗↔¬→𝜑¬𝜓⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓] into ax-1 | |
| 6695 | →↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓⋀𝜑𝜓 | Modus ponens pm4.63, 6694 | |
| 6696 | ↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜒, 𝜒↗¬→𝜑¬𝜓] into pm5.74 | |
| 6697 | →↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜓↗↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓] into biimp | |
| 6698 | →→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 6696, 6697 | |
| 6699 | ↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 6693, 6698 | |
| 6700 | ↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓⋀𝜑𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓 | Subs [𝜑↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗⋀𝜑𝜓] into pm5.74 | |
| 6701 | →↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓⋀𝜑𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓⋀𝜑𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓 | Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓⋀𝜑𝜓, 𝜓↗↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓] into biimp | |
| 6702 | →→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓⋀𝜑𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓 | Modus ponens 6700, 6701 | |
| 6703 | ↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓 | Modus ponens 6695, 6702 | |
| 6704 | →↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓 | Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓] into biimp | |
| 6705 | →→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓 | Modus ponens 6703, 6704 | |
| 6706 | →↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓] into biimp | |
| 6707 | →→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 6699, 6706 | |
| 6708 | →→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓 | Subs [𝜑↗→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-1 | |
| 6709 | →→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓 | Modus ponens 6705, 6708 | |
| 6710 | →→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓 | Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜒↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓] into ax-2 | |
| 6711 | →→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓 | Modus ponens 6709, 6710 | |
| 6712 | →→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓 | Modus ponens 6707, 6711 | |
| 6713 | →↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓] into bicom1 | |
| 6714 | ↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 6703, 6713 | |
| 6715 | →↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓] into biimp | |
| 6716 | →→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 6714, 6715 | |
| 6717 | →↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓] into bicom1 | |
| 6718 | ↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6699, 6717 | |
| 6719 | →↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒] into biimp | |
| 6720 | →→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6718, 6719 | |
| 6721 | →→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓] into ax-1 | |
| 6722 | →→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6720, 6721 | |
| 6723 | →→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜒↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-2 | |
| 6724 | →→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6722, 6723 | |
| 6725 | →→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6716, 6724 | |
| 6726 | →→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓 | Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓] into impbi | |
| 6727 | →→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓 | Modus ponens 6712, 6726 | |
| 6728 | ↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓 | Modus ponens 6725, 6727 | |
| 6729 | ↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓 | Subs [𝜑↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜒, 𝜒↗⋀𝜑𝜓] into pm5.74 | |
| 6730 | →↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓↔↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓 | Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓] into bicom1 | |
| 6731 | ↔↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓 | Modus ponens 6729, 6730 | |
| 6732 | →↔↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓→↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓 | Subs [𝜑↗↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓] into biimp | |
| 6733 | →↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓 | Modus ponens 6731, 6732 | |
| 6734 | →↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓 | Modus ponens 6728, 6733 | |
| 6735 | →→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓 | Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓] into impbi | |
| 6736 | →→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓 | Modus ponens 6692, 6735 | |
| 6737 | ↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓 | Modus ponens 6734, 6736 | |
| 6738 | ↔↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗¬→𝜑¬𝜒, 𝜓↗¬→𝜑¬𝜓] into bicom | |
| 6739 | →↔↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into biimp | |
| 6740 | →↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6738, 6739 | |
| 6741 | →↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓 | Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓] into biimp | |
| 6742 | →→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜒⋀𝜑𝜓] into ax-1 | |
| 6743 | →↔¬→𝜑¬𝜒⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6740, 6742 | |
| 6744 | →→↔¬→𝜑¬𝜒⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜒↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-2 | |
| 6745 | →→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6743, 6744 | |
| 6746 | →↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6692, 6745 | |
| 6747 | →↔↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒¬→𝜑¬𝜓 | Subs [𝜑↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into bicom1 | |
| 6748 | ↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒¬→𝜑¬𝜓 | Modus ponens 6738, 6747 | |
| 6749 | →↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒¬→𝜑¬𝜓→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒¬→𝜑¬𝜓 | Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓] into biimp | |
| 6750 | →↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒¬→𝜑¬𝜓 | Modus ponens 6748, 6749 | |
| 6751 | →↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓 | Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓] into bicom1 | |
| 6752 | ↔↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓 | Modus ponens 6737, 6751 | |
| 6753 | →↔↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓 | Subs [𝜑↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜓↗↔¬→𝜑¬𝜒⋀𝜑𝜓] into biimp | |
| 6754 | →→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓 | Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-1 | |
| 6755 | →↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓 | Modus ponens 6734, 6754 | |
| 6756 | →→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒¬→𝜑¬𝜓→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓 | Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜒↗↔¬→𝜑¬𝜒⋀𝜑𝜓] into ax-2 | |
| 6757 | →→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒¬→𝜑¬𝜓→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓 | Modus ponens 6755, 6756 | |
| 6758 | →↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓 | Modus ponens 6750, 6757 | |
| 6759 | →→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into impbi | |
| 6760 | →→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6746, 6759 | |
| 6761 | ↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6758, 6760 | |
| 6762 | →↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into biimp | |
| 6763 | →↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓 | Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜒⋀𝜑𝜓] into biimp | |
| 6764 | →↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓 | Modus ponens 6650, 6763 | |
| 6765 | →→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into ax-1 | |
| 6766 | →↔⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6746, 6765 | |
| 6767 | →→↔⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜒↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-2 | |
| 6768 | →→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6766, 6767 | |
| 6769 | →↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6764, 6768 | |
| 6770 | →↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓 | Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into bicom1 | |
| 6771 | ↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓 | Modus ponens 6761, 6770 | |
| 6772 | →↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓 | Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜒⋀𝜑𝜓] into biimp | |
| 6773 | →↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒 | Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜒⋀𝜑𝜓] into bicom1 | |
| 6774 | ↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒 | Modus ponens 6650, 6773 | |
| 6775 | →↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒 | Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into biimp | |
| 6776 | →↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒 | Modus ponens 6774, 6775 | |
| 6777 | →→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒 | Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-1 | |
| 6778 | →↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒 | Modus ponens 6776, 6777 | |
| 6779 | →→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒 | Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜒↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into ax-2 | |
| 6780 | →→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒 | Modus ponens 6778, 6779 | |
| 6781 | →↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒 | Modus ponens 6758, 6780 | |
| 6782 | →→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into impbi | |
| 6783 | →→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6769, 6782 | |
| 6784 | ↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6781, 6783 | |
| 6785 | →↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into biimp | |
| 6786 | →↔↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒 | Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into biimp | |
| 6787 | →→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔⋀𝜑𝜓⋀𝜑𝜒] into ax-1 | |
| 6788 | →↔⋀𝜑𝜓⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6769, 6787 | |
| 6789 | →→↔⋀𝜑𝜓⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜒↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-2 | |
| 6790 | →→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6788, 6789 | |
| 6791 | →↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6602, 6790 | |
| 6792 | →↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒 | Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into bicom1 | |
| 6793 | ↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒 | Modus ponens 6784, 6792 | |
| 6794 | →↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒 | Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into biimp | |
| 6795 | →↔↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into bicom1 | |
| 6796 | ↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 6649, 6795 | |
| 6797 | →↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔⋀𝜑𝜓⋀𝜑𝜒] into biimp | |
| 6798 | →→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-1 | |
| 6799 | →↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 6646, 6798 | |
| 6800 | →→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜒↗↔⋀𝜑𝜓⋀𝜑𝜒] into ax-2 | |
| 6801 | →→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 6799, 6800 | |
| 6802 | →↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 6781, 6801 | |
| 6803 | →→↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into impbi | |
| 6804 | →→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6791, 6803 | |
| 6805 | ↔↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Modus ponens 6802, 6804 | |
| 6806 | →↔↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into bicom1 | |
| 6807 | ↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 6805, 6806 | |
| 6808 | →↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔⋀𝜑𝜓⋀𝜑𝜒] into biimp | |
| 6809 | →↔→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into biimp | |
| 6810 | →→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒→→𝜑↔𝜓𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1 | |
| 6811 | →→𝜑↔𝜓𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 6802, 6810 | |
| 6812 | →→→𝜑↔𝜓𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒→→→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔𝜓𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜒↗↔⋀𝜑𝜓⋀𝜑𝜒] into ax-2 | |
| 6813 | →→→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔𝜓𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 6811, 6812 | |
| 6814 | →→𝜑↔𝜓𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 6544, 6813 | |
| 6815 | →↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔⋀𝜑𝜓⋀𝜑𝜒] into bicom1 | |
| 6816 | →↔↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒 | Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into biimp | |
| 6817 | →↔→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into bicom1 | |
| 6818 | ↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒 | Modus ponens 6559, 6817 | |
| 6819 | →↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒 | Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→𝜑↔𝜓𝜒] into biimp | |
| 6820 | →→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒→↔⋀𝜑𝜓⋀𝜑𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒 | Subs [𝜑↗→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒, 𝜓↗↔⋀𝜑𝜓⋀𝜑𝜒] into ax-1 | |
| 6821 | →↔⋀𝜑𝜓⋀𝜑𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒 | Modus ponens 6556, 6820 | |
| 6822 | →→↔⋀𝜑𝜓⋀𝜑𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒→𝜑↔𝜓𝜒 | Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜒↗→𝜑↔𝜓𝜒] into ax-2 | |
| 6823 | →→↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒→𝜑↔𝜓𝜒 | Modus ponens 6821, 6822 | |
| 6824 | →↔⋀𝜑𝜓⋀𝜑𝜒→𝜑↔𝜓𝜒 | Modus ponens 6791, 6823 | |
| 6825 | →→→𝜑↔𝜓𝜒↔⋀𝜑𝜓⋀𝜑𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗↔⋀𝜑𝜓⋀𝜑𝜒] into impbi | |
| 6826 | →→↔⋀𝜑𝜓⋀𝜑𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 6814, 6825 | |
| 6827 | ↔→𝜑↔𝜓𝜒↔⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 6824, 6826 | pm5.32 |
| 6828 | →→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀𝜓𝜒] into idd | |
| 6829 | →⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 6830 | →→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→⋀𝜓𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 6831 | →⋀𝜓𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6829, 6830 | |
| 6832 | →→⋀𝜓𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 6833 | →→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6831, 6832 | |
| 6834 | →→→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀𝜓𝜒, 𝜒↗⋀𝜓𝜒] into ax-2 | |
| 6835 | →→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6828, 6834 | |
| 6836 | →→→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→⋀𝜓𝜒→→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 6837 | →⋀𝜓𝜒→→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6835, 6836 | |
| 6838 | →→⋀𝜓𝜒→→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 6839 | →→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6837, 6838 | |
| 6840 | →→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→¬→𝜓¬𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒] into ax-1 | |
| 6841 | →¬→𝜓¬𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6829, 6840 | |
| 6842 | →→¬→𝜓¬𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 6843 | →→¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6841, 6842 | |
| 6844 | →¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 5017, 6843 | |
| 6845 | →→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 6846 | →𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6844, 6845 | |
| 6847 | →→𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒¬→𝜓¬𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 6848 | →→𝜒¬→𝜓¬𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6846, 6847 | |
| 6849 | →→→𝜒¬→𝜓¬𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜒¬→𝜓¬𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜒¬→𝜓¬𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 6850 | →𝜓→→𝜒¬→𝜓¬𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6848, 6849 | |
| 6851 | →→𝜓→→𝜒¬→𝜓¬𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→𝜒¬→𝜓¬𝜒→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→𝜒¬→𝜓¬𝜒, 𝜒↗→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 6852 | →→𝜓→𝜒¬→𝜓¬𝜒→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6850, 6851 | |
| 6853 | →𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 5023, 6852 | |
| 6854 | →→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀𝜓𝜒] into pm2.27 | |
| 6855 | →→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒] into ax-1 | |
| 6856 | →𝜓→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒 | Modus ponens 6854, 6855 | |
| 6857 | →→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 6858 | →→→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 6859 | →𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6857, 6858 | |
| 6860 | →→𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 6861 | →→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6859, 6860 | |
| 6862 | →𝜓→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6853, 6861 | |
| 6863 | →→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into imim2 | |
| 6864 | →→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜑𝜓→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒 | Subs [𝜑↗→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 6865 | →→𝜑𝜓→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒 | Modus ponens 6863, 6864 | |
| 6866 | →→→𝜑𝜓→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒] into ax-2 | |
| 6867 | →→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒 | Modus ponens 6865, 6866 | |
| 6868 | →→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒] into ax-1 | |
| 6869 | →𝜓→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒 | Modus ponens 6867, 6868 | |
| 6870 | →→𝜓→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒] into ax-2 | |
| 6871 | →→𝜓→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒 | Modus ponens 6869, 6870 | |
| 6872 | →𝜓→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒 | Modus ponens 6856, 6871 | |
| 6873 | →→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→𝜒⋀𝜓𝜒] into ax-2 | |
| 6874 | →→→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒] into ax-1 | |
| 6875 | →𝜓→→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒 | Modus ponens 6873, 6874 | |
| 6876 | →→𝜓→→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒, 𝜒↗→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒] into ax-2 | |
| 6877 | →→𝜓→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒 | Modus ponens 6875, 6876 | |
| 6878 | →𝜓→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒 | Modus ponens 6872, 6877 | |
| 6879 | →→𝜓→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜒⋀𝜓𝜒] into ax-2 | |
| 6880 | →→𝜓→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒 | Modus ponens 6878, 6879 | |
| 6881 | →𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒 | Modus ponens 6862, 6880 | |
| 6882 | →→𝜑𝜓→𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓] into ax-1 | |
| 6883 | →→→𝜑𝜓→𝜓→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→𝜓→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→𝜓→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 6884 | →→𝜑𝜓→→𝜑𝜓→𝜓→𝜑𝜓 | Modus ponens 6882, 6883 | |
| 6885 | →→→𝜑𝜓→→𝜑𝜓→𝜓→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜓→𝜑𝜓] into ax-2 | |
| 6886 | →→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→𝜓→𝜑𝜓 | Modus ponens 6884, 6885 | |
| 6887 | →→𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜓→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜒⋀𝜓𝜒] into ax-2 | |
| 6888 | →→𝜓→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒 | Modus ponens 6881, 6887 | |
| 6889 | →→→𝜓→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒 | Subs [𝜑↗→→𝜓→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 6890 | →→𝜑𝜓→→𝜓→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒 | Modus ponens 6888, 6889 | |
| 6891 | →→→𝜑𝜓→→𝜓→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓→𝜑𝜓→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓→𝜑𝜓, 𝜒↗→𝜓→𝜒⋀𝜓𝜒] into ax-2 | |
| 6892 | →→→𝜑𝜓→𝜓→𝜑𝜓→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒 | Modus ponens 6890, 6891 | |
| 6893 | →→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒 | Modus ponens 6882, 6892 | |
| 6894 | →𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗⋀𝜓𝜒] into pm2.27 | |
| 6895 | →→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 6896 | →→𝜑𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒 | Modus ponens 6894, 6895 | |
| 6897 | →→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓→𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜓→𝜒⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 6898 | →→→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓→𝜒⋀𝜓𝜒 | Subs [𝜑↗→→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓→𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 6899 | →→𝜑𝜓→→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓→𝜒⋀𝜓𝜒 | Modus ponens 6897, 6898 | |
| 6900 | →→→𝜑𝜓→→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜓→𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓→𝜒⋀𝜓𝜒, 𝜒↗→𝜒→𝜓→𝜒⋀𝜓𝜒] into ax-2 | |
| 6901 | →→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜓→𝜒⋀𝜓𝜒 | Modus ponens 6899, 6900 | |
| 6902 | →→𝜑𝜓→𝜒→𝜓→𝜒⋀𝜓𝜒 | Modus ponens 6893, 6901 | |
| 6903 | →→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗→𝜒⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗𝜓] into imim2 | |
| 6904 | →→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 6905 | →𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒 | Modus ponens 6903, 6904 | |
| 6906 | →→𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→→𝜒⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒] into ax-2 | |
| 6907 | →→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒 | Modus ponens 6905, 6906 | |
| 6908 | →→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 6909 | →→𝜑𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒 | Modus ponens 6907, 6908 | |
| 6910 | →→→𝜑𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒] into ax-2 | |
| 6911 | →→→𝜑𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒 | Modus ponens 6909, 6910 | |
| 6912 | →→𝜑𝜓→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒 | Modus ponens 6896, 6911 | |
| 6913 | →→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜓→𝜒⋀𝜓𝜒, 𝜒↗→𝜓⋀𝜓𝜒] into ax-2 | |
| 6914 | →→→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 6915 | →→𝜑𝜓→→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒 | Modus ponens 6913, 6914 | |
| 6916 | →→→𝜑𝜓→→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒, 𝜒↗→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒] into ax-2 | |
| 6917 | →→→𝜑𝜓→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒 | Modus ponens 6915, 6916 | |
| 6918 | →→𝜑𝜓→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒 | Modus ponens 6912, 6917 | |
| 6919 | →→→𝜑𝜓→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜒→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→𝜓→𝜒⋀𝜓𝜒, 𝜒↗→𝜒→𝜓⋀𝜓𝜒] into ax-2 | |
| 6920 | →→→𝜑𝜓→𝜒→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒 | Modus ponens 6918, 6919 | |
| 6921 | →→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒 | Modus ponens 6902, 6920 | |
| 6922 | →𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗⋀𝜓𝜒] into pm2.27 | |
| 6923 | →→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 6924 | →→𝜑𝜓→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒 | Modus ponens 6922, 6923 | |
| 6925 | →→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗→𝜒→𝜓⋀𝜓𝜒] into ax-1 | |
| 6926 | →→→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒→𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 6927 | →→𝜑𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒→𝜓⋀𝜓𝜒 | Modus ponens 6925, 6926 | |
| 6928 | →→→𝜑𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→𝜓⋀𝜓𝜒, 𝜒↗→𝜓→𝜒→𝜓⋀𝜓𝜒] into ax-2 | |
| 6929 | →→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→𝜒→𝜓⋀𝜓𝜒 | Modus ponens 6927, 6928 | |
| 6930 | →→𝜑𝜓→𝜓→𝜒→𝜓⋀𝜓𝜒 | Modus ponens 6921, 6929 | |
| 6931 | →→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜓⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into imim2 | |
| 6932 | →→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→𝜓→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒 | Subs [𝜑↗→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒] into ax-1 | |
| 6933 | →𝜓→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒 | Modus ponens 6931, 6932 | |
| 6934 | →→𝜓→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→→𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒] into ax-2 | |
| 6935 | →→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒 | Modus ponens 6933, 6934 | |
| 6936 | →→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒 | Subs [𝜑↗→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 6937 | →→𝜑𝜓→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒 | Modus ponens 6935, 6936 | |
| 6938 | →→→𝜑𝜓→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒] into ax-2 | |
| 6939 | →→→𝜑𝜓→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒 | Modus ponens 6937, 6938 | |
| 6940 | →→𝜑𝜓→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒 | Modus ponens 6924, 6939 | |
| 6941 | →→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→𝜒→𝜓⋀𝜓𝜒, 𝜒↗→𝜒⋀𝜓𝜒] into ax-2 | |
| 6942 | →→→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒 | Subs [𝜑↗→→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 6943 | →→𝜑𝜓→→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒 | Modus ponens 6941, 6942 | |
| 6944 | →→→𝜑𝜓→→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒, 𝜒↗→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒] into ax-2 | |
| 6945 | →→→𝜑𝜓→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒 | Modus ponens 6943, 6944 | |
| 6946 | →→𝜑𝜓→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒 | Modus ponens 6940, 6945 | |
| 6947 | →→→𝜑𝜓→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓→𝜒→𝜓⋀𝜓𝜒, 𝜒↗→𝜓→𝜒⋀𝜓𝜒] into ax-2 | |
| 6948 | →→→𝜑𝜓→𝜓→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒 | Modus ponens 6946, 6947 | |
| 6949 | →𝜓→→𝜑𝜓𝜓 | Subs [𝜑↗𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 6950 | →→𝜓→→𝜑𝜓𝜓→𝜓→𝜓→→𝜑𝜓𝜓 | Subs [𝜑↗→𝜓→→𝜑𝜓𝜓] into ax-1 | |
| 6951 | →𝜓→𝜓→→𝜑𝜓𝜓 | Modus ponens 6949, 6950 | |
| 6952 | →→𝜓→𝜓→→𝜑𝜓𝜓→→𝜓𝜓→𝜓→→𝜑𝜓𝜓 | Subs [𝜑↗𝜓, 𝜒↗→→𝜑𝜓𝜓] into ax-2 | |
| 6953 | →→𝜓𝜓→𝜓→→𝜑𝜓𝜓 | Modus ponens 6951, 6952 | |
| 6954 | →→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒→→→𝜑𝜓𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜒↗→𝜒⋀𝜓𝜒] into ax-2 | |
| 6955 | →→→𝜑𝜓𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒 | Modus ponens 6893, 6954 | |
| 6956 | →→→→𝜑𝜓𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜓𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒] into ax-1 | |
| 6957 | →𝜓→→→𝜑𝜓𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒 | Modus ponens 6955, 6956 | |
| 6958 | →→𝜓→→→𝜑𝜓𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓𝜓→𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜓𝜓, 𝜒↗→→𝜑𝜓→𝜒⋀𝜓𝜒] into ax-2 | |
| 6959 | →→𝜓→→𝜑𝜓𝜓→𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒 | Modus ponens 6957, 6958 | |
| 6960 | →→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒] into ax-1 | |
| 6961 | →𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒 | Modus ponens 6894, 6960 | |
| 6962 | →→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜒⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 6963 | →→→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒] into ax-1 | |
| 6964 | →𝜓→→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒 | Modus ponens 6962, 6963 | |
| 6965 | →→𝜓→→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜓→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜓→𝜒⋀𝜓𝜒, 𝜒↗→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒] into ax-2 | |
| 6966 | →→𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜓→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒 | Modus ponens 6964, 6965 | |
| 6967 | →𝜓→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒 | Modus ponens 6881, 6966 | |
| 6968 | →→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→𝜒⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜑𝜓] into imim2 | |
| 6969 | →→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 6970 | →𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6968, 6969 | |
| 6971 | →→𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→→𝜒⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 6972 | →→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6970, 6971 | |
| 6973 | →→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 6974 | →𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6972, 6973 | |
| 6975 | →→𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜓→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 6976 | →→𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜓→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6974, 6975 | |
| 6977 | →𝜓→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6961, 6976 | |
| 6978 | →→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓→𝜒⋀𝜓𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 6979 | →→→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 6980 | →𝜓→→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6978, 6979 | |
| 6981 | →→𝜓→→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 6982 | →→𝜓→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6980, 6981 | |
| 6983 | →𝜓→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6977, 6982 | |
| 6984 | →→𝜓→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒, 𝜒↗→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 6985 | →→𝜓→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6983, 6984 | |
| 6986 | →→𝜒→𝜓𝜒→𝜒→𝜒→𝜓𝜒 | Subs [𝜑↗→𝜒→𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 6987 | →𝜒→𝜒→𝜓𝜒 | Modus ponens 5362, 6986 | |
| 6988 | →→𝜒→𝜒→𝜓𝜒→→𝜒𝜒→𝜒→𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗𝜒, 𝜒↗→𝜓𝜒] into ax-2 | |
| 6989 | →→𝜒𝜒→𝜒→𝜓𝜒 | Modus ponens 6987, 6988 | |
| 6990 | →→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 6991 | →→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6853, 6990 | |
| 6992 | →→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 6993 | →𝜒→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6991, 6992 | |
| 6994 | →→𝜒→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜓𝜒→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→𝜓→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 6995 | →→𝜒→𝜓𝜒→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6993, 6994 | |
| 6996 | →𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 5362, 6995 | |
| 6997 | ↔⋀𝜒𝜓¬→𝜒¬𝜓 | Subs [𝜑↗𝜒] into df-an | |
| 6998 | →→𝜓→𝜒𝜓→¬¬𝜓→𝜓→𝜒𝜓 | Subs [𝜑↗→𝜓→𝜒𝜓, 𝜓↗¬¬𝜓] into ax-1 | |
| 6999 | →¬¬𝜓→𝜓→𝜒𝜓 | Modus ponens 5350, 6998 | |
| 7000 | →→¬¬𝜓→𝜓→𝜒𝜓→→¬¬𝜓𝜓→¬¬𝜓→𝜒𝜓 | Subs [𝜑↗¬¬𝜓, 𝜒↗→𝜒𝜓] into ax-2 | |
| 7001 | →→¬¬𝜓𝜓→¬¬𝜓→𝜒𝜓 | Modus ponens 6999, 7000 | |
| 7002 | →¬¬𝜓→𝜒𝜓 | Modus ponens 570, 7001 | |
| 7003 | →→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7004 | →→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6996, 7003 | |
| 7005 | →→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬¬𝜓] into ax-1 | |
| 7006 | →¬¬𝜓→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7004, 7005 | |
| 7007 | →→¬¬𝜓→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→¬¬𝜓→𝜒𝜓→¬¬𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜒𝜓, 𝜒↗→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7008 | →→¬¬𝜓→𝜒𝜓→¬¬𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7006, 7007 | |
| 7009 | →¬¬𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7002, 7008 | |
| 7010 | →𝜒→¬¬𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗¬¬𝜓] into ax-1 | |
| 7011 | →→𝜒→¬¬𝜓𝜒→𝜒→𝜒→¬¬𝜓𝜒 | Subs [𝜑↗→𝜒→¬¬𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 7012 | →𝜒→𝜒→¬¬𝜓𝜒 | Modus ponens 7010, 7011 | |
| 7013 | →→𝜒→𝜒→¬¬𝜓𝜒→→𝜒𝜒→𝜒→¬¬𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗𝜒, 𝜒↗→¬¬𝜓𝜒] into ax-2 | |
| 7014 | →→𝜒𝜒→𝜒→¬¬𝜓𝜒 | Modus ponens 7012, 7013 | |
| 7015 | →→¬¬𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→¬¬𝜓𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗¬¬𝜓, 𝜓↗𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7016 | →→¬¬𝜓𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7009, 7015 | |
| 7017 | →→→¬¬𝜓𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→¬¬𝜓𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→¬¬𝜓𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 7018 | →𝜒→→¬¬𝜓𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7016, 7017 | |
| 7019 | →→𝜒→→¬¬𝜓𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜒→¬¬𝜓𝜒→𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→¬¬𝜓𝜒, 𝜒↗→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7020 | →→𝜒→¬¬𝜓𝜒→𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7018, 7019 | |
| 7021 | →𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7010, 7020 | |
| 7022 | →→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓⋀𝜓𝜒] into notnot | |
| 7023 | →→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬¬𝜓] into ax-1 | |
| 7024 | →¬¬𝜓→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7022, 7023 | |
| 7025 | →→¬¬𝜓→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗¬¬𝜓, 𝜓↗→→𝜑𝜓⋀𝜓𝜒, 𝜒↗¬¬→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7026 | →→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7024, 7025 | |
| 7027 | →→→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→𝜒→→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 7028 | →𝜒→→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7026, 7027 | |
| 7029 | →→𝜒→→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→→𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7030 | →→𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7028, 7029 | |
| 7031 | →𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7021, 7030 | |
| 7032 | →→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-3 | |
| 7033 | →→→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓→𝜒→→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓 | Subs [𝜑↗→→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓, 𝜓↗𝜒] into ax-1 | |
| 7034 | →𝜒→→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓 | Modus ponens 7032, 7033 | |
| 7035 | →→𝜒→→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓→→𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓 | Subs [𝜑↗𝜒, 𝜓↗→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓] into ax-2 | |
| 7036 | →→𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓 | Modus ponens 7034, 7035 | |
| 7037 | →𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓 | Modus ponens 7031, 7036 | |
| 7038 | →¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒] into id | |
| 7039 | →¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 7040 | →→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7041 | →¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7039, 7040 | |
| 7042 | →→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→𝜒¬→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7043 | →→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7041, 7042 | |
| 7044 | →→𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓→→𝜒¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓 | Subs [𝜑↗𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗¬𝜓] into ax-2 | |
| 7045 | →→𝜒¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓 | Modus ponens 7037, 7044 | |
| 7046 | →→→𝜒¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒→→𝜒¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓 | Subs [𝜑↗→→𝜒¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7047 | →¬→→𝜑𝜓⋀𝜓𝜒→→𝜒¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓 | Modus ponens 7045, 7046 | |
| 7048 | →→¬→→𝜑𝜓⋀𝜓𝜒→→𝜒¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓→→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→𝜒¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→𝜒¬𝜓] into ax-2 | |
| 7049 | →→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓 | Modus ponens 7047, 7048 | |
| 7050 | →¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓 | Modus ponens 7039, 7049 | |
| 7051 | →¬→𝜒¬𝜓¬→𝜒¬𝜓 | Subs [𝜑↗¬→𝜒¬𝜓] into id | |
| 7052 | →→¬→𝜒¬𝜓¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜒¬𝜓¬→𝜒¬𝜓 | Subs [𝜑↗→¬→𝜒¬𝜓¬→𝜒¬𝜓, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7053 | →¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜒¬𝜓¬→𝜒¬𝜓 | Modus ponens 7051, 7052 | |
| 7054 | →¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓 | Subs [𝜑↗¬→𝜒¬𝜓] into notnotr | |
| 7055 | →¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓 | Subs [𝜑↗¬→𝜒¬𝜓, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7056 | →→¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓 | Subs [𝜑↗→¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓, 𝜓↗¬¬¬→𝜒¬𝜓] into ax-1 | |
| 7057 | →¬¬¬→𝜒¬𝜓→¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓 | Modus ponens 7055, 7056 | |
| 7058 | →→¬¬¬→𝜒¬𝜓→¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓 | Subs [𝜑↗¬¬¬→𝜒¬𝜓, 𝜓↗¬→𝜒¬𝜓, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓] into ax-2 | |
| 7059 | →→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓 | Modus ponens 7057, 7058 | |
| 7060 | →¬¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓 | Modus ponens 7054, 7059 | |
| 7061 | →→¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜒¬𝜓¬→𝜒¬𝜓→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→𝜒¬𝜓, 𝜒↗¬→𝜒¬𝜓] into ax-2 | |
| 7062 | →→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓 | Modus ponens 7053, 7061 | |
| 7063 | →→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓 | Subs [𝜑↗→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓, 𝜓↗¬¬¬→𝜒¬𝜓] into ax-1 | |
| 7064 | →¬¬¬→𝜒¬𝜓→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓 | Modus ponens 7062, 7063 | |
| 7065 | →→¬¬¬→𝜒¬𝜓→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→→¬¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓 | Subs [𝜑↗¬¬¬→𝜒¬𝜓, 𝜓↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓] into ax-2 | |
| 7066 | →→¬¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓 | Modus ponens 7064, 7065 | |
| 7067 | →¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬¬¬→𝜒¬𝜓] into ax-1 | |
| 7068 | →→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7069 | →¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7067, 7068 | |
| 7070 | →→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7071 | →→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7069, 7070 | |
| 7072 | →→¬¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓 | Subs [𝜑↗¬¬¬→𝜒¬𝜓, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗¬→𝜒¬𝜓] into ax-2 | |
| 7073 | →→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓 | Modus ponens 7060, 7072 | |
| 7074 | →→→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓 | Subs [𝜑↗→→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7075 | →¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓 | Modus ponens 7073, 7074 | |
| 7076 | →→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓] into ax-2 | |
| 7077 | →→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓 | Modus ponens 7075, 7076 | |
| 7078 | →¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓 | Modus ponens 7067, 7077 | |
| 7079 | →→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓 | Subs [𝜑↗¬¬→𝜒¬𝜓, 𝜓↗→𝜒¬𝜓] into ax-3 | |
| 7080 | →→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓 | Subs [𝜑↗→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7081 | →¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓 | Modus ponens 7079, 7080 | |
| 7082 | →→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒→→𝜒¬𝜓¬¬→𝜒¬𝜓 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓, 𝜒↗→→𝜒¬𝜓¬¬→𝜒¬𝜓] into ax-2 | |
| 7083 | →→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒→→𝜒¬𝜓¬¬→𝜒¬𝜓 | Modus ponens 7081, 7082 | |
| 7084 | →¬→→𝜑𝜓⋀𝜓𝜒→→𝜒¬𝜓¬¬→𝜒¬𝜓 | Modus ponens 7078, 7083 | |
| 7085 | →→¬→→𝜑𝜓⋀𝜓𝜒→→𝜒¬𝜓¬¬→𝜒¬𝜓→→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜒¬𝜓 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→𝜒¬𝜓, 𝜒↗¬¬→𝜒¬𝜓] into ax-2 | |
| 7086 | →→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜒¬𝜓 | Modus ponens 7084, 7085 | |
| 7087 | →¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜒¬𝜓 | Modus ponens 7050, 7086 | |
| 7088 | →→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜒¬𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→𝜒¬𝜓] into ax-3 | |
| 7089 | →¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7087, 7088 | |
| 7090 | →↔⋀𝜒𝜓¬→𝜒¬𝜓→⋀𝜒𝜓¬→𝜒¬𝜓 | Subs [𝜑↗⋀𝜒𝜓, 𝜓↗¬→𝜒¬𝜓] into biimp | |
| 7091 | →⋀𝜒𝜓¬→𝜒¬𝜓 | Modus ponens 6997, 7090 | |
| 7092 | →→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒→⋀𝜒𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗⋀𝜒𝜓] into ax-1 | |
| 7093 | →⋀𝜒𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7089, 7092 | |
| 7094 | →→⋀𝜒𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒→→⋀𝜒𝜓¬→𝜒¬𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗⋀𝜒𝜓, 𝜓↗¬→𝜒¬𝜓, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7095 | →→⋀𝜒𝜓¬→𝜒¬𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7093, 7094 | |
| 7096 | →⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7091, 7095 | |
| 7097 | →→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀𝜒𝜓] into ax-1 | |
| 7098 | →→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 7099 | →→𝜑𝜓→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓 | Modus ponens 7097, 7098 | |
| 7100 | →→→𝜑𝜓→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→⋀𝜒𝜓→𝜑𝜓] into ax-2 | |
| 7101 | →→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓 | Modus ponens 7099, 7100 | |
| 7102 | →→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒→→⋀𝜒𝜓→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒 | Subs [𝜑↗⋀𝜒𝜓, 𝜓↗→𝜑𝜓, 𝜒↗⋀𝜓𝜒] into ax-2 | |
| 7103 | →→⋀𝜒𝜓→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒 | Modus ponens 7096, 7102 | |
| 7104 | →→→⋀𝜒𝜓→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒→→𝜑𝜓→→⋀𝜒𝜓→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒 | Subs [𝜑↗→→⋀𝜒𝜓→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 7105 | →→𝜑𝜓→→⋀𝜒𝜓→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒 | Modus ponens 7103, 7104 | |
| 7106 | →→→𝜑𝜓→→⋀𝜒𝜓→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒→→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓→→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜒𝜓→𝜑𝜓, 𝜒↗→⋀𝜒𝜓⋀𝜓𝜒] into ax-2 | |
| 7107 | →→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓→→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒 | Modus ponens 7105, 7106 | |
| 7108 | →→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒 | Modus ponens 7097, 7107 | |
| 7109 | →⋀𝜒𝜓⋀𝜒𝜓 | Subs [𝜑↗⋀𝜒𝜓] into id | |
| 7110 | →⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓 | Subs [𝜑↗⋀𝜒𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 7111 | →→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓→⋀𝜒𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓 | Subs [𝜑↗→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓, 𝜓↗⋀𝜒𝜓] into ax-1 | |
| 7112 | →⋀𝜒𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓 | Modus ponens 7110, 7111 | |
| 7113 | →→⋀𝜒𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓→→⋀𝜒𝜓⋀𝜒𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓 | Subs [𝜑↗⋀𝜒𝜓, 𝜓↗⋀𝜒𝜓, 𝜒↗→→𝜑𝜓⋀𝜒𝜓] into ax-2 | |
| 7114 | →→⋀𝜒𝜓⋀𝜒𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓 | Modus ponens 7112, 7113 | |
| 7115 | →→→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒→→→𝜑𝜓⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀𝜒𝜓, 𝜒↗⋀𝜓𝜒] into ax-2 | |
| 7116 | →→→𝜑𝜓⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7108, 7115 | |
| 7117 | →→→→𝜑𝜓⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒→⋀𝜒𝜓→→→𝜑𝜓⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜓⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗⋀𝜒𝜓] into ax-1 | |
| 7118 | →⋀𝜒𝜓→→→𝜑𝜓⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7116, 7117 | |
| 7119 | →→⋀𝜒𝜓→→→𝜑𝜓⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒→→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗⋀𝜒𝜓, 𝜓↗→→𝜑𝜓⋀𝜒𝜓, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7120 | →→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7118, 7119 | |
| 7121 | →↔⋀𝜒𝜓¬→𝜒¬𝜓↔¬→𝜒¬𝜓⋀𝜒𝜓 | Subs [𝜑↗⋀𝜒𝜓, 𝜓↗¬→𝜒¬𝜓] into bicom1 | |
| 7122 | ↔¬→𝜒¬𝜓⋀𝜒𝜓 | Modus ponens 6997, 7121 | |
| 7123 | →↔¬→𝜒¬𝜓⋀𝜒𝜓→¬→𝜒¬𝜓⋀𝜒𝜓 | Subs [𝜑↗¬→𝜒¬𝜓, 𝜓↗⋀𝜒𝜓] into biimp | |
| 7124 | →¬→𝜒¬𝜓⋀𝜒𝜓 | Modus ponens 7122, 7123 | |
| 7125 | →→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒→¬→𝜒¬𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→𝜒¬𝜓] into ax-1 | |
| 7126 | →¬→𝜒¬𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7096, 7125 | |
| 7127 | →→¬→𝜒¬𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒→→¬→𝜒¬𝜓⋀𝜒𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗¬→𝜒¬𝜓, 𝜓↗⋀𝜒𝜓, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7128 | →→¬→𝜒¬𝜓⋀𝜒𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7126, 7127 | |
| 7129 | →𝜒→𝜓¬→𝜒¬𝜓 | Subs [𝜑↗𝜒] into pm3.2im | |
| 7130 | →→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7131 | →𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7089, 7130 | |
| 7132 | →→𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜓¬→𝜒¬𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗¬→𝜒¬𝜓, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7133 | →→𝜓¬→𝜒¬𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7131, 7132 | |
| 7134 | →→→𝜓¬→𝜒¬𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜓¬→𝜒¬𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜓¬→𝜒¬𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 7135 | →𝜒→→𝜓¬→𝜒¬𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7133, 7134 | |
| 7136 | →→𝜒→→𝜓¬→𝜒¬𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜓¬→𝜒¬𝜓→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜓¬→𝜒¬𝜓, 𝜒↗→𝜓→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7137 | →→𝜒→𝜓¬→𝜒¬𝜓→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7135, 7136 | |
| 7138 | →→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 7139 | →𝜒→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒 | Modus ponens 6854, 7138 | |
| 7140 | →→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 7141 | →→→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 7142 | →𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7140, 7141 | |
| 7143 | →→𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7144 | →→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7142, 7143 | |
| 7145 | →𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6996, 7144 | |
| 7146 | →→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗𝜓] into imim2 | |
| 7147 | →→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 7148 | →→𝜑𝜓→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒 | Modus ponens 7146, 7147 | |
| 7149 | →→→𝜑𝜓→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒] into ax-2 | |
| 7150 | →→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒 | Modus ponens 7148, 7149 | |
| 7151 | →→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→𝜒→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 7152 | →𝜒→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒 | Modus ponens 7150, 7151 | |
| 7153 | →→𝜒→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒] into ax-2 | |
| 7154 | →→𝜒→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒 | Modus ponens 7152, 7153 | |
| 7155 | →𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒 | Modus ponens 7139, 7154 | |
| 7156 | →→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→𝜓⋀𝜓𝜒] into ax-2 | |
| 7157 | →→→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜒→→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 7158 | →𝜒→→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒 | Modus ponens 7156, 7157 | |
| 7159 | →→𝜒→→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒, 𝜒↗→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒] into ax-2 | |
| 7160 | →→𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒 | Modus ponens 7158, 7159 | |
| 7161 | →𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒 | Modus ponens 7155, 7160 | |
| 7162 | →→𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜓⋀𝜓𝜒] into ax-2 | |
| 7163 | →→𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒 | Modus ponens 7161, 7162 | |
| 7164 | →𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒 | Modus ponens 7145, 7163 | |
| 7165 | →→𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜒→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜓⋀𝜓𝜒] into ax-2 | |
| 7166 | →→𝜒→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒 | Modus ponens 7164, 7165 | |
| 7167 | →→→𝜒→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜒→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 7168 | →→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒 | Modus ponens 7166, 7167 | |
| 7169 | →→→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜒→𝜑𝜓→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→𝜑𝜓, 𝜒↗→𝜒→𝜓⋀𝜓𝜒] into ax-2 | |
| 7170 | →→→𝜑𝜓→𝜒→𝜑𝜓→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒 | Modus ponens 7168, 7169 | |
| 7171 | →→𝜒→𝜓⋀𝜓𝜒→𝜒→𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗→𝜒→𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 7172 | →→→𝜒→𝜓⋀𝜓𝜒→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒→𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜒→𝜓⋀𝜓𝜒→𝜒→𝜒→𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 7173 | →→𝜑𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒→𝜒→𝜓⋀𝜓𝜒 | Modus ponens 7171, 7172 | |
| 7174 | →→→𝜑𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒→𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→𝜓⋀𝜓𝜒, 𝜒↗→𝜒→𝜒→𝜓⋀𝜓𝜒] into ax-2 | |
| 7175 | →→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜒→𝜓⋀𝜓𝜒 | Modus ponens 7173, 7174 | |
| 7176 | →→𝜑𝜓→𝜒→𝜒→𝜓⋀𝜓𝜒 | Modus ponens 6921, 7175 | |
| 7177 | →→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗𝜒, 𝜒↗→𝜓⋀𝜓𝜒] into ax-2 | |
| 7178 | →→→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 7179 | →→𝜑𝜓→→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒 | Modus ponens 7177, 7178 | |
| 7180 | →→→𝜑𝜓→→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→𝜒→𝜓⋀𝜓𝜒, 𝜒↗→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒] into ax-2 | |
| 7181 | →→→𝜑𝜓→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒 | Modus ponens 7179, 7180 | |
| 7182 | →→𝜑𝜓→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒 | Modus ponens 7176, 7181 | |
| 7183 | →→→𝜑𝜓→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜒𝜒→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒𝜒, 𝜒↗→𝜒→𝜓⋀𝜓𝜒] into ax-2 | |
| 7184 | →→→𝜑𝜓→𝜒𝜒→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒 | Modus ponens 7182, 7183 | |
| 7185 | →𝜒→→𝜑𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 7186 | →→𝜒→→𝜑𝜓𝜒→𝜒→𝜒→→𝜑𝜓𝜒 | Subs [𝜑↗→𝜒→→𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 7187 | →𝜒→𝜒→→𝜑𝜓𝜒 | Modus ponens 7185, 7186 | |
| 7188 | →→𝜒→𝜒→→𝜑𝜓𝜒→→𝜒𝜒→𝜒→→𝜑𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗𝜒, 𝜒↗→→𝜑𝜓𝜒] into ax-2 | |
| 7189 | →→𝜒𝜒→𝜒→→𝜑𝜓𝜒 | Modus ponens 7187, 7188 | |
| 7190 | →→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→𝜓⋀𝜓𝜒] into ax-2 | |
| 7191 | →→→𝜑𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒 | Modus ponens 6921, 7190 | |
| 7192 | →→→→𝜑𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 7193 | →𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒 | Modus ponens 7191, 7192 | |
| 7194 | →→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓𝜒→𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜓⋀𝜓𝜒] into ax-2 | |
| 7195 | →→𝜒→→𝜑𝜓𝜒→𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒 | Modus ponens 7193, 7194 | |
| 7196 | →→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜒→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 7197 | →𝜒→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒 | Modus ponens 6922, 7196 | |
| 7198 | →→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜓⋀𝜓𝜒] into ax-1 | |
| 7199 | →→→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 7200 | →𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒 | Modus ponens 7198, 7199 | |
| 7201 | →→𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓→𝜓⋀𝜓𝜒, 𝜒↗→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒] into ax-2 | |
| 7202 | →→𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒 | Modus ponens 7200, 7201 | |
| 7203 | →𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒 | Modus ponens 7164, 7202 | |
| 7204 | →→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→𝜓⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜑𝜓] into imim2 | |
| 7205 | →→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7206 | →𝜓→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7204, 7205 | |
| 7207 | →→𝜓→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→→𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7208 | →→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7206, 7207 | |
| 7209 | →→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 7210 | →𝜒→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7208, 7209 | |
| 7211 | →→𝜒→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7212 | →→𝜒→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7210, 7211 | |
| 7213 | →𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7197, 7212 | |
| 7214 | →→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜓→𝜓⋀𝜓𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7215 | →→→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 7216 | →𝜒→→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7214, 7215 | |
| 7217 | →→𝜒→→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7218 | →→𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7216, 7217 | |
| 7219 | →𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7213, 7218 | |
| 7220 | →→𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒, 𝜒↗→𝜓→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7221 | →→𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7219, 7220 | |
| 7222 | →→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7223 | →𝜓→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7004, 7222 | |
| 7224 | →→𝜓→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→𝜒𝜓→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→𝜒𝜓, 𝜒↗→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7225 | →→𝜓→𝜒𝜓→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7223, 7224 | |
| 7226 | →→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1 | |
| 7227 | →¬¬𝜒→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6991, 7226 | |
| 7228 | →→¬¬𝜒→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→→¬¬𝜒→𝜓𝜒→¬¬𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→𝜓→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7229 | →→¬¬𝜒→𝜓𝜒→¬¬𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7227, 7228 | |
| 7230 | →¬¬𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 5367, 7229 | |
| 7231 | →→¬¬𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→→¬¬𝜒𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗¬¬𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7232 | →→¬¬𝜒𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7230, 7231 | |
| 7233 | →→→¬¬𝜒𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→¬¬𝜒𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→¬¬𝜒𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7234 | →𝜓→→¬¬𝜒𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7232, 7233 | |
| 7235 | →→𝜓→→¬¬𝜒𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒𝜓, 𝜒↗→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7236 | →→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7234, 7235 | |
| 7237 | →𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 5375, 7236 | |
| 7238 | →→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1 | |
| 7239 | →¬¬𝜒→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7022, 7238 | |
| 7240 | →→¬¬𝜒→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗¬¬𝜒, 𝜓↗→→𝜑𝜓⋀𝜓𝜒, 𝜒↗¬¬→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7241 | →→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7239, 7240 | |
| 7242 | →→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→𝜓→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7243 | →𝜓→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7241, 7242 | |
| 7244 | →→𝜓→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→→𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7245 | →→𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7243, 7244 | |
| 7246 | →𝜓→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7237, 7245 | |
| 7247 | →→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-3 | |
| 7248 | →→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒→𝜓→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒 | Subs [𝜑↗→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒] into ax-1 | |
| 7249 | →𝜓→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒 | Modus ponens 7247, 7248 | |
| 7250 | →→𝜓→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒→→𝜓→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒 | Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒] into ax-2 | |
| 7251 | →→𝜓→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒 | Modus ponens 7249, 7250 | |
| 7252 | →𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒 | Modus ponens 7246, 7251 | |
| 7253 | →¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7254 | →→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7255 | →¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7253, 7254 | |
| 7256 | →→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→𝜓¬→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7257 | →→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7255, 7256 | |
| 7258 | →→𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒→→𝜓¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒 | Subs [𝜑↗𝜓, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗¬𝜒] into ax-2 | |
| 7259 | →→𝜓¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒 | Modus ponens 7252, 7258 | |
| 7260 | →→→𝜓¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→𝜓¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒 | Subs [𝜑↗→→𝜓¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7261 | →¬→→𝜑𝜓⋀𝜓𝜒→→𝜓¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒 | Modus ponens 7259, 7260 | |
| 7262 | →→¬→→𝜑𝜓⋀𝜓𝜒→→𝜓¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→𝜓¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→𝜓¬𝜒] into ax-2 | |
| 7263 | →→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒 | Modus ponens 7261, 7262 | |
| 7264 | →¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒 | Modus ponens 7253, 7263 | |
| 7265 | →→¬→𝜓¬𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒 | Subs [𝜑↗→¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7266 | →¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒 | Modus ponens 5416, 7265 | |
| 7267 | →¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒 | Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7268 | →→¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒 | Subs [𝜑↗→¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1 | |
| 7269 | →¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒 | Modus ponens 7267, 7268 | |
| 7270 | →→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒 | Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒] into ax-2 | |
| 7271 | →→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒 | Modus ponens 7269, 7270 | |
| 7272 | →¬¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒 | Modus ponens 5419, 7271 | |
| 7273 | →→¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗¬→𝜓¬𝜒] into ax-2 | |
| 7274 | →→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒 | Modus ponens 7266, 7273 | |
| 7275 | →→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒 | Subs [𝜑↗→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1 | |
| 7276 | →¬¬¬→𝜓¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒 | Modus ponens 7274, 7275 | |
| 7277 | →→¬¬¬→𝜓¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒 | Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒] into ax-2 | |
| 7278 | →→¬¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒 | Modus ponens 7276, 7277 | |
| 7279 | →¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1 | |
| 7280 | →→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7281 | →¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7279, 7280 | |
| 7282 | →→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7283 | →→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7281, 7282 | |
| 7284 | →→¬¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗¬→𝜓¬𝜒] into ax-2 | |
| 7285 | →→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Modus ponens 7272, 7284 | |
| 7286 | →→→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Subs [𝜑↗→→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7287 | →¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Modus ponens 7285, 7286 | |
| 7288 | →→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒] into ax-2 | |
| 7289 | →→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Modus ponens 7287, 7288 | |
| 7290 | →¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Modus ponens 7279, 7289 | |
| 7291 | →→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒 | Subs [𝜑↗→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7292 | →¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒 | Modus ponens 5444, 7291 | |
| 7293 | →→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜒↗→→𝜓¬𝜒¬¬→𝜓¬𝜒] into ax-2 | |
| 7294 | →→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒 | Modus ponens 7292, 7293 | |
| 7295 | →¬→→𝜑𝜓⋀𝜓𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒 | Modus ponens 7290, 7294 | |
| 7296 | →→¬→→𝜑𝜓⋀𝜓𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜓¬𝜒 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→𝜓¬𝜒, 𝜒↗¬¬→𝜓¬𝜒] into ax-2 | |
| 7297 | →→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜓¬𝜒 | Modus ponens 7295, 7296 | |
| 7298 | →¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜓¬𝜒 | Modus ponens 7264, 7297 | |
| 7299 | →→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒] into ax-3 | |
| 7300 | →→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒→⋀𝜓𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 7301 | →⋀𝜓𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 6844, 7300 | |
| 7302 | →→⋀𝜓𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒→→⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7303 | →→⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7301, 7302 | |
| 7304 | →→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 7305 | →→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 7306 | →→𝜑𝜓→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓 | Modus ponens 7304, 7305 | |
| 7307 | →→→𝜑𝜓→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→⋀𝜓𝜒→𝜑𝜓] into ax-2 | |
| 7308 | →→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓 | Modus ponens 7306, 7307 | |
| 7309 | →→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→⋀𝜓𝜒→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→𝜑𝜓, 𝜒↗⋀𝜓𝜒] into ax-2 | |
| 7310 | →→⋀𝜓𝜒→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒 | Modus ponens 6829, 7309 | |
| 7311 | →→→⋀𝜓𝜒→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→⋀𝜓𝜒→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒 | Subs [𝜑↗→→⋀𝜓𝜒→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 7312 | →→𝜑𝜓→→⋀𝜓𝜒→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒 | Modus ponens 7310, 7311 | |
| 7313 | →→→𝜑𝜓→→⋀𝜓𝜒→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓→→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜓𝜒→𝜑𝜓, 𝜒↗→⋀𝜓𝜒⋀𝜓𝜒] into ax-2 | |
| 7314 | →→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓→→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒 | Modus ponens 7312, 7313 | |
| 7315 | →→→𝜓→𝜒⋀𝜓𝜒→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→𝜒⋀𝜓𝜒→𝜑→𝜓→𝜒⋀𝜓𝜒 | Subs [𝜑↗→→𝜓→𝜒⋀𝜓𝜒→𝜑→𝜓→𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 7316 | →→𝜑𝜓→→𝜓→𝜒⋀𝜓𝜒→𝜑→𝜓→𝜒⋀𝜓𝜒 | Modus ponens 5591, 7315 | |
| 7317 | →→→𝜑𝜓→→𝜓→𝜒⋀𝜓𝜒→𝜑→𝜓→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜓→𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓→𝜒⋀𝜓𝜒, 𝜒↗→𝜑→𝜓→𝜒⋀𝜓𝜒] into ax-2 | |
| 7318 | →→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜓→𝜒⋀𝜓𝜒 | Modus ponens 7316, 7317 | |
| 7319 | →→𝜑𝜓→𝜑→𝜓→𝜒⋀𝜓𝜒 | Modus ponens 6893, 7318 | |
| 7320 | →→→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒 | Subs [𝜑↗→→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 7321 | →→𝜑𝜓→→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒 | Modus ponens 5593, 7320 | |
| 7322 | →→→𝜑𝜓→→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑→𝜓→𝜒⋀𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒] into ax-2 | |
| 7323 | →→→𝜑𝜓→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒 | Modus ponens 7321, 7322 | |
| 7324 | →→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒 | Modus ponens 7319, 7323 | |
| 7325 | →→→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑→𝜒⋀𝜓𝜒] into ax-2 | |
| 7326 | →→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒 | Modus ponens 7324, 7325 | |
| 7327 | →→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑→𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜑→𝜒⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 7328 | →→→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑→𝜒⋀𝜓𝜒 | Subs [𝜑↗→→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑→𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 7329 | →→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑→𝜒⋀𝜓𝜒 | Modus ponens 7327, 7328 | |
| 7330 | →→→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜑→𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑→𝜒⋀𝜓𝜒, 𝜒↗→𝜒→𝜑→𝜒⋀𝜓𝜒] into ax-2 | |
| 7331 | →→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜑→𝜒⋀𝜓𝜒 | Modus ponens 7329, 7330 | |
| 7332 | →→𝜑𝜓→𝜒→𝜑→𝜒⋀𝜓𝜒 | Modus ponens 5594, 7331 | |
| 7333 | →→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜒⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗𝜑] into imim2 | |
| 7334 | →→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 7335 | →𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Modus ponens 7333, 7334 | |
| 7336 | →→𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→→𝜒⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒] into ax-2 | |
| 7337 | →→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Modus ponens 7335, 7336 | |
| 7338 | →→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 7339 | →→𝜑𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Modus ponens 7337, 7338 | |
| 7340 | →→→𝜑𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒] into ax-2 | |
| 7341 | →→→𝜑𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Modus ponens 7339, 7340 | |
| 7342 | →→𝜑𝜓→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Modus ponens 6896, 7341 | |
| 7343 | →→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜑→𝜒⋀𝜓𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2 | |
| 7344 | →→→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗→→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 7345 | →→𝜑𝜓→→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒 | Modus ponens 7343, 7344 | |
| 7346 | →→→𝜑𝜓→→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒, 𝜒↗→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒] into ax-2 | |
| 7347 | →→→𝜑𝜓→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒 | Modus ponens 7345, 7346 | |
| 7348 | →→𝜑𝜓→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒 | Modus ponens 7342, 7347 | |
| 7349 | →→→𝜑𝜓→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜒→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→𝜑→𝜒⋀𝜓𝜒, 𝜒↗→𝜒→𝜑⋀𝜓𝜒] into ax-2 | |
| 7350 | →→→𝜑𝜓→𝜒→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜑⋀𝜓𝜒 | Modus ponens 7348, 7349 | |
| 7351 | →→𝜑𝜓→𝜒→𝜑⋀𝜓𝜒 | Modus ponens 7332, 7350 | |
| 7352 | →→→𝜑𝜓→𝜒→𝜑⋀𝜓𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2 | |
| 7353 | →→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Modus ponens 7351, 7352 | |
| 7354 | →→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 7355 | →𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Modus ponens 7353, 7354 | |
| 7356 | →→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜒→→𝜑𝜓𝜒→𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜑⋀𝜓𝜒] into ax-2 | |
| 7357 | →→𝜒→→𝜑𝜓𝜒→𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Modus ponens 7355, 7356 | |
| 7358 | →𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒 | Modus ponens 7185, 7357 | |
| 7359 | →𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒 | Subs [𝜓↗⋀𝜓𝜒] into pm2.27 | |
| 7360 | →→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜒→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 7361 | →𝜒→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒 | Modus ponens 7359, 7360 | |
| 7362 | →→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 7363 | →→→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 7364 | →𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒 | Modus ponens 7362, 7363 | |
| 7365 | →→𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜒↗→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒] into ax-2 | |
| 7366 | →→𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒 | Modus ponens 7364, 7365 | |
| 7367 | →𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒 | Modus ponens 7358, 7366 | |
| 7368 | →→→𝜑⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜑𝜓] into imim2 | |
| 7369 | →→→→𝜑⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜑→→→𝜑⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→→𝜑⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 7370 | →𝜑→→→𝜑⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7368, 7369 | |
| 7371 | →→𝜑→→→𝜑⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜓↗→→𝜑⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7372 | →→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7370, 7371 | |
| 7373 | →→→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 7374 | →𝜒→→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7372, 7373 | |
| 7375 | →→𝜒→→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7376 | →→𝜒→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7374, 7375 | |
| 7377 | →𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7361, 7376 | |
| 7378 | →→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜓↗→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7379 | →→→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 7380 | →𝜒→→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7378, 7379 | |
| 7381 | →→𝜒→→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7382 | →→𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7380, 7381 | |
| 7383 | →𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7377, 7382 | |
| 7384 | →→𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜒↗→𝜑→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7385 | →→𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7383, 7384 | |
| 7386 | →𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7367, 7385 | |
| 7387 | →→𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒→→𝜒𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗𝜑, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7388 | →→𝜒𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7386, 7387 | |
| 7389 | →→→𝜒𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜑→→𝜒𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜒𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 7390 | →𝜑→→𝜒𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7388, 7389 | |
| 7391 | →→𝜑→→𝜒𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→𝜒𝜑→𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜓↗→𝜒𝜑, 𝜒↗→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7392 | →→𝜑→𝜒𝜑→𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7390, 7391 | |
| 7393 | →𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 13, 7392 | |
| 7394 | →→𝜒→𝜑𝜒→¬¬𝜒→𝜒→𝜑𝜒 | Subs [𝜑↗→𝜒→𝜑𝜒, 𝜓↗¬¬𝜒] into ax-1 | |
| 7395 | →¬¬𝜒→𝜒→𝜑𝜒 | Modus ponens 1834, 7394 | |
| 7396 | →→¬¬𝜒→𝜒→𝜑𝜒→→¬¬𝜒𝜒→¬¬𝜒→𝜑𝜒 | Subs [𝜑↗¬¬𝜒, 𝜓↗𝜒, 𝜒↗→𝜑𝜒] into ax-2 | |
| 7397 | →→¬¬𝜒𝜒→¬¬𝜒→𝜑𝜒 | Modus ponens 7395, 7396 | |
| 7398 | →¬¬𝜒→𝜑𝜒 | Modus ponens 5153, 7397 | |
| 7399 | →→𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜓↗𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7400 | →→𝜑𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7393, 7399 | |
| 7401 | →→→𝜑𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒→→𝜑𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜑𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1 | |
| 7402 | →¬¬𝜒→→𝜑𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7400, 7401 | |
| 7403 | →→¬¬𝜒→→𝜑𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒→→¬¬𝜒→𝜑𝜒→¬¬𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7404 | →→¬¬𝜒→𝜑𝜒→¬¬𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7402, 7403 | |
| 7405 | →¬¬𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7398, 7404 | |
| 7406 | →𝜑→¬¬𝜒𝜑 | Subs [𝜓↗¬¬𝜒] into ax-1 | |
| 7407 | →→𝜑→¬¬𝜒𝜑→𝜑→𝜑→¬¬𝜒𝜑 | Subs [𝜑↗→𝜑→¬¬𝜒𝜑, 𝜓↗𝜑] into ax-1 | |
| 7408 | →𝜑→𝜑→¬¬𝜒𝜑 | Modus ponens 7406, 7407 | |
| 7409 | →→𝜑→𝜑→¬¬𝜒𝜑→→𝜑𝜑→𝜑→¬¬𝜒𝜑 | Subs [𝜓↗𝜑, 𝜒↗→¬¬𝜒𝜑] into ax-2 | |
| 7410 | →→𝜑𝜑→𝜑→¬¬𝜒𝜑 | Modus ponens 7408, 7409 | |
| 7411 | →→¬¬𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒→→¬¬𝜒𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗¬¬𝜒, 𝜓↗𝜑, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7412 | →→¬¬𝜒𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7405, 7411 | |
| 7413 | →→→¬¬𝜒𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→𝜑→→¬¬𝜒𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→¬¬𝜒𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 7414 | →𝜑→→¬¬𝜒𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7412, 7413 | |
| 7415 | →→𝜑→→¬¬𝜒𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→¬¬𝜒𝜑→𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜓↗→¬¬𝜒𝜑, 𝜒↗→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7416 | →→𝜑→¬¬𝜒𝜑→𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7414, 7415 | |
| 7417 | →𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7406, 7416 | |
| 7418 | →→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→𝜑→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 7419 | →𝜑→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7241, 7418 | |
| 7420 | →→𝜑→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→→𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→𝜑→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜓↗→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7421 | →→𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→𝜑→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7419, 7420 | |
| 7422 | →𝜑→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7417, 7421 | |
| 7423 | →→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒→𝜑→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒 | Subs [𝜑↗→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒, 𝜓↗𝜑] into ax-1 | |
| 7424 | →𝜑→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒 | Modus ponens 7247, 7423 | |
| 7425 | →→𝜑→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒→→𝜑→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→𝜑→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒 | Subs [𝜓↗→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒] into ax-2 | |
| 7426 | →→𝜑→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→𝜑→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒 | Modus ponens 7424, 7425 | |
| 7427 | →𝜑→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒 | Modus ponens 7422, 7426 | |
| 7428 | →¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 7429 | →→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7430 | →¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7428, 7429 | |
| 7431 | →→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→𝜑¬→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7432 | →→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7430, 7431 | |
| 7433 | →→𝜑→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒→→𝜑¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒 | Subs [𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗¬𝜒] into ax-2 | |
| 7434 | →→𝜑¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒 | Modus ponens 7427, 7433 | |
| 7435 | →→→𝜑¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→𝜑¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒 | Subs [𝜑↗→→𝜑¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7436 | →¬→→𝜑𝜓⋀𝜓𝜒→→𝜑¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒 | Modus ponens 7434, 7435 | |
| 7437 | →→¬→→𝜑𝜓⋀𝜓𝜒→→𝜑¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→𝜑¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→𝜑¬𝜒] into ax-2 | |
| 7438 | →→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒 | Modus ponens 7436, 7437 | |
| 7439 | →¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒 | Modus ponens 7428, 7438 | |
| 7440 | →¬→𝜑¬𝜒¬→𝜑¬𝜒 | Subs [𝜑↗¬→𝜑¬𝜒] into id | |
| 7441 | →→¬→𝜑¬𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜑¬𝜒¬→𝜑¬𝜒 | Subs [𝜑↗→¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7442 | →¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜑¬𝜒¬→𝜑¬𝜒 | Modus ponens 7440, 7441 | |
| 7443 | →¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒 | Subs [𝜑↗¬→𝜑¬𝜒] into notnotr | |
| 7444 | →¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒 | Subs [𝜑↗¬→𝜑¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7445 | →→¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒 | Subs [𝜑↗→¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒, 𝜓↗¬¬¬→𝜑¬𝜒] into ax-1 | |
| 7446 | →¬¬¬→𝜑¬𝜒→¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒 | Modus ponens 7444, 7445 | |
| 7447 | →→¬¬¬→𝜑¬𝜒→¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒 | Subs [𝜑↗¬¬¬→𝜑¬𝜒, 𝜓↗¬→𝜑¬𝜒, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒] into ax-2 | |
| 7448 | →→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒 | Modus ponens 7446, 7447 | |
| 7449 | →¬¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒 | Modus ponens 7443, 7448 | |
| 7450 | →→¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜑¬𝜒¬→𝜑¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→𝜑¬𝜒, 𝜒↗¬→𝜑¬𝜒] into ax-2 | |
| 7451 | →→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒 | Modus ponens 7442, 7450 | |
| 7452 | →→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒 | Subs [𝜑↗→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒, 𝜓↗¬¬¬→𝜑¬𝜒] into ax-1 | |
| 7453 | →¬¬¬→𝜑¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒 | Modus ponens 7451, 7452 | |
| 7454 | →→¬¬¬→𝜑¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→→¬¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒 | Subs [𝜑↗¬¬¬→𝜑¬𝜒, 𝜓↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒] into ax-2 | |
| 7455 | →→¬¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒 | Modus ponens 7453, 7454 | |
| 7456 | →¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬𝜒] into ax-1 | |
| 7457 | →→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7458 | →¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7456, 7457 | |
| 7459 | →→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7460 | →→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7458, 7459 | |
| 7461 | →→¬¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒 | Subs [𝜑↗¬¬¬→𝜑¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗¬→𝜑¬𝜒] into ax-2 | |
| 7462 | →→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒 | Modus ponens 7449, 7461 | |
| 7463 | →→→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒 | Subs [𝜑↗→→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7464 | →¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒 | Modus ponens 7462, 7463 | |
| 7465 | →→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒] into ax-2 | |
| 7466 | →→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒 | Modus ponens 7464, 7465 | |
| 7467 | →¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒 | Modus ponens 7456, 7466 | |
| 7468 | →→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒 | Subs [𝜑↗¬¬→𝜑¬𝜒, 𝜓↗→𝜑¬𝜒] into ax-3 | |
| 7469 | →→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒 | Subs [𝜑↗→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7470 | →¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒 | Modus ponens 7468, 7469 | |
| 7471 | →→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜒↗→→𝜑¬𝜒¬¬→𝜑¬𝜒] into ax-2 | |
| 7472 | →→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒 | Modus ponens 7470, 7471 | |
| 7473 | →¬→→𝜑𝜓⋀𝜓𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒 | Modus ponens 7467, 7472 | |
| 7474 | →→¬→→𝜑𝜓⋀𝜓𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜑¬𝜒 | Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→𝜑¬𝜒, 𝜒↗¬¬→𝜑¬𝜒] into ax-2 | |
| 7475 | →→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜑¬𝜒 | Modus ponens 7473, 7474 | |
| 7476 | →¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜑¬𝜒 | Modus ponens 7439, 7475 | |
| 7477 | →→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜑¬𝜒→¬→𝜑¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→𝜑¬𝜒] into ax-3 | |
| 7478 | →¬→𝜑¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7476, 7477 | |
| 7479 | →↔⋀𝜑𝜒¬→𝜑¬𝜒→⋀𝜑𝜒¬→𝜑¬𝜒 | Subs [𝜑↗⋀𝜑𝜒, 𝜓↗¬→𝜑¬𝜒] into biimp | |
| 7480 | →⋀𝜑𝜒¬→𝜑¬𝜒 | Modus ponens 6560, 7479 | |
| 7481 | →→¬→𝜑¬𝜒→→𝜑𝜓⋀𝜓𝜒→⋀𝜑𝜒→¬→𝜑¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→¬→𝜑¬𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗⋀𝜑𝜒] into ax-1 | |
| 7482 | →⋀𝜑𝜒→¬→𝜑¬𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7478, 7481 | |
| 7483 | →→⋀𝜑𝜒→¬→𝜑¬𝜒→→𝜑𝜓⋀𝜓𝜒→→⋀𝜑𝜒¬→𝜑¬𝜒→⋀𝜑𝜒→→𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑𝜒, 𝜓↗¬→𝜑¬𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7484 | →→⋀𝜑𝜒¬→𝜑¬𝜒→⋀𝜑𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7482, 7483 | |
| 7485 | →⋀𝜑𝜒→→𝜑𝜓⋀𝜓𝜒 | Modus ponens 7480, 7484 | |
| 7486 | →→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀𝜑𝜒] into ax-1 | |
| 7487 | →→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 7488 | →→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓 | Modus ponens 7486, 7487 | |
| 7489 | →→→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→⋀𝜑𝜒→𝜑𝜓] into ax-2 | |
| 7490 | →→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓 | Modus ponens 7488, 7489 | |
| 7491 | →→⋀𝜑𝜒→→𝜑𝜓⋀𝜓𝜒→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑𝜒, 𝜓↗→𝜑𝜓, 𝜒↗⋀𝜓𝜒] into ax-2 | |
| 7492 | →→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒 | Modus ponens 7485, 7491 | |
| 7493 | →→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒→→𝜑𝜓→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒 | Subs [𝜑↗→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 7494 | →→𝜑𝜓→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒 | Modus ponens 7492, 7493 | |
| 7495 | →→→𝜑𝜓→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒→→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜑𝜒→𝜑𝜓, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜒] into ax-2 | |
| 7496 | →→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒 | Modus ponens 7494, 7495 | |
| 7497 | →→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒 | Modus ponens 7486, 7496 | pm3.45 |
| 7498 | ↔→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓 | Subs [𝜑↗𝜒, 𝜓↗𝜑, 𝜒↗𝜓] into pm5.32 | |
| 7499 | →↔→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓→→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓 | Subs [𝜑↗→𝜒↔𝜑𝜓, 𝜓↗↔⋀𝜒𝜑⋀𝜒𝜓] into biimp | |
| 7500 | →→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓 | Modus ponens 7498, 7499 | |
| 7501 | →→→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓→↔𝜑𝜓→→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓 | Subs [𝜑↗→→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 7502 | →↔𝜑𝜓→→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓 | Modus ponens 7500, 7501 | |
| 7503 | →→↔𝜑𝜓→→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓→→↔𝜑𝜓→𝜒↔𝜑𝜓→↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜒↔𝜑𝜓, 𝜒↗↔⋀𝜒𝜑⋀𝜒𝜓] into ax-2 | |
| 7504 | →→↔𝜑𝜓→𝜒↔𝜑𝜓→↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓 | Modus ponens 7502, 7503 | |
| 7505 | →↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓 | Modus ponens 2521, 7504 | anbi2 |
| 7506 | ↔⋀𝜑𝜒⋀𝜒𝜑 | Subs [𝜓↗𝜒] into ancom | |
| 7507 | ↔⋀𝜓𝜒⋀𝜒𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜒] into ancom | |
| 7508 | →↔⋀𝜑𝜒⋀𝜒𝜑→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜑 | Subs [𝜑↗↔⋀𝜑𝜒⋀𝜒𝜑, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 7509 | →↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜑 | Modus ponens 7506, 7508 | |
| 7510 | ↔→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜑↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀𝜑𝜒, 𝜒↗⋀𝜒𝜑] into pm5.74 | |
| 7511 | →↔→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜑↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑→→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜑↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑 | Subs [𝜑↗→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜑, 𝜓↗↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑] into biimp | |
| 7512 | →→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜑↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑 | Modus ponens 7510, 7511 | |
| 7513 | ↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑 | Modus ponens 7509, 7512 | |
| 7514 | ↔→↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀𝜒𝜑, 𝜒↗⋀𝜒𝜓] into pm5.74 | |
| 7515 | →↔→↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓 | Subs [𝜑↗→↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓, 𝜓↗↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓] into biimp | |
| 7516 | →→↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓 | Modus ponens 7514, 7515 | |
| 7517 | ↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓 | Modus ponens anbi2, 7516 | |
| 7518 | →↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓 | Subs [𝜑↗→↔𝜑𝜓⋀𝜒𝜑, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓] into biimp | |
| 7519 | →→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓 | Modus ponens 7517, 7518 | |
| 7520 | →↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑 | Subs [𝜑↗→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜑] into biimp | |
| 7521 | →→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑 | Modus ponens 7513, 7520 | |
| 7522 | →→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓 | Subs [𝜑↗→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓, 𝜓↗→↔𝜑𝜓⋀𝜑𝜒] into ax-1 | |
| 7523 | →→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓 | Modus ponens 7519, 7522 | |
| 7524 | →→→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓→→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓 | Subs [𝜑↗→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜑, 𝜒↗→↔𝜑𝜓⋀𝜒𝜓] into ax-2 | |
| 7525 | →→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓 | Modus ponens 7523, 7524 | |
| 7526 | →→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓 | Modus ponens 7521, 7525 | |
| 7527 | →↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜒𝜑 | Subs [𝜑↗→↔𝜑𝜓⋀𝜒𝜑, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓] into bicom1 | |
| 7528 | ↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜒𝜑 | Modus ponens 7517, 7527 | |
| 7529 | →↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜒𝜑→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜒𝜑 | Subs [𝜑↗→↔𝜑𝜓⋀𝜒𝜓, 𝜓↗→↔𝜑𝜓⋀𝜒𝜑] into biimp | |
| 7530 | →→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜒𝜑 | Modus ponens 7528, 7529 | |
| 7531 | →↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜑] into bicom1 | |
| 7532 | ↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒 | Modus ponens 7513, 7531 | |
| 7533 | →↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗→↔𝜑𝜓⋀𝜒𝜑, 𝜓↗→↔𝜑𝜓⋀𝜑𝜒] into biimp | |
| 7534 | →→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒 | Modus ponens 7532, 7533 | |
| 7535 | →→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓] into ax-1 | |
| 7536 | →→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒 | Modus ponens 7534, 7535 | |
| 7537 | →→→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒→→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜒𝜑→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗→↔𝜑𝜓⋀𝜒𝜓, 𝜓↗→↔𝜑𝜓⋀𝜒𝜑, 𝜒↗→↔𝜑𝜓⋀𝜑𝜒] into ax-2 | |
| 7538 | →→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜒𝜑→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒 | Modus ponens 7536, 7537 | |
| 7539 | →→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒 | Modus ponens 7530, 7538 | |
| 7540 | →→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓 | Subs [𝜑↗→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓] into impbi | |
| 7541 | →→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓 | Modus ponens 7526, 7540 | |
| 7542 | ↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓 | Modus ponens 7539, 7541 | |
| 7543 | ↔→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀𝜑𝜒, 𝜒↗⋀𝜒𝜓] into pm5.74 | |
| 7544 | →↔→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓↔↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓 | Subs [𝜑↗→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓, 𝜓↗↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓] into bicom1 | |
| 7545 | ↔↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓 | Modus ponens 7543, 7544 | |
| 7546 | →↔↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓→↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓 | Subs [𝜑↗↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓, 𝜓↗→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓] into biimp | |
| 7547 | →↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓 | Modus ponens 7545, 7546 | |
| 7548 | →↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓 | Modus ponens 7542, 7547 | |
| 7549 | →↔⋀𝜓𝜒⋀𝜒𝜓↔⋀𝜒𝜓⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗⋀𝜒𝜓] into bicom1 | |
| 7550 | ↔⋀𝜒𝜓⋀𝜓𝜒 | Modus ponens 7507, 7549 | |
| 7551 | →↔⋀𝜒𝜓⋀𝜓𝜒→↔𝜑𝜓↔⋀𝜒𝜓⋀𝜓𝜒 | Subs [𝜑↗↔⋀𝜒𝜓⋀𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 7552 | →↔𝜑𝜓↔⋀𝜒𝜓⋀𝜓𝜒 | Modus ponens 7550, 7551 | |
| 7553 | →↔→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓 | Subs [𝜑↗→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓, 𝜓↗↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓] into biimp | |
| 7554 | →→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓 | Modus ponens 7543, 7553 | |
| 7555 | ↔→↔𝜑𝜓↔⋀𝜒𝜓⋀𝜓𝜒↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀𝜒𝜓, 𝜒↗⋀𝜓𝜒] into pm5.74 | |
| 7556 | →↔→↔𝜑𝜓↔⋀𝜒𝜓⋀𝜓𝜒↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒→→↔𝜑𝜓↔⋀𝜒𝜓⋀𝜓𝜒↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→↔𝜑𝜓↔⋀𝜒𝜓⋀𝜓𝜒, 𝜓↗↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒] into biimp | |
| 7557 | →→↔𝜑𝜓↔⋀𝜒𝜓⋀𝜓𝜒↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒 | Modus ponens 7555, 7556 | |
| 7558 | ↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒 | Modus ponens 7552, 7557 | |
| 7559 | →↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→↔𝜑𝜓⋀𝜒𝜓, 𝜓↗→↔𝜑𝜓⋀𝜓𝜒] into biimp | |
| 7560 | →→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒 | Modus ponens 7558, 7559 | |
| 7561 | →↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓 | Subs [𝜑↗→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓] into biimp | |
| 7562 | →→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒→→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒, 𝜓↗→↔𝜑𝜓⋀𝜑𝜒] into ax-1 | |
| 7563 | →→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒 | Modus ponens 7560, 7562 | |
| 7564 | →→→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒→→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓, 𝜒↗→↔𝜑𝜓⋀𝜓𝜒] into ax-2 | |
| 7565 | →→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒 | Modus ponens 7563, 7564 | |
| 7566 | →→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒 | Modus ponens 7526, 7565 | |
| 7567 | →↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒↔→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜒𝜓 | Subs [𝜑↗→↔𝜑𝜓⋀𝜒𝜓, 𝜓↗→↔𝜑𝜓⋀𝜓𝜒] into bicom1 | |
| 7568 | ↔→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜒𝜓 | Modus ponens 7558, 7567 | |
| 7569 | →↔→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜒𝜓 | Subs [𝜑↗→↔𝜑𝜓⋀𝜓𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓] into biimp | |
| 7570 | →→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜒𝜓 | Modus ponens 7568, 7569 | |
| 7571 | →↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓] into bicom1 | |
| 7572 | ↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒 | Modus ponens 7542, 7571 | |
| 7573 | →↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗→↔𝜑𝜓⋀𝜒𝜓, 𝜓↗→↔𝜑𝜓⋀𝜑𝜒] into biimp | |
| 7574 | →→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜓𝜒→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜓𝜒] into ax-1 | |
| 7575 | →→↔𝜑𝜓⋀𝜓𝜒→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒 | Modus ponens 7539, 7574 | |
| 7576 | →→→↔𝜑𝜓⋀𝜓𝜒→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒→→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗→↔𝜑𝜓⋀𝜓𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓, 𝜒↗→↔𝜑𝜓⋀𝜑𝜒] into ax-2 | |
| 7577 | →→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜑𝜒 | Modus ponens 7575, 7576 | |
| 7578 | →→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜑𝜒 | Modus ponens 7570, 7577 | |
| 7579 | →→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒→→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜑𝜒↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜓𝜒] into impbi | |
| 7580 | →→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜑𝜒↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒 | Modus ponens 7566, 7579 | |
| 7581 | ↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒 | Modus ponens 7578, 7580 | |
| 7582 | ↔→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀𝜑𝜒, 𝜒↗⋀𝜓𝜒] into pm5.74 | |
| 7583 | →↔→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒↔↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒 | Subs [𝜑↗→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒, 𝜓↗↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒] into bicom1 | |
| 7584 | ↔↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒 | Modus ponens 7582, 7583 | |
| 7585 | →↔↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒→↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒 | Subs [𝜑↗↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒, 𝜓↗→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒] into biimp | |
| 7586 | →↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒 | Modus ponens 7584, 7585 | |
| 7587 | →↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒 | Modus ponens 7581, 7586 | anbi1 |
| 7588 | ↔⋀𝜒𝜃⋀𝜃𝜒 | Subs [𝜑↗𝜒, 𝜓↗𝜃] into ancom | |
| 7589 | →↔⋀𝜒𝜃⋀𝜃𝜒→⋀𝜑𝜓↔⋀𝜒𝜃⋀𝜃𝜒 | Subs [𝜑↗↔⋀𝜒𝜃⋀𝜃𝜒, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 7590 | →⋀𝜑𝜓↔⋀𝜒𝜃⋀𝜃𝜒 | Modus ponens 7588, 7589 | |
| 7591 | ↔→⋀𝜑𝜓↔⋀𝜒𝜃⋀𝜃𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜒𝜃, 𝜒↗⋀𝜃𝜒] into pm5.32 | |
| 7592 | →↔→⋀𝜑𝜓↔⋀𝜒𝜃⋀𝜃𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒→→⋀𝜑𝜓↔⋀𝜒𝜃⋀𝜃𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒 | Subs [𝜑↗→⋀𝜑𝜓↔⋀𝜒𝜃⋀𝜃𝜒, 𝜓↗↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒] into biimp | |
| 7593 | →→⋀𝜑𝜓↔⋀𝜒𝜃⋀𝜃𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒 | Modus ponens 7591, 7592 | |
| 7594 | ↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒 | Modus ponens 7590, 7593 | |
| 7595 | →↔⋀𝜑𝜓⋀𝜓𝜑→⋀𝜃𝜒↔⋀𝜑𝜓⋀𝜓𝜑 | Subs [𝜑↗↔⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗⋀𝜃𝜒] into ax-1 | |
| 7596 | →⋀𝜃𝜒↔⋀𝜑𝜓⋀𝜓𝜑 | Modus ponens ancom, 7595 | |
| 7597 | ↔→⋀𝜃𝜒↔⋀𝜑𝜓⋀𝜓𝜑↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑 | Subs [𝜑↗⋀𝜃𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜓𝜑] into pm5.32 | |
| 7598 | →↔→⋀𝜃𝜒↔⋀𝜑𝜓⋀𝜓𝜑↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑→→⋀𝜃𝜒↔⋀𝜑𝜓⋀𝜓𝜑↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑 | Subs [𝜑↗→⋀𝜃𝜒↔⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑] into biimp | |
| 7599 | →→⋀𝜃𝜒↔⋀𝜑𝜓⋀𝜓𝜑↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑 | Modus ponens 7597, 7598 | |
| 7600 | ↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑 | Modus ponens 7596, 7599 | |
| 7601 | ↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜃𝜒] into ancom | |
| 7602 | ↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜓𝜑 | Subs [𝜑↗⋀𝜓𝜑, 𝜓↗⋀𝜃𝜒] into ancom | |
| 7603 | →↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜓𝜑↔⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒 | Subs [𝜑↗⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜓𝜑] into bicom1 | |
| 7604 | ↔⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒 | Modus ponens 7602, 7603 | |
| 7605 | →↔⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒 | Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into biimp | |
| 7606 | →⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒 | Modus ponens 7604, 7605 | |
| 7607 | →↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑 | Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜃𝜒⋀𝜓𝜑] into biimp | |
| 7608 | →⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑 | Modus ponens 7600, 7607 | |
| 7609 | →→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒 | Subs [𝜑↗→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜑𝜓] into ax-1 | |
| 7610 | →⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒 | Modus ponens 7606, 7609 | |
| 7611 | →→⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒→→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒 | Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜃𝜒⋀𝜓𝜑, 𝜒↗⋀⋀𝜓𝜑⋀𝜃𝜒] into ax-2 | |
| 7612 | →→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒 | Modus ponens 7610, 7611 | |
| 7613 | →⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒 | Modus ponens 7608, 7612 | |
| 7614 | →↔⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜓𝜑 | Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into bicom1 | |
| 7615 | →↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜓𝜑 | Subs [𝜑↗⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜓𝜑] into biimp | |
| 7616 | →⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜓𝜑 | Modus ponens 7602, 7615 | |
| 7617 | →↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑↔⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓 | Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜃𝜒⋀𝜓𝜑] into bicom1 | |
| 7618 | ↔⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓 | Modus ponens 7600, 7617 | |
| 7619 | →↔⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓 | Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜃𝜒⋀𝜑𝜓] into biimp | |
| 7620 | →⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓 | Modus ponens 7618, 7619 | |
| 7621 | →→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓 | Subs [𝜑↗→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into ax-1 | |
| 7622 | →⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓 | Modus ponens 7620, 7621 | |
| 7623 | →→⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓 | Subs [𝜑↗⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜓𝜑, 𝜒↗⋀⋀𝜃𝜒⋀𝜑𝜓] into ax-2 | |
| 7624 | →→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓 | Modus ponens 7622, 7623 | |
| 7625 | →⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓 | Modus ponens 7616, 7624 | |
| 7626 | →→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒 | Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into impbi | |
| 7627 | →→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒 | Modus ponens 7613, 7626 | |
| 7628 | ↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒 | Modus ponens 7625, 7627 | |
| 7629 | →↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒 | Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into biimp | |
| 7630 | →↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜑𝜓] into biimp | |
| 7631 | →⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓 | Modus ponens 7601, 7630 | |
| 7632 | →→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒 | Subs [𝜑↗→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜃𝜒] into ax-1 | |
| 7633 | →⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒 | Modus ponens 7613, 7632 | |
| 7634 | →→⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒→→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜒↗⋀⋀𝜓𝜑⋀𝜃𝜒] into ax-2 | |
| 7635 | →→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒 | Modus ponens 7633, 7634 | |
| 7636 | →⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒 | Modus ponens 7631, 7635 | |
| 7637 | →↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓 | Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into bicom1 | |
| 7638 | ↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓 | Modus ponens 7628, 7637 | |
| 7639 | →↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓 | Subs [𝜑↗⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜑𝜓] into biimp | |
| 7640 | →↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜑𝜓] into bicom1 | |
| 7641 | ↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒 | Modus ponens 7601, 7640 | |
| 7642 | →↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒 | Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓⋀𝜃𝜒] into biimp | |
| 7643 | →⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒 | Modus ponens 7641, 7642 | |
| 7644 | →→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒 | Subs [𝜑↗→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into ax-1 | |
| 7645 | →⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒 | Modus ponens 7643, 7644 | |
| 7646 | →→⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒 | Subs [𝜑↗⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜒↗⋀⋀𝜑𝜓⋀𝜃𝜒] into ax-2 | |
| 7647 | →→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒 | Modus ponens 7645, 7646 | |
| 7648 | →⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒 | Modus ponens 7625, 7647 | |
| 7649 | →→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into impbi | |
| 7650 | →→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒 | Modus ponens 7636, 7649 | |
| 7651 | ↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒 | Modus ponens 7648, 7650 | |
| 7652 | →↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into biimp | |
| 7653 | →↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜓⋀𝜃𝜒] into biimp | |
| 7654 | →⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒 | Modus ponens 7594, 7653 | |
| 7655 | →→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒 | Subs [𝜑↗→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜃] into ax-1 | |
| 7656 | →⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒 | Modus ponens 7636, 7655 | |
| 7657 | →→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜓𝜑⋀𝜃𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜒↗⋀⋀𝜓𝜑⋀𝜃𝜒] into ax-2 | |
| 7658 | →→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜓𝜑⋀𝜃𝜒 | Modus ponens 7656, 7657 | |
| 7659 | →⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜓𝜑⋀𝜃𝜒 | Modus ponens 7654, 7658 | |
| 7660 | →↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into bicom1 | |
| 7661 | ↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒 | Modus ponens 7651, 7660 | |
| 7662 | →↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒 | Subs [𝜑↗⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜃𝜒] into biimp | |
| 7663 | →↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜓⋀𝜃𝜒] into bicom1 | |
| 7664 | ↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃 | Modus ponens 7594, 7663 | |
| 7665 | →↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜃] into biimp | |
| 7666 | →⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃 | Modus ponens 7664, 7665 | |
| 7667 | →→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃 | Subs [𝜑↗→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into ax-1 | |
| 7668 | →⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃 | Modus ponens 7666, 7667 | |
| 7669 | →→⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜒↗⋀⋀𝜑𝜓⋀𝜒𝜃] into ax-2 | |
| 7670 | →→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃 | Modus ponens 7668, 7669 | |
| 7671 | →⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃 | Modus ponens 7648, 7670 | |
| 7672 | →→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜓𝜑⋀𝜃𝜒→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜓𝜑⋀𝜃𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into impbi | |
| 7673 | →→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜓𝜑⋀𝜃𝜒 | Modus ponens 7659, 7672 | |
| 7674 | ↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜓𝜑⋀𝜃𝜒 | Modus ponens 7671, 7673 | an2anr |
| 7675 | →⋀↔𝜑𝜒↔𝜓𝜃↔𝜑𝜒 | Subs [𝜑↗↔𝜑𝜒, 𝜓↗↔𝜓𝜃] into simpl | |
| 7676 | →⋀↔𝜑𝜒↔𝜓𝜃↔𝜓𝜃 | Subs [𝜑↗↔𝜑𝜒, 𝜓↗↔𝜓𝜃] into simpr | |
| 7677 | →↔𝜑𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗↔𝜑𝜒] into ax-1 | |
| 7678 | →→↔𝜑𝜒→𝜓↔𝜑𝜒→⋀↔𝜑𝜒↔𝜓𝜃→↔𝜑𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗→↔𝜑𝜒→𝜓↔𝜑𝜒, 𝜓↗⋀↔𝜑𝜒↔𝜓𝜃] into ax-1 | |
| 7679 | →⋀↔𝜑𝜒↔𝜓𝜃→↔𝜑𝜒→𝜓↔𝜑𝜒 | Modus ponens 7677, 7678 | |
| 7680 | →→⋀↔𝜑𝜒↔𝜓𝜃→↔𝜑𝜒→𝜓↔𝜑𝜒→→⋀↔𝜑𝜒↔𝜓𝜃↔𝜑𝜒→⋀↔𝜑𝜒↔𝜓𝜃→𝜓↔𝜑𝜒 | Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗↔𝜑𝜒, 𝜒↗→𝜓↔𝜑𝜒] into ax-2 | |
| 7681 | →→⋀↔𝜑𝜒↔𝜓𝜃↔𝜑𝜒→⋀↔𝜑𝜒↔𝜓𝜃→𝜓↔𝜑𝜒 | Modus ponens 7679, 7680 | |
| 7682 | →⋀↔𝜑𝜒↔𝜓𝜃→𝜓↔𝜑𝜒 | Modus ponens 7675, 7681 | |
| 7683 | ↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗𝜑] into pm5.32 | |
| 7684 | →↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜓↔𝜑𝜒, 𝜓↗↔⋀𝜓𝜑⋀𝜓𝜒] into biimp | |
| 7685 | →→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 7683, 7684 | |
| 7686 | →→→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃→→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗→→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗⋀↔𝜑𝜒↔𝜓𝜃] into ax-1 | |
| 7687 | →⋀↔𝜑𝜒↔𝜓𝜃→→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 7685, 7686 | |
| 7688 | →→⋀↔𝜑𝜒↔𝜓𝜃→→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃→𝜓↔𝜑𝜒→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗→𝜓↔𝜑𝜒, 𝜒↗↔⋀𝜓𝜑⋀𝜓𝜒] into ax-2 | |
| 7689 | →→⋀↔𝜑𝜒↔𝜓𝜃→𝜓↔𝜑𝜒→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 7687, 7688 | |
| 7690 | →⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 7682, 7689 | |
| 7691 | →↔⋀𝜑𝜓⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜑 | Subs [𝜑↗↔⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗⋀↔𝜑𝜒↔𝜓𝜃] into ax-1 | |
| 7692 | →⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜑 | Modus ponens ancom, 7691 | |
| 7693 | ↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜑↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑 | Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜓𝜑] into pm5.74 | |
| 7694 | →↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜑↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜑↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑] into biimp | |
| 7695 | →→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜑↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑 | Modus ponens 7693, 7694 | |
| 7696 | ↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑 | Modus ponens 7692, 7695 | |
| 7697 | ↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜑⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒 | Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗⋀𝜓𝜑, 𝜒↗⋀𝜓𝜒] into pm5.74 | |
| 7698 | →↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜑⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜑⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into biimp | |
| 7699 | →→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜑⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒 | Modus ponens 7697, 7698 | |
| 7700 | ↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒 | Modus ponens 7690, 7699 | |
| 7701 | →↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into biimp | |
| 7702 | →→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒 | Modus ponens 7700, 7701 | |
| 7703 | →↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑] into biimp | |
| 7704 | →→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑 | Modus ponens 7696, 7703 | |
| 7705 | →→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒 | Subs [𝜑↗→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into ax-1 | |
| 7706 | →→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒 | Modus ponens 7702, 7705 | |
| 7707 | →→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑, 𝜒↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into ax-2 | |
| 7708 | →→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒 | Modus ponens 7706, 7707 | |
| 7709 | →→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒 | Modus ponens 7704, 7708 | |
| 7710 | →↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into bicom1 | |
| 7711 | ↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑 | Modus ponens 7700, 7710 | |
| 7712 | →↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑] into biimp | |
| 7713 | →→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑 | Modus ponens 7711, 7712 | |
| 7714 | →↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑] into bicom1 | |
| 7715 | ↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Modus ponens 7696, 7714 | |
| 7716 | →↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into biimp | |
| 7717 | →→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Modus ponens 7715, 7716 | |
| 7718 | →→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Subs [𝜑↗→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into ax-1 | |
| 7719 | →→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Modus ponens 7717, 7718 | |
| 7720 | →→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑, 𝜒↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into ax-2 | |
| 7721 | →→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Modus ponens 7719, 7720 | |
| 7722 | →→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Modus ponens 7713, 7721 | |
| 7723 | →→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into impbi | |
| 7724 | →→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒 | Modus ponens 7709, 7723 | |
| 7725 | ↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒 | Modus ponens 7722, 7724 | |
| 7726 | ↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒 | Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜓𝜒] into pm5.74 | |
| 7727 | →↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into bicom1 | |
| 7728 | ↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒 | Modus ponens 7726, 7727 | |
| 7729 | →↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒 | Subs [𝜑↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒] into biimp | |
| 7730 | →↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒 | Modus ponens 7728, 7729 | |
| 7731 | →⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒 | Modus ponens 7725, 7730 | |
| 7732 | →↔⋀𝜒𝜓⋀𝜓𝜒↔⋀𝜓𝜒⋀𝜒𝜓 | Subs [𝜑↗⋀𝜒𝜓, 𝜓↗⋀𝜓𝜒] into bicom1 | |
| 7733 | →↔⋀𝜓𝜒⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜒⋀𝜒𝜓 | Subs [𝜑↗↔⋀𝜓𝜒⋀𝜒𝜓, 𝜓↗⋀↔𝜑𝜒↔𝜓𝜃] into ax-1 | |
| 7734 | →⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜒⋀𝜒𝜓 | Modus ponens 7507, 7733 | |
| 7735 | →↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into biimp | |
| 7736 | →→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒 | Modus ponens 7726, 7735 | |
| 7737 | ↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜒⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓 | Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗⋀𝜓𝜒, 𝜒↗⋀𝜒𝜓] into pm5.74 | |
| 7738 | →↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜒⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜒⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜒⋀𝜒𝜓, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into biimp | |
| 7739 | →→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜒⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓 | Modus ponens 7737, 7738 | |
| 7740 | ↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓 | Modus ponens 7734, 7739 | |
| 7741 | →↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into biimp | |
| 7742 | →→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓 | Modus ponens 7740, 7741 | |
| 7743 | →↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into biimp | |
| 7744 | →→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓 | Subs [𝜑↗→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into ax-1 | |
| 7745 | →→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓 | Modus ponens 7742, 7744 | |
| 7746 | →→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜒↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into ax-2 | |
| 7747 | →→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓 | Modus ponens 7745, 7746 | |
| 7748 | →→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓 | Modus ponens 7709, 7747 | |
| 7749 | →↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into bicom1 | |
| 7750 | ↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒 | Modus ponens 7740, 7749 | |
| 7751 | →↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into biimp | |
| 7752 | →→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒 | Modus ponens 7750, 7751 | |
| 7753 | →↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into bicom1 | |
| 7754 | ↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Modus ponens 7725, 7753 | |
| 7755 | →↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into biimp | |
| 7756 | →→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Subs [𝜑↗→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into ax-1 | |
| 7757 | →→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Modus ponens 7722, 7756 | |
| 7758 | →→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜒↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into ax-2 | |
| 7759 | →→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Modus ponens 7757, 7758 | |
| 7760 | →→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Modus ponens 7752, 7759 | |
| 7761 | →→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into impbi | |
| 7762 | →→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓 | Modus ponens 7748, 7761 | |
| 7763 | ↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓 | Modus ponens 7760, 7762 | |
| 7764 | ↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓 | Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜒𝜓] into pm5.74 | |
| 7765 | →↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into bicom1 | |
| 7766 | ↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓 | Modus ponens 7764, 7765 | |
| 7767 | →↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓 | Subs [𝜑↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓] into biimp | |
| 7768 | →↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓 | Modus ponens 7766, 7767 | |
| 7769 | →⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓 | Modus ponens 7763, 7768 | |
| 7770 | →↔𝜓𝜃→𝜒↔𝜓𝜃 | Subs [𝜑↗↔𝜓𝜃, 𝜓↗𝜒] into ax-1 | |
| 7771 | →→↔𝜓𝜃→𝜒↔𝜓𝜃→⋀↔𝜑𝜒↔𝜓𝜃→↔𝜓𝜃→𝜒↔𝜓𝜃 | Subs [𝜑↗→↔𝜓𝜃→𝜒↔𝜓𝜃, 𝜓↗⋀↔𝜑𝜒↔𝜓𝜃] into ax-1 | |
| 7772 | →⋀↔𝜑𝜒↔𝜓𝜃→↔𝜓𝜃→𝜒↔𝜓𝜃 | Modus ponens 7770, 7771 | |
| 7773 | →→⋀↔𝜑𝜒↔𝜓𝜃→↔𝜓𝜃→𝜒↔𝜓𝜃→→⋀↔𝜑𝜒↔𝜓𝜃↔𝜓𝜃→⋀↔𝜑𝜒↔𝜓𝜃→𝜒↔𝜓𝜃 | Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗↔𝜓𝜃, 𝜒↗→𝜒↔𝜓𝜃] into ax-2 | |
| 7774 | →→⋀↔𝜑𝜒↔𝜓𝜃↔𝜓𝜃→⋀↔𝜑𝜒↔𝜓𝜃→𝜒↔𝜓𝜃 | Modus ponens 7772, 7773 | |
| 7775 | →⋀↔𝜑𝜒↔𝜓𝜃→𝜒↔𝜓𝜃 | Modus ponens 7676, 7774 | |
| 7776 | ↔→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃 | Subs [𝜑↗𝜒, 𝜒↗𝜃] into pm5.32 | |
| 7777 | →↔→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃→→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃 | Subs [𝜑↗→𝜒↔𝜓𝜃, 𝜓↗↔⋀𝜒𝜓⋀𝜒𝜃] into biimp | |
| 7778 | →→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃 | Modus ponens 7776, 7777 | |
| 7779 | →→→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃→→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃 | Subs [𝜑↗→→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃, 𝜓↗⋀↔𝜑𝜒↔𝜓𝜃] into ax-1 | |
| 7780 | →⋀↔𝜑𝜒↔𝜓𝜃→→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃 | Modus ponens 7778, 7779 | |
| 7781 | →→⋀↔𝜑𝜒↔𝜓𝜃→→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃→→⋀↔𝜑𝜒↔𝜓𝜃→𝜒↔𝜓𝜃→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗→𝜒↔𝜓𝜃, 𝜒↗↔⋀𝜒𝜓⋀𝜒𝜃] into ax-2 | |
| 7782 | →→⋀↔𝜑𝜒↔𝜓𝜃→𝜒↔𝜓𝜃→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃 | Modus ponens 7780, 7781 | |
| 7783 | →⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃 | Modus ponens 7775, 7782 | |
| 7784 | →↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into biimp | |
| 7785 | →→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓 | Modus ponens 7764, 7784 | |
| 7786 | ↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃 | Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗⋀𝜒𝜓, 𝜒↗⋀𝜒𝜃] into pm5.74 | |
| 7787 | →↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃] into biimp | |
| 7788 | →→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃 | Modus ponens 7786, 7787 | |
| 7789 | ↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃 | Modus ponens 7783, 7788 | |
| 7790 | →↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃] into biimp | |
| 7791 | →→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃 | Modus ponens 7789, 7790 | |
| 7792 | →↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into biimp | |
| 7793 | →→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃 | Subs [𝜑↗→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into ax-1 | |
| 7794 | →→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃 | Modus ponens 7791, 7793 | |
| 7795 | →→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜒↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃] into ax-2 | |
| 7796 | →→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃 | Modus ponens 7794, 7795 | |
| 7797 | →→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃 | Modus ponens 7748, 7796 | |
| 7798 | →↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃] into bicom1 | |
| 7799 | ↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓 | Modus ponens 7789, 7798 | |
| 7800 | →↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into biimp | |
| 7801 | →→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓 | Modus ponens 7799, 7800 | |
| 7802 | →↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into bicom1 | |
| 7803 | ↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Modus ponens 7763, 7802 | |
| 7804 | →↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into biimp | |
| 7805 | →→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Subs [𝜑↗→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃] into ax-1 | |
| 7806 | →→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Modus ponens 7760, 7805 | |
| 7807 | →→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜒↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into ax-2 | |
| 7808 | →→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Modus ponens 7806, 7807 | |
| 7809 | →→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓 | Modus ponens 7801, 7808 | |
| 7810 | →→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃] into impbi | |
| 7811 | →→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃 | Modus ponens 7797, 7810 | |
| 7812 | ↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃 | Modus ponens 7809, 7811 | |
| 7813 | ↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃 | Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜒𝜃] into pm5.74 | |
| 7814 | →↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃 | Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃] into bicom1 | |
| 7815 | ↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃 | Modus ponens 7813, 7814 | |
| 7816 | →↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃 | Subs [𝜑↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃] into biimp | |
| 7817 | →↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃 | Modus ponens 7815, 7816 | |
| 7818 | →⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃 | Modus ponens 7812, 7817 | pm4.38 |
| 7819 | ↔⋀𝜑𝜒⋀𝜑𝜒 | Subs [𝜑↗⋀𝜑𝜒] into biid | |
| 7820 | →↔⋀𝜑𝜒⋀𝜑𝜒→𝜓↔⋀𝜑𝜒⋀𝜑𝜒 | Subs [𝜑↗↔⋀𝜑𝜒⋀𝜑𝜒] into ax-1 | |
| 7821 | →𝜓↔⋀𝜑𝜒⋀𝜑𝜒 | Modus ponens 7819, 7820 | |
| 7822 | ↔→𝜓↔⋀𝜑𝜒⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒 | Subs [𝜑↗𝜓, 𝜓↗⋀𝜑𝜒, 𝜒↗⋀𝜑𝜒] into pm5.32 | |
| 7823 | →↔→𝜓↔⋀𝜑𝜒⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒→→𝜓↔⋀𝜑𝜒⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒 | Subs [𝜑↗→𝜓↔⋀𝜑𝜒⋀𝜑𝜒, 𝜓↗↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒] into biimp | |
| 7824 | →→𝜓↔⋀𝜑𝜒⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒 | Modus ponens 7822, 7823 | |
| 7825 | ↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒 | Modus ponens 7821, 7824 | |
| 7826 | ↔⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒 | Subs [𝜑↗𝜓, 𝜓↗𝜑] into anass | |
| 7827 | →↔⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒 | Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into bicom1 | |
| 7828 | ↔⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒 | Modus ponens 7826, 7827 | |
| 7829 | →↔⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒 | Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒] into biimp | |
| 7830 | →⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒 | Modus ponens 7828, 7829 | |
| 7831 | →↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒 | Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into biimp | |
| 7832 | →⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒 | Modus ponens 7825, 7831 | |
| 7833 | →→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒→⋀𝜓⋀𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒 | Subs [𝜑↗→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into ax-1 | |
| 7834 | →⋀𝜓⋀𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒 | Modus ponens 7830, 7833 | |
| 7835 | →→⋀𝜓⋀𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒→→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒 | Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒, 𝜒↗⋀⋀𝜓𝜑𝜒] into ax-2 | |
| 7836 | →→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒 | Modus ponens 7834, 7835 | |
| 7837 | →↔⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒↔⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒 | Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒] into bicom1 | |
| 7838 | →↔⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒 | Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into biimp | |
| 7839 | →⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒 | Modus ponens 7826, 7838 | |
| 7840 | →↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒 | Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into bicom1 | |
| 7841 | →→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒→⋀⋀𝜓𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒 | Subs [𝜑↗→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒] into ax-1 | |
| 7842 | →⋀⋀𝜓𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒 | Modus ponens 7832, 7841 | |
| 7843 | →→⋀⋀𝜓𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒→→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒 | Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒, 𝜒↗⋀𝜓⋀𝜑𝜒] into ax-2 | |
| 7844 | →→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒 | Modus ponens 7842, 7843 | |
| 7845 | →→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒→→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒 | Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒] into impbi | |
| 7846 | →→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒 | Modus ponens 7830, 7845 | |
| 7847 | →↔⋀𝜓𝜑⋀𝜑𝜓→𝜒↔⋀𝜓𝜑⋀𝜑𝜓 | Subs [𝜑↗↔⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗𝜒] into ax-1 | |
| 7848 | →𝜒↔⋀𝜓𝜑⋀𝜑𝜓 | Modus ponens 6162, 7847 | |
| 7849 | ↔→𝜒↔⋀𝜓𝜑⋀𝜑𝜓↔⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓 | Subs [𝜑↗𝜒, 𝜓↗⋀𝜓𝜑, 𝜒↗⋀𝜑𝜓] into pm5.32 | |
| 7850 | →↔→𝜒↔⋀𝜓𝜑⋀𝜑𝜓↔⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓→→𝜒↔⋀𝜓𝜑⋀𝜑𝜓↔⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓 | Subs [𝜑↗→𝜒↔⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗↔⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓] into biimp | |
| 7851 | →→𝜒↔⋀𝜓𝜑⋀𝜑𝜓↔⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓 | Modus ponens 7849, 7850 | |
| 7852 | ↔⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓 | Modus ponens 7848, 7851 | |
| 7853 | ↔⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑 | Subs [𝜑↗⋀𝜓𝜑, 𝜓↗𝜒] into ancom | |
| 7854 | ↔⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒] into ancom | |
| 7855 | →↔⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜑𝜓↔⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜒⋀𝜑𝜓] into bicom1 | |
| 7856 | ↔⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒 | Modus ponens 7854, 7855 | |
| 7857 | →↔⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into biimp | |
| 7858 | →⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒 | Modus ponens 7856, 7857 | |
| 7859 | →↔⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓→⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓 | Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀𝜒⋀𝜑𝜓] into biimp | |
| 7860 | →⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓 | Modus ponens 7852, 7859 | |
| 7861 | →→⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜓𝜑→⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑] into ax-1 | |
| 7862 | →⋀𝜒⋀𝜓𝜑→⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒 | Modus ponens 7858, 7861 | |
| 7863 | →→⋀𝜒⋀𝜓𝜑→⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒→→⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀𝜒⋀𝜑𝜓, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 7864 | →→⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 7862, 7863 | |
| 7865 | →⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 7860, 7864 | |
| 7866 | →↔⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜑𝜓 | Subs [𝜑↗⋀𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into bicom1 | |
| 7867 | →↔⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜑𝜓 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜒⋀𝜑𝜓] into biimp | |
| 7868 | →⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜑𝜓 | Modus ponens 7854, 7867 | |
| 7869 | →↔⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓↔⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑 | Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀𝜒⋀𝜑𝜓] into bicom1 | |
| 7870 | ↔⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑 | Modus ponens 7852, 7869 | |
| 7871 | →↔⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑→⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑 | Subs [𝜑↗⋀𝜒⋀𝜑𝜓, 𝜓↗⋀𝜒⋀𝜓𝜑] into biimp | |
| 7872 | →⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑 | Modus ponens 7870, 7871 | |
| 7873 | →→⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑→⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑 | Subs [𝜑↗→⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 7874 | →⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑 | Modus ponens 7872, 7873 | |
| 7875 | →→⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑→→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜒⋀𝜑𝜓, 𝜒↗⋀𝜒⋀𝜓𝜑] into ax-2 | |
| 7876 | →→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑 | Modus ponens 7874, 7875 | |
| 7877 | →⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑 | Modus ponens 7868, 7876 | |
| 7878 | →→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒→→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑↔⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into impbi | |
| 7879 | →→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑↔⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 7865, 7878 | |
| 7880 | ↔⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 7877, 7879 | |
| 7881 | →↔⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into biimp | |
| 7882 | →↔⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑 | Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑] into biimp | |
| 7883 | →⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑 | Modus ponens 7853, 7882 | |
| 7884 | →→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒→⋀⋀𝜓𝜑𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒] into ax-1 | |
| 7885 | →⋀⋀𝜓𝜑𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 7865, 7884 | |
| 7886 | →→⋀⋀𝜓𝜑𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒→→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 7887 | →→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 7885, 7886 | |
| 7888 | →⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 7883, 7887 | |
| 7889 | →↔⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑 | Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into bicom1 | |
| 7890 | ↔⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑 | Modus ponens 7880, 7889 | |
| 7891 | →↔⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑] into biimp | |
| 7892 | →↔⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑↔⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒 | Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑] into bicom1 | |
| 7893 | ↔⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒 | Modus ponens 7853, 7892 | |
| 7894 | →↔⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒 | Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜓𝜑𝜒] into biimp | |
| 7895 | →⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒 | Modus ponens 7893, 7894 | |
| 7896 | →→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒→⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒 | Subs [𝜑↗→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 7897 | →⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒 | Modus ponens 7895, 7896 | |
| 7898 | →→⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒→→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑→⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑, 𝜒↗⋀⋀𝜓𝜑𝜒] into ax-2 | |
| 7899 | →→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑→⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒 | Modus ponens 7897, 7898 | |
| 7900 | →⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒 | Modus ponens 7877, 7899 | |
| 7901 | →→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒→→⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒↔⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into impbi | |
| 7902 | →→⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒↔⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 7888, 7901 | |
| 7903 | ↔⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 7900, 7902 | |
| 7904 | →↔⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into biimp | |
| 7905 | →→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒→⋀𝜓⋀𝜑𝜒→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into ax-1 | |
| 7906 | →⋀𝜓⋀𝜑𝜒→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 7888, 7905 | |
| 7907 | →→⋀𝜓⋀𝜑𝜒→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒→→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 7908 | →→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 7906, 7907 | |
| 7909 | →⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 7830, 7908 | |
| 7910 | →↔⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒 | Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into bicom1 | |
| 7911 | ↔⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒 | Modus ponens 7903, 7910 | |
| 7912 | →↔⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒] into biimp | |
| 7913 | →→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜓𝜒→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒 | Subs [𝜑↗→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 7914 | →⋀⋀𝜑𝜓𝜒→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒 | Modus ponens 7839, 7913 | |
| 7915 | →→⋀⋀𝜑𝜓𝜒→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒→→⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒→⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒, 𝜒↗⋀𝜓⋀𝜑𝜒] into ax-2 | |
| 7916 | →→⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒→⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒 | Modus ponens 7914, 7915 | |
| 7917 | →⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒 | Modus ponens 7900, 7916 | |
| 7918 | →→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒→→⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into impbi | |
| 7919 | →→⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 7909, 7918 | |
| 7920 | ↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 7917, 7919 | |
| 7921 | →↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒 | Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into bicom1 | |
| 7922 | ↔⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒 | Modus ponens 7920, 7921 | an21 |
| 7923 | →↔⋀𝜓𝜒⋀𝜒𝜓→𝜑↔⋀𝜓𝜒⋀𝜒𝜓 | Subs [𝜑↗↔⋀𝜓𝜒⋀𝜒𝜓, 𝜓↗𝜑] into ax-1 | |
| 7924 | →𝜑↔⋀𝜓𝜒⋀𝜒𝜓 | Modus ponens 7507, 7923 | |
| 7925 | ↔→𝜑↔⋀𝜓𝜒⋀𝜒𝜓↔⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓 | Subs [𝜓↗⋀𝜓𝜒, 𝜒↗⋀𝜒𝜓] into pm5.32 | |
| 7926 | →↔→𝜑↔⋀𝜓𝜒⋀𝜒𝜓↔⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓→→𝜑↔⋀𝜓𝜒⋀𝜒𝜓↔⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓 | Subs [𝜑↗→𝜑↔⋀𝜓𝜒⋀𝜒𝜓, 𝜓↗↔⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓] into biimp | |
| 7927 | →→𝜑↔⋀𝜓𝜒⋀𝜒𝜓↔⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓 | Modus ponens 7925, 7926 | |
| 7928 | ↔⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓 | Modus ponens 7924, 7927 | |
| 7929 | ↔⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜒𝜓 | Subs [𝜓↗𝜒, 𝜒↗𝜓] into anass | |
| 7930 | →↔⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜒𝜓↔⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓 | Subs [𝜑↗⋀⋀𝜑𝜒𝜓, 𝜓↗⋀𝜑⋀𝜒𝜓] into bicom1 | |
| 7931 | ↔⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓 | Modus ponens 7929, 7930 | |
| 7932 | →↔⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓→⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓 | Subs [𝜑↗⋀𝜑⋀𝜒𝜓, 𝜓↗⋀⋀𝜑𝜒𝜓] into biimp | |
| 7933 | →⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓 | Modus ponens 7931, 7932 | |
| 7934 | →↔⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜒𝜓] into biimp | |
| 7935 | →⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓 | Modus ponens 7928, 7934 | |
| 7936 | →→⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓 | Subs [𝜑↗→⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 7937 | →⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓 | Modus ponens 7933, 7936 | |
| 7938 | →→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓→→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜒𝜓, 𝜒↗⋀⋀𝜑𝜒𝜓] into ax-2 | |
| 7939 | →→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓 | Modus ponens 7937, 7938 | |
| 7940 | →⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓 | Modus ponens 7935, 7939 | |
| 7941 | →↔⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓↔⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜒𝜓 | Subs [𝜑↗⋀𝜑⋀𝜒𝜓, 𝜓↗⋀⋀𝜑𝜒𝜓] into bicom1 | |
| 7942 | →↔⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜒𝜓→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜒𝜓 | Subs [𝜑↗⋀⋀𝜑𝜒𝜓, 𝜓↗⋀𝜑⋀𝜒𝜓] into biimp | |
| 7943 | →⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜒𝜓 | Modus ponens 7929, 7942 | |
| 7944 | →↔⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓↔⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜒𝜓] into bicom1 | |
| 7945 | ↔⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒 | Modus ponens 7928, 7944 | |
| 7946 | →↔⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑⋀𝜒𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp | |
| 7947 | →⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒 | Modus ponens 7945, 7946 | |
| 7948 | →→⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜒𝜓→⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓] into ax-1 | |
| 7949 | →⋀⋀𝜑𝜒𝜓→⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒 | Modus ponens 7947, 7948 | |
| 7950 | →→⋀⋀𝜑𝜒𝜓→⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒→→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜒𝜓→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜒𝜓, 𝜓↗⋀𝜑⋀𝜒𝜓, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 7951 | →→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜒𝜓→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒 | Modus ponens 7949, 7950 | |
| 7952 | →⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒 | Modus ponens 7943, 7951 | |
| 7953 | →→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓→→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓] into impbi | |
| 7954 | →→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓 | Modus ponens 7940, 7953 | |
| 7955 | ↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓 | Modus ponens 7952, 7954 | |
| 7956 | ↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓 | Subs [𝜑↗𝜓, 𝜓↗⋀𝜑𝜒] into ancom | |
| 7957 | →↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓↔⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒 | Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓] into bicom1 | |
| 7958 | ↔⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒 | Modus ponens 7956, 7957 | |
| 7959 | →↔⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒 | Subs [𝜑↗⋀⋀𝜑𝜒𝜓, 𝜓↗⋀𝜓⋀𝜑𝜒] into biimp | |
| 7960 | →⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒 | Modus ponens 7958, 7959 | |
| 7961 | →↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓] into biimp | |
| 7962 | →→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒→⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒 | Subs [𝜑↗→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 7963 | →⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒 | Modus ponens 7960, 7962 | |
| 7964 | →→⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓→⋀𝜑⋀𝜓𝜒⋀𝜓⋀𝜑𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓, 𝜒↗⋀𝜓⋀𝜑𝜒] into ax-2 | |
| 7965 | →→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓→⋀𝜑⋀𝜓𝜒⋀𝜓⋀𝜑𝜒 | Modus ponens 7963, 7964 | |
| 7966 | →⋀𝜑⋀𝜓𝜒⋀𝜓⋀𝜑𝜒 | Modus ponens 7940, 7965 | |
| 7967 | →↔⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓 | Subs [𝜑↗⋀⋀𝜑𝜒𝜓, 𝜓↗⋀𝜓⋀𝜑𝜒] into bicom1 | |
| 7968 | →↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓 | Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓] into biimp | |
| 7969 | →⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓 | Modus ponens 7956, 7968 | |
| 7970 | →↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓↔⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓] into bicom1 | |
| 7971 | ↔⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒 | Modus ponens 7955, 7970 | |
| 7972 | →↔⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜒𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp | |
| 7973 | →→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒→⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into ax-1 | |
| 7974 | →⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒 | Modus ponens 7952, 7973 | |
| 7975 | →→⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒→→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓→⋀𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 7976 | →→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓→⋀𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 7974, 7975 | |
| 7977 | →⋀𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 7969, 7976 | |
| 7978 | →→⋀𝜑⋀𝜓𝜒⋀𝜓⋀𝜑𝜒→→⋀𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀𝜓⋀𝜑𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into impbi | |
| 7979 | →→⋀𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀𝜓⋀𝜑𝜒 | Modus ponens 7966, 7978 | |
| 7980 | ↔⋀𝜑⋀𝜓𝜒⋀𝜓⋀𝜑𝜒 | Modus ponens 7977, 7979 | an12 |
| 7981 | →↔⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into biimp | |
| 7982 | →→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓→⋀⋀𝜑𝜓𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓 | Subs [𝜑↗→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 7983 | →⋀⋀𝜑𝜓𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓 | Modus ponens 7969, 7982 | |
| 7984 | →→⋀⋀𝜑𝜓𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓→→⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒𝜓 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒, 𝜒↗⋀⋀𝜑𝜒𝜓] into ax-2 | |
| 7985 | →→⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒𝜓 | Modus ponens 7983, 7984 | |
| 7986 | →⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒𝜓 | Modus ponens 7917, 7985 | |
| 7987 | →↔⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into bicom1 | |
| 7988 | →↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into biimp | |
| 7989 | →→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜒𝜓→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓] into ax-1 | |
| 7990 | →⋀⋀𝜑𝜒𝜓→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 7909, 7989 | |
| 7991 | →→⋀⋀𝜑𝜒𝜓→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒→→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜒𝜓⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜒𝜓, 𝜓↗⋀𝜓⋀𝜑𝜒, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 7992 | →→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜒𝜓⋀⋀𝜑𝜓𝜒 | Modus ponens 7990, 7991 | |
| 7993 | →⋀⋀𝜑𝜒𝜓⋀⋀𝜑𝜓𝜒 | Modus ponens 7960, 7992 | |
| 7994 | →→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒𝜓→→⋀⋀𝜑𝜒𝜓⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒𝜓 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓] into impbi | |
| 7995 | →→⋀⋀𝜑𝜒𝜓⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒𝜓 | Modus ponens 7986, 7994 | |
| 7996 | ↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒𝜓 | Modus ponens 7993, 7995 | an32 |
| 7997 | ↔⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗𝜑] into an21 | |
| 7998 | →↔⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜑𝜒 | Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into bicom1 | |
| 7999 | ↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜑𝜒 | Modus ponens 7997, 7998 | |
| 8000 | →↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜑𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜑𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒] into biimp | |
| 8001 | →⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜑𝜒 | Modus ponens 7999, 8000 | |
| 8002 | →→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑→⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑 | Subs [𝜑↗→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 8003 | →⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑 | Modus ponens 7883, 8002 | |
| 8004 | →→⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑→→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜑𝜒→⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒, 𝜒↗⋀𝜒⋀𝜓𝜑] into ax-2 | |
| 8005 | →→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜑𝜒→⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑 | Modus ponens 8003, 8004 | |
| 8006 | →⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑 | Modus ponens 8001, 8005 | |
| 8007 | →↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜑𝜒↔⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒] into bicom1 | |
| 8008 | →↔⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp | |
| 8009 | →⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 7997, 8008 | |
| 8010 | →→⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒→⋀𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑] into ax-1 | |
| 8011 | →⋀𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 8009, 8010 | |
| 8012 | →→⋀𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒→→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜓𝜑𝜒, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 8013 | →→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 8011, 8012 | |
| 8014 | →⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 7895, 8013 | |
| 8015 | →→⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑→→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑] into impbi | |
| 8016 | →→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑 | Modus ponens 8006, 8015 | |
| 8017 | ↔⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑 | Modus ponens 8014, 8016 | an13 |
| 8018 | ↔⋀⋀𝜒𝜓𝜑⋀𝜒⋀𝜓𝜑 | Subs [𝜑↗𝜒, 𝜒↗𝜑] into anass | |
| 8019 | →↔⋀⋀𝜒𝜓𝜑⋀𝜒⋀𝜓𝜑↔⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑 | Subs [𝜑↗⋀⋀𝜒𝜓𝜑, 𝜓↗⋀𝜒⋀𝜓𝜑] into bicom1 | |
| 8020 | ↔⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑 | Modus ponens 8018, 8019 | |
| 8021 | →↔⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑→⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑 | Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜒𝜓𝜑] into biimp | |
| 8022 | →⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑 | Modus ponens 8020, 8021 | |
| 8023 | →↔⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑→⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑] into biimp | |
| 8024 | →→⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑→⋀𝜑⋀𝜓𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑 | Subs [𝜑↗→⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 8025 | →⋀𝜑⋀𝜓𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑 | Modus ponens 8022, 8024 | |
| 8026 | →→⋀𝜑⋀𝜓𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑→→⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑, 𝜒↗⋀⋀𝜒𝜓𝜑] into ax-2 | |
| 8027 | →→⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑 | Modus ponens 8025, 8026 | |
| 8028 | →⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑 | Modus ponens 8006, 8027 | |
| 8029 | →↔⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑↔⋀⋀𝜒𝜓𝜑⋀𝜒⋀𝜓𝜑 | Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜒𝜓𝜑] into bicom1 | |
| 8030 | →↔⋀⋀𝜒𝜓𝜑⋀𝜒⋀𝜓𝜑→⋀⋀𝜒𝜓𝜑⋀𝜒⋀𝜓𝜑 | Subs [𝜑↗⋀⋀𝜒𝜓𝜑, 𝜓↗⋀𝜒⋀𝜓𝜑] into biimp | |
| 8031 | →⋀⋀𝜒𝜓𝜑⋀𝜒⋀𝜓𝜑 | Modus ponens 8018, 8030 | |
| 8032 | →↔⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑↔⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑] into bicom1 | |
| 8033 | ↔⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens an13, 8032 | |
| 8034 | →↔⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp | |
| 8035 | →→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒→⋀⋀𝜒𝜓𝜑→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜒𝜓𝜑] into ax-1 | |
| 8036 | →⋀⋀𝜒𝜓𝜑→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 8014, 8035 | |
| 8037 | →→⋀⋀𝜒𝜓𝜑→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒→→⋀⋀𝜒𝜓𝜑⋀𝜒⋀𝜓𝜑→⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜒𝜓𝜑, 𝜓↗⋀𝜒⋀𝜓𝜑, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 8038 | →→⋀⋀𝜒𝜓𝜑⋀𝜒⋀𝜓𝜑→⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 8036, 8037 | |
| 8039 | →⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 8031, 8038 | |
| 8040 | →→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑→→⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜒𝜓𝜑] into impbi | |
| 8041 | →→⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑 | Modus ponens 8028, 8040 | |
| 8042 | ↔⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑 | Modus ponens 8039, 8041 | |
| 8043 | →↔⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜒𝜓𝜑] into biimp | |
| 8044 | →↔⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp | |
| 8045 | →→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑→⋀⋀𝜑𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑 | Subs [𝜑↗→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 8046 | →⋀⋀𝜑𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑 | Modus ponens 8028, 8045 | |
| 8047 | →→⋀⋀𝜑𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑→→⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜒𝜓𝜑 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗⋀⋀𝜒𝜓𝜑] into ax-2 | |
| 8048 | →→⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜒𝜓𝜑 | Modus ponens 8046, 8047 | |
| 8049 | →⋀⋀𝜑𝜓𝜒⋀⋀𝜒𝜓𝜑 | Modus ponens 5253, 8048 | |
| 8050 | →↔⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑↔⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜒𝜓𝜑] into bicom1 | |
| 8051 | ↔⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 8042, 8050 | |
| 8052 | →↔⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒→⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜒𝜓𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp | |
| 8053 | →↔⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into bicom1 | |
| 8054 | ↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens anass, 8053 | |
| 8055 | →↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into biimp | |
| 8056 | →→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜒𝜓𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜒𝜓𝜑] into ax-1 | |
| 8057 | →⋀⋀𝜒𝜓𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 5573, 8056 | |
| 8058 | →→⋀⋀𝜒𝜓𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→→⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒→⋀⋀𝜒𝜓𝜑⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀⋀𝜒𝜓𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 8059 | →→⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒→⋀⋀𝜒𝜓𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 8057, 8058 | |
| 8060 | →⋀⋀𝜒𝜓𝜑⋀⋀𝜑𝜓𝜒 | Modus ponens 8039, 8059 | |
| 8061 | →→⋀⋀𝜑𝜓𝜒⋀⋀𝜒𝜓𝜑→→⋀⋀𝜒𝜓𝜑⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀⋀𝜒𝜓𝜑 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜒𝜓𝜑] into impbi | |
| 8062 | →→⋀⋀𝜒𝜓𝜑⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀⋀𝜒𝜓𝜑 | Modus ponens 8049, 8061 | |
| 8063 | ↔⋀⋀𝜑𝜓𝜒⋀⋀𝜒𝜓𝜑 | Modus ponens 8060, 8062 | an31 |
| 8064 | ↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑⋀𝜓⋀𝜒𝜃 | Subs [𝜒↗⋀𝜒𝜃] into anass | |
| 8065 | ↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃 | Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗𝜃] into an12 | |
| 8066 | →↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃→𝜑↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃 | Subs [𝜑↗↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃, 𝜓↗𝜑] into ax-1 | |
| 8067 | →𝜑↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃 | Modus ponens 8065, 8066 | |
| 8068 | ↔→𝜑↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃 | Subs [𝜓↗⋀𝜓⋀𝜒𝜃, 𝜒↗⋀𝜒⋀𝜓𝜃] into pm5.32 | |
| 8069 | →↔→𝜑↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃→→𝜑↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃 | Subs [𝜑↗→𝜑↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃, 𝜓↗↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃] into biimp | |
| 8070 | →→𝜑↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃 | Modus ponens 8068, 8069 | |
| 8071 | ↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃 | Modus ponens 8067, 8070 | |
| 8072 | ↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜒⋀𝜓𝜃 | Subs [𝜓↗𝜒, 𝜒↗⋀𝜓𝜃] into anass | |
| 8073 | →↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜒⋀𝜓𝜃↔⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀𝜑⋀𝜒⋀𝜓𝜃] into bicom1 | |
| 8074 | ↔⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 8072, 8073 | |
| 8075 | →↔⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗⋀𝜑⋀𝜒⋀𝜓𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into biimp | |
| 8076 | →⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 8074, 8075 | |
| 8077 | →↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃 | Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀𝜑⋀𝜒⋀𝜓𝜃] into biimp | |
| 8078 | →⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃 | Modus ponens 8071, 8077 | |
| 8079 | →→⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 8080 | →⋀𝜑⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 8076, 8079 | |
| 8081 | →→⋀𝜑⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→→⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀𝜑⋀𝜒⋀𝜓𝜃, 𝜒↗⋀⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 8082 | →→⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 8080, 8081 | |
| 8083 | →⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 8078, 8082 | |
| 8084 | →↔⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜒⋀𝜓𝜃 | Subs [𝜑↗⋀𝜑⋀𝜒⋀𝜓𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into bicom1 | |
| 8085 | →↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜒⋀𝜓𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜒⋀𝜓𝜃 | Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀𝜑⋀𝜒⋀𝜓𝜃] into biimp | |
| 8086 | →⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜒⋀𝜓𝜃 | Modus ponens 8072, 8085 | |
| 8087 | →↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃↔⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀𝜑⋀𝜒⋀𝜓𝜃] into bicom1 | |
| 8088 | ↔⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃 | Modus ponens 8071, 8087 | |
| 8089 | →↔⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀𝜑⋀𝜒⋀𝜓𝜃, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃] into biimp | |
| 8090 | →⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃 | Modus ponens 8088, 8089 | |
| 8091 | →→⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗→⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into ax-1 | |
| 8092 | →⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃 | Modus ponens 8090, 8091 | |
| 8093 | →→⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜒⋀𝜓𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀𝜑⋀𝜒⋀𝜓𝜃, 𝜒↗⋀𝜑⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 8094 | →→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜒⋀𝜓𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃 | Modus ponens 8092, 8093 | |
| 8095 | →⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃 | Modus ponens 8086, 8094 | |
| 8096 | →→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into impbi | |
| 8097 | →→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 8083, 8096 | |
| 8098 | ↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 8095, 8097 | |
| 8099 | →↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into biimp | |
| 8100 | →↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃] into biimp | |
| 8101 | →⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑⋀𝜓⋀𝜒𝜃 | Modus ponens 8064, 8100 | |
| 8102 | →→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜃] into ax-1 | |
| 8103 | →⋀⋀𝜑𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 8083, 8102 | |
| 8104 | →→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜒↗⋀⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 8105 | →→⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 8103, 8104 | |
| 8106 | →⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 8101, 8105 | |
| 8107 | →↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into bicom1 | |
| 8108 | ↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃 | Modus ponens 8098, 8107 | |
| 8109 | →↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃] into biimp | |
| 8110 | →↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑⋀𝜓⋀𝜒𝜃↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃] into bicom1 | |
| 8111 | ↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃 | Modus ponens 8064, 8110 | |
| 8112 | →↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜃] into biimp | |
| 8113 | →⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃 | Modus ponens 8111, 8112 | |
| 8114 | →→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃 | Subs [𝜑↗→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into ax-1 | |
| 8115 | →⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃 | Modus ponens 8113, 8114 | |
| 8116 | →→⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃→→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜒↗⋀⋀𝜑𝜓⋀𝜒𝜃] into ax-2 | |
| 8117 | →→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃 | Modus ponens 8115, 8116 | |
| 8118 | →⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃 | Modus ponens 8095, 8117 | |
| 8119 | →→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into impbi | |
| 8120 | →→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 8106, 8119 | |
| 8121 | ↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 8118, 8120 | an4 |
| 8122 | ↔⋀𝜓𝜃⋀𝜃𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜃] into ancom | |
| 8123 | →↔⋀𝜓𝜃⋀𝜃𝜓→⋀𝜑𝜒↔⋀𝜓𝜃⋀𝜃𝜓 | Subs [𝜑↗↔⋀𝜓𝜃⋀𝜃𝜓, 𝜓↗⋀𝜑𝜒] into ax-1 | |
| 8124 | →⋀𝜑𝜒↔⋀𝜓𝜃⋀𝜃𝜓 | Modus ponens 8122, 8123 | |
| 8125 | ↔→⋀𝜑𝜒↔⋀𝜓𝜃⋀𝜃𝜓↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓 | Subs [𝜑↗⋀𝜑𝜒, 𝜓↗⋀𝜓𝜃, 𝜒↗⋀𝜃𝜓] into pm5.32 | |
| 8126 | →↔→⋀𝜑𝜒↔⋀𝜓𝜃⋀𝜃𝜓↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓→→⋀𝜑𝜒↔⋀𝜓𝜃⋀𝜃𝜓↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓 | Subs [𝜑↗→⋀𝜑𝜒↔⋀𝜓𝜃⋀𝜃𝜓, 𝜓↗↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓] into biimp | |
| 8127 | →→⋀𝜑𝜒↔⋀𝜓𝜃⋀𝜃𝜓↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓 | Modus ponens 8125, 8126 | |
| 8128 | ↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓 | Modus ponens 8124, 8127 | |
| 8129 | →↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓 | Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜃𝜓] into biimp | |
| 8130 | →⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓 | Modus ponens 8128, 8129 | |
| 8131 | →↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into biimp | |
| 8132 | →→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓 | Subs [𝜑↗→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜃] into ax-1 | |
| 8133 | →⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓 | Modus ponens 8130, 8132 | |
| 8134 | →→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜃𝜓 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗⋀⋀𝜑𝜒⋀𝜃𝜓] into ax-2 | |
| 8135 | →→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜃𝜓 | Modus ponens 8133, 8134 | |
| 8136 | →⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜃𝜓 | Modus ponens 8106, 8135 | |
| 8137 | →↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓↔⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜃𝜓] into bicom1 | |
| 8138 | ↔⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 8128, 8137 | |
| 8139 | →↔⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜒⋀𝜓𝜃→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜃𝜓, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into biimp | |
| 8140 | →⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 8138, 8139 | |
| 8141 | →↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into bicom1 | |
| 8142 | ↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃 | Modus ponens an4, 8141 | |
| 8143 | →↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜃] into biimp | |
| 8144 | →→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜃𝜓→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃 | Subs [𝜑↗→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜃𝜓] into ax-1 | |
| 8145 | →⋀⋀𝜑𝜒⋀𝜃𝜓→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃 | Modus ponens 8118, 8144 | |
| 8146 | →→⋀⋀𝜑𝜒⋀𝜃𝜓→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃→→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜒⋀𝜓𝜃→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜃𝜓, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗⋀⋀𝜑𝜓⋀𝜒𝜃] into ax-2 | |
| 8147 | →→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜒⋀𝜓𝜃→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜓⋀𝜒𝜃 | Modus ponens 8145, 8146 | |
| 8148 | →⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜓⋀𝜒𝜃 | Modus ponens 8140, 8147 | |
| 8149 | →→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜃𝜓→→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜓⋀𝜒𝜃↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜃𝜓 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜃𝜓] into impbi | |
| 8150 | →→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜓⋀𝜒𝜃↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜃𝜓 | Modus ponens 8136, 8149 | |
| 8151 | ↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜃𝜓 | Modus ponens 8148, 8150 | an42 |
| 8152 | ↔⋀⋀𝜑𝜃⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜃 | Subs [𝜓↗𝜃, 𝜒↗𝜓, 𝜃↗𝜒] into an42 | |
| 8153 | →↔⋀⋀𝜑𝜃⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜃↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜃⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜃⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜃] into bicom1 | |
| 8154 | ↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜃⋀𝜓𝜒 | Modus ponens 8152, 8153 | an43 |
| 8155 | →↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜃⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜃⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜃⋀𝜓𝜒] into biimp | |
| 8156 | →⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜃⋀𝜓𝜒 | Modus ponens an43, 8155 | |
| 8157 | →⋀⋀𝜑𝜃⋀𝜓𝜒⋀𝜑𝜃 | Subs [𝜑↗⋀𝜑𝜃, 𝜓↗⋀𝜓𝜒] into simpl | |
| 8158 | →→⋀⋀𝜑𝜃⋀𝜓𝜒⋀𝜑𝜃→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜃⋀𝜓𝜒⋀𝜑𝜃 | Subs [𝜑↗→⋀⋀𝜑𝜃⋀𝜓𝜒⋀𝜑𝜃, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜃] into ax-1 | |
| 8159 | →⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜃⋀𝜓𝜒⋀𝜑𝜃 | Modus ponens 8157, 8158 | |
| 8160 | →→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜃⋀𝜓𝜒⋀𝜑𝜃→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜃⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑𝜃 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜃⋀𝜓𝜒, 𝜒↗⋀𝜑𝜃] into ax-2 | |
| 8161 | →→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜃⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑𝜃 | Modus ponens 8159, 8160 | |
| 8162 | →⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑𝜃 | Modus ponens 8156, 8161 | an3 |
| 8163 | ↔→⋀𝜑𝜓𝜑↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜑 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜑] into pm4.71 | |
| 8164 | →↔→⋀𝜑𝜓𝜑↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜑→→⋀𝜑𝜓𝜑↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜑 | Subs [𝜑↗→⋀𝜑𝜓𝜑, 𝜓↗↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜑] into biimp | |
| 8165 | →→⋀𝜑𝜓𝜑↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜑 | Modus ponens 8163, 8164 | |
| 8166 | ↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜑 | Modus ponens simpl, 8165 | |
| 8167 | →↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜑↔⋀⋀𝜑𝜓𝜑⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜑] into bicom1 | |
| 8168 | ↔⋀⋀𝜑𝜓𝜑⋀𝜑𝜓 | Modus ponens 8166, 8167 | anabs1 |
| 8169 | ↔↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓 | Subs [𝜑↗𝜓, 𝜓↗⋀𝜑𝜓] into bicom | |
| 8170 | →↔↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓→↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓 | Subs [𝜑↗↔𝜓⋀𝜑𝜓, 𝜓↗↔⋀𝜑𝜓𝜓] into biimp | |
| 8171 | →↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓 | Modus ponens 8169, 8170 | |
| 8172 | →→↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓→𝜑→↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓 | Subs [𝜑↗→↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1 | |
| 8173 | →𝜑→↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓 | Modus ponens 8171, 8172 | |
| 8174 | →→𝜑→↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓→→𝜑↔𝜓⋀𝜑𝜓→𝜑↔⋀𝜑𝜓𝜓 | Subs [𝜓↗↔𝜓⋀𝜑𝜓, 𝜒↗↔⋀𝜑𝜓𝜓] into ax-2 | |
| 8175 | →→𝜑↔𝜓⋀𝜑𝜓→𝜑↔⋀𝜑𝜓𝜓 | Modus ponens 8173, 8174 | |
| 8176 | →𝜑↔⋀𝜑𝜓𝜓 | Modus ponens ibar, 8175 | |
| 8177 | ↔→𝜑↔⋀𝜑𝜓𝜓↔⋀𝜑⋀𝜑𝜓⋀𝜑𝜓 | Subs [𝜓↗⋀𝜑𝜓, 𝜒↗𝜓] into pm5.32 | |
| 8178 | →↔→𝜑↔⋀𝜑𝜓𝜓↔⋀𝜑⋀𝜑𝜓⋀𝜑𝜓→→𝜑↔⋀𝜑𝜓𝜓↔⋀𝜑⋀𝜑𝜓⋀𝜑𝜓 | Subs [𝜑↗→𝜑↔⋀𝜑𝜓𝜓, 𝜓↗↔⋀𝜑⋀𝜑𝜓⋀𝜑𝜓] into biimp | |
| 8179 | →→𝜑↔⋀𝜑𝜓𝜓↔⋀𝜑⋀𝜑𝜓⋀𝜑𝜓 | Modus ponens 8177, 8178 | |
| 8180 | ↔⋀𝜑⋀𝜑𝜓⋀𝜑𝜓 | Modus ponens 8176, 8179 | anabs5 |
| 8181 | ↔→⋀𝜑𝜓𝜓↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜓 | Subs [𝜑↗⋀𝜑𝜓] into pm4.71 | |
| 8182 | →↔→⋀𝜑𝜓𝜓↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜓→→⋀𝜑𝜓𝜓↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜓 | Subs [𝜑↗→⋀𝜑𝜓𝜓, 𝜓↗↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜓] into biimp | |
| 8183 | →→⋀𝜑𝜓𝜓↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜓 | Modus ponens 8181, 8182 | |
| 8184 | ↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜓 | Modus ponens simpr, 8183 | |
| 8185 | ↔⋀𝜓⋀𝜑𝜓⋀⋀𝜑𝜓𝜓 | Subs [𝜑↗𝜓, 𝜓↗⋀𝜑𝜓] into ancom | |
| 8186 | →↔⋀𝜓⋀𝜑𝜓⋀⋀𝜑𝜓𝜓↔⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓 | Subs [𝜑↗⋀𝜓⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜓] into bicom1 | |
| 8187 | ↔⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓 | Modus ponens 8185, 8186 | |
| 8188 | →↔⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓→⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓 | Subs [𝜑↗⋀⋀𝜑𝜓𝜓, 𝜓↗⋀𝜓⋀𝜑𝜓] into biimp | |
| 8189 | →⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓 | Modus ponens 8187, 8188 | |
| 8190 | →↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜓→⋀𝜑𝜓⋀⋀𝜑𝜓𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜓] into biimp | |
| 8191 | →⋀𝜑𝜓⋀⋀𝜑𝜓𝜓 | Modus ponens 8184, 8190 | |
| 8192 | →→⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓→⋀𝜑𝜓→⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓 | Subs [𝜑↗→⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 8193 | →⋀𝜑𝜓→⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓 | Modus ponens 8189, 8192 | |
| 8194 | →→⋀𝜑𝜓→⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓→→⋀𝜑𝜓⋀⋀𝜑𝜓𝜓→⋀𝜑𝜓⋀𝜓⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜓, 𝜒↗⋀𝜓⋀𝜑𝜓] into ax-2 | |
| 8195 | →→⋀𝜑𝜓⋀⋀𝜑𝜓𝜓→⋀𝜑𝜓⋀𝜓⋀𝜑𝜓 | Modus ponens 8193, 8194 | |
| 8196 | →⋀𝜑𝜓⋀𝜓⋀𝜑𝜓 | Modus ponens 8191, 8195 | |
| 8197 | →↔⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓↔⋀𝜓⋀𝜑𝜓⋀⋀𝜑𝜓𝜓 | Subs [𝜑↗⋀⋀𝜑𝜓𝜓, 𝜓↗⋀𝜓⋀𝜑𝜓] into bicom1 | |
| 8198 | →↔⋀𝜓⋀𝜑𝜓⋀⋀𝜑𝜓𝜓→⋀𝜓⋀𝜑𝜓⋀⋀𝜑𝜓𝜓 | Subs [𝜑↗⋀𝜓⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜓] into biimp | |
| 8199 | →⋀𝜓⋀𝜑𝜓⋀⋀𝜑𝜓𝜓 | Modus ponens 8185, 8198 | |
| 8200 | →↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜓↔⋀⋀𝜑𝜓𝜓⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜓] into bicom1 | |
| 8201 | ↔⋀⋀𝜑𝜓𝜓⋀𝜑𝜓 | Modus ponens 8184, 8200 | |
| 8202 | →↔⋀⋀𝜑𝜓𝜓⋀𝜑𝜓→⋀⋀𝜑𝜓𝜓⋀𝜑𝜓 | Subs [𝜑↗⋀⋀𝜑𝜓𝜓, 𝜓↗⋀𝜑𝜓] into biimp | |
| 8203 | →⋀⋀𝜑𝜓𝜓⋀𝜑𝜓 | Modus ponens 8201, 8202 | |
| 8204 | →→⋀⋀𝜑𝜓𝜓⋀𝜑𝜓→⋀𝜓⋀𝜑𝜓→⋀⋀𝜑𝜓𝜓⋀𝜑𝜓 | Subs [𝜑↗→⋀⋀𝜑𝜓𝜓⋀𝜑𝜓, 𝜓↗⋀𝜓⋀𝜑𝜓] into ax-1 | |
| 8205 | →⋀𝜓⋀𝜑𝜓→⋀⋀𝜑𝜓𝜓⋀𝜑𝜓 | Modus ponens 8203, 8204 | |
| 8206 | →→⋀𝜓⋀𝜑𝜓→⋀⋀𝜑𝜓𝜓⋀𝜑𝜓→→⋀𝜓⋀𝜑𝜓⋀⋀𝜑𝜓𝜓→⋀𝜓⋀𝜑𝜓⋀𝜑𝜓 | Subs [𝜑↗⋀𝜓⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜓, 𝜒↗⋀𝜑𝜓] into ax-2 | |
| 8207 | →→⋀𝜓⋀𝜑𝜓⋀⋀𝜑𝜓𝜓→⋀𝜓⋀𝜑𝜓⋀𝜑𝜓 | Modus ponens 8205, 8206 | |
| 8208 | →⋀𝜓⋀𝜑𝜓⋀𝜑𝜓 | Modus ponens 8199, 8207 | |
| 8209 | →→⋀𝜑𝜓⋀𝜓⋀𝜑𝜓→→⋀𝜓⋀𝜑𝜓⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜓⋀𝜑𝜓] into impbi | |
| 8210 | →→⋀𝜓⋀𝜑𝜓⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓⋀𝜑𝜓 | Modus ponens 8196, 8209 | |
| 8211 | ↔⋀𝜑𝜓⋀𝜓⋀𝜑𝜓 | Modus ponens 8208, 8210 | |
| 8212 | →↔⋀𝜑𝜓⋀𝜓⋀𝜑𝜓↔⋀𝜓⋀𝜑𝜓⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜓⋀𝜑𝜓] into bicom1 | |
| 8213 | ↔⋀𝜓⋀𝜑𝜓⋀𝜑𝜓 | Modus ponens 8211, 8212 | anabs7 |
| 8214 | →↔⋀𝜑𝜑𝜑→⋀𝜓𝜒↔⋀𝜑𝜑𝜑 | Subs [𝜑↗↔⋀𝜑𝜑𝜑, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 8215 | →⋀𝜓𝜒↔⋀𝜑𝜑𝜑 | Modus ponens anidm, 8214 | |
| 8216 | ↔→⋀𝜓𝜒↔⋀𝜑𝜑𝜑↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗⋀𝜑𝜑, 𝜒↗𝜑] into pm5.32 | |
| 8217 | →↔→⋀𝜓𝜒↔⋀𝜑𝜑𝜑↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑→→⋀𝜓𝜒↔⋀𝜑𝜑𝜑↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑 | Subs [𝜑↗→⋀𝜓𝜒↔⋀𝜑𝜑𝜑, 𝜓↗↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑] into biimp | |
| 8218 | →→⋀𝜓𝜒↔⋀𝜑𝜑𝜑↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑 | Modus ponens 8216, 8217 | |
| 8219 | ↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑 | Modus ponens 8215, 8218 | |
| 8220 | ↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑 | Subs [𝜑↗⋀𝜑𝜑, 𝜓↗⋀𝜓𝜒] into ancom | |
| 8221 | ↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒𝜑 | Subs [𝜓↗⋀𝜓𝜒] into ancom | |
| 8222 | →↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒𝜑↔⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒𝜑] into bicom1 | |
| 8223 | ↔⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 8221, 8222 | |
| 8224 | →↔⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜓𝜒𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp | |
| 8225 | →⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 8223, 8224 | |
| 8226 | →↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑 | Subs [𝜑↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜓↗⋀⋀𝜓𝜒𝜑] into biimp | |
| 8227 | →⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑 | Modus ponens 8219, 8226 | |
| 8228 | →→⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑→⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒⋀𝜑𝜑] into ax-1 | |
| 8229 | →⋀⋀𝜓𝜒⋀𝜑𝜑→⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 8225, 8228 | |
| 8230 | →→⋀⋀𝜓𝜒⋀𝜑𝜑→⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒→→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜓↗⋀⋀𝜓𝜒𝜑, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 8231 | →→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 8229, 8230 | |
| 8232 | →⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 8227, 8231 | |
| 8233 | →↔⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒𝜑 | Subs [𝜑↗⋀⋀𝜓𝜒𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into bicom1 | |
| 8234 | →↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒𝜑 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒𝜑] into biimp | |
| 8235 | →⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒𝜑 | Modus ponens 8221, 8234 | |
| 8236 | →↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑↔⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑 | Subs [𝜑↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜓↗⋀⋀𝜓𝜒𝜑] into bicom1 | |
| 8237 | ↔⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑 | Modus ponens 8219, 8236 | |
| 8238 | →↔⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑→⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑 | Subs [𝜑↗⋀⋀𝜓𝜒𝜑, 𝜓↗⋀⋀𝜓𝜒⋀𝜑𝜑] into biimp | |
| 8239 | →⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑 | Modus ponens 8237, 8238 | |
| 8240 | →→⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑→⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑 | Subs [𝜑↗→⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 8241 | →⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑 | Modus ponens 8239, 8240 | |
| 8242 | →→⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑→→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒𝜑, 𝜒↗⋀⋀𝜓𝜒⋀𝜑𝜑] into ax-2 | |
| 8243 | →→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑 | Modus ponens 8241, 8242 | |
| 8244 | →⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑 | Modus ponens 8235, 8243 | |
| 8245 | →→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒→→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into impbi | |
| 8246 | →→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 8232, 8245 | |
| 8247 | ↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 8244, 8246 | |
| 8248 | →↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp | |
| 8249 | →↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑 | Subs [𝜑↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒⋀𝜑𝜑] into biimp | |
| 8250 | →⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑 | Modus ponens 8220, 8249 | |
| 8251 | →→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜑⋀𝜓𝜒] into ax-1 | |
| 8252 | →⋀⋀𝜑𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒 | Modus ponens 8232, 8251 | |
| 8253 | →→⋀⋀𝜑𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒→→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 8254 | →→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 8252, 8253 | |
| 8255 | →⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 8250, 8254 | |
| 8256 | →↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑 | Subs [𝜑↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into bicom1 | |
| 8257 | ↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑 | Modus ponens 8247, 8256 | |
| 8258 | →↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒⋀𝜑𝜑] into biimp | |
| 8259 | →↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒⋀𝜑𝜑] into bicom1 | |
| 8260 | ↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒 | Modus ponens 8220, 8259 | |
| 8261 | →↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜓↗⋀⋀𝜑𝜑⋀𝜓𝜒] into biimp | |
| 8262 | →⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒 | Modus ponens 8260, 8261 | |
| 8263 | →→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒 | Subs [𝜑↗→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 8264 | →⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒 | Modus ponens 8262, 8263 | |
| 8265 | →→⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒→→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜒↗⋀⋀𝜑𝜑⋀𝜓𝜒] into ax-2 | |
| 8266 | →→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒 | Modus ponens 8264, 8265 | |
| 8267 | →⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒 | Modus ponens 8244, 8266 | |
| 8268 | →→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into impbi | |
| 8269 | →→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 8255, 8268 | |
| 8270 | ↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 8267, 8269 | |
| 8271 | ↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒 | Subs [𝜓↗𝜑, 𝜒↗𝜓, 𝜃↗𝜒] into an4 | |
| 8272 | →↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into bicom1 | |
| 8273 | ↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒 | Modus ponens 8270, 8272 | |
| 8274 | →↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜑𝜒] into biimp | |
| 8275 | →⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 8271, 8274 | |
| 8276 | →↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜑⋀𝜓𝜒] into biimp | |
| 8277 | →→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒→⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 8278 | →⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 8275, 8277 | |
| 8279 | →→⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜒↗⋀⋀𝜑𝜓⋀𝜑𝜒] into ax-2 | |
| 8280 | →→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 8278, 8279 | |
| 8281 | →⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 8267, 8280 | |
| 8282 | →↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒↔⋀⋀𝜑𝜓⋀𝜑𝜒⋀⋀𝜑𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜑𝜒] into bicom1 | |
| 8283 | ↔⋀⋀𝜑𝜓⋀𝜑𝜒⋀⋀𝜑𝜑⋀𝜓𝜒 | Modus ponens 8271, 8282 | |
| 8284 | →↔⋀⋀𝜑𝜓⋀𝜑𝜒⋀⋀𝜑𝜑⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜑𝜒⋀⋀𝜑𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜑⋀𝜓𝜒] into biimp | |
| 8285 | →⋀⋀𝜑𝜓⋀𝜑𝜒⋀⋀𝜑𝜑⋀𝜓𝜒 | Modus ponens 8283, 8284 | |
| 8286 | →↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜑⋀𝜓𝜒] into bicom1 | |
| 8287 | →↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp | |
| 8288 | →→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜑𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜑𝜒] into ax-1 | |
| 8289 | →⋀⋀𝜑𝜓⋀𝜑𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 8255, 8288 | |
| 8290 | →→⋀⋀𝜑𝜓⋀𝜑𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→⋀⋀𝜑𝜓⋀𝜑𝜒⋀⋀𝜑𝜑⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 8291 | →→⋀⋀𝜑𝜓⋀𝜑𝜒⋀⋀𝜑𝜑⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 8289, 8290 | |
| 8292 | →⋀⋀𝜑𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒 | Modus ponens 8285, 8291 | |
| 8293 | →→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒→→⋀⋀𝜑𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜑𝜒] into impbi | |
| 8294 | →→⋀⋀𝜑𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 8281, 8293 | |
| 8295 | ↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒 | Modus ponens 8292, 8294 | anandi |
| 8296 | ↔⋀𝜒𝜒𝜒 | Subs [𝜑↗𝜒] into anidm | |
| 8297 | →↔⋀𝜒𝜒𝜒→⋀𝜑𝜓↔⋀𝜒𝜒𝜒 | Subs [𝜑↗↔⋀𝜒𝜒𝜒, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 8298 | →⋀𝜑𝜓↔⋀𝜒𝜒𝜒 | Modus ponens 8296, 8297 | |
| 8299 | ↔→⋀𝜑𝜓↔⋀𝜒𝜒𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜒𝜒] into pm5.32 | |
| 8300 | →↔→⋀𝜑𝜓↔⋀𝜒𝜒𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒→→⋀𝜑𝜓↔⋀𝜒𝜒𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→⋀𝜑𝜓↔⋀𝜒𝜒𝜒, 𝜓↗↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒] into biimp | |
| 8301 | →→⋀𝜑𝜓↔⋀𝜒𝜒𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 8299, 8300 | |
| 8302 | ↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 8298, 8301 | |
| 8303 | ↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒 | Subs [𝜃↗𝜒] into an4 | |
| 8304 | →↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into bicom1 | |
| 8305 | ↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒 | Modus ponens 8302, 8304 | |
| 8306 | →↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜒, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜒] into biimp | |
| 8307 | →⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒 | Modus ponens 8303, 8306 | |
| 8308 | →↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜒] into biimp | |
| 8309 | →⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒 | Modus ponens 8305, 8308 | |
| 8310 | →→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒 | Subs [𝜑↗→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 8311 | →⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒 | Modus ponens 8307, 8310 | |
| 8312 | →→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜒, 𝜒↗⋀⋀𝜑𝜒⋀𝜓𝜒] into ax-2 | |
| 8313 | →→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒⋀𝜓𝜒 | Modus ponens 8311, 8312 | |
| 8314 | →⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒⋀𝜓𝜒 | Modus ponens 8309, 8313 | |
| 8315 | →↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒↔⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜒, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜒] into bicom1 | |
| 8316 | ↔⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒 | Modus ponens 8303, 8315 | |
| 8317 | →↔⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒 | Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜒] into biimp | |
| 8318 | →⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒 | Modus ponens 8316, 8317 | |
| 8319 | →↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜒] into bicom1 | |
| 8320 | →↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into biimp | |
| 8321 | →⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 8302, 8320 | |
| 8322 | →→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜒⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜒] into ax-1 | |
| 8323 | →⋀⋀𝜑𝜒⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 8321, 8322 | |
| 8324 | →→⋀⋀𝜑𝜒⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒→→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜒, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 8325 | →→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 8323, 8324 | |
| 8326 | →⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓𝜒 | Modus ponens 8318, 8325 | |
| 8327 | →→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒⋀𝜓𝜒→→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜒] into impbi | |
| 8328 | →→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒⋀𝜓𝜒 | Modus ponens 8314, 8327 | |
| 8329 | ↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒⋀𝜓𝜒 | Modus ponens 8326, 8328 | anandir |
| 8330 | ↔⋀→𝜑𝜓→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜒] into df-an | |
| 8331 | →¬¬→𝜓𝜒→𝜓𝜒 | Subs [𝜑↗→𝜓𝜒] into notnotr | |
| 8332 | →→𝜓𝜒→→𝜑𝜓→𝜓𝜒 | Subs [𝜑↗→𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 8333 | →→→𝜓𝜒→→𝜑𝜓→𝜓𝜒→¬¬→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜓𝜒 | Subs [𝜑↗→→𝜓𝜒→→𝜑𝜓→𝜓𝜒, 𝜓↗¬¬→𝜓𝜒] into ax-1 | |
| 8334 | →¬¬→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜓𝜒 | Modus ponens 8332, 8333 | |
| 8335 | →→¬¬→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜓𝜒→→¬¬→𝜓𝜒→𝜓𝜒→¬¬→𝜓𝜒→→𝜑𝜓→𝜓𝜒 | Subs [𝜑↗¬¬→𝜓𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜓𝜒] into ax-2 | |
| 8336 | →→¬¬→𝜓𝜒→𝜓𝜒→¬¬→𝜓𝜒→→𝜑𝜓→𝜓𝜒 | Modus ponens 8334, 8335 | |
| 8337 | →¬¬→𝜓𝜒→→𝜑𝜓→𝜓𝜒 | Modus ponens 8331, 8336 | |
| 8338 | →→→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→→𝜑𝜓→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜒, 𝜒↗→𝜑𝜒] into ax-2 | |
| 8339 | →→→𝜑𝜓→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens imim1, 8338 | |
| 8340 | →→→→𝜑𝜓→𝜓𝜒→→𝜑𝜓→𝜑𝜒→¬¬→𝜓𝜒→→→𝜑𝜓→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→→𝜑𝜓→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗¬¬→𝜓𝜒] into ax-1 | |
| 8341 | →¬¬→𝜓𝜒→→→𝜑𝜓→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 8339, 8340 | |
| 8342 | →→¬¬→𝜓𝜒→→→𝜑𝜓→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→¬¬→𝜓𝜒→→𝜑𝜓→𝜓𝜒→¬¬→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗¬¬→𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 8343 | →→¬¬→𝜓𝜒→→𝜑𝜓→𝜓𝜒→¬¬→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 8341, 8342 | |
| 8344 | →¬¬→𝜓𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 8337, 8343 | |
| 8345 | →→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗¬¬→𝜓𝜒] into ax-1 | |
| 8346 | →→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 8347 | →→𝜑𝜓→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓 | Modus ponens 8345, 8346 | |
| 8348 | →→→𝜑𝜓→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→¬¬→𝜓𝜒→𝜑𝜓] into ax-2 | |
| 8349 | →→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓 | Modus ponens 8347, 8348 | |
| 8350 | →→¬¬→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→¬¬→𝜓𝜒→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗¬¬→𝜓𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜒] into ax-2 | |
| 8351 | →→¬¬→𝜓𝜒→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒 | Modus ponens 8344, 8350 | |
| 8352 | →→→¬¬→𝜓𝜒→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒→→𝜑𝜓→→¬¬→𝜓𝜒→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→→¬¬→𝜓𝜒→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 8353 | →→𝜑𝜓→→¬¬→𝜓𝜒→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒 | Modus ponens 8351, 8352 | |
| 8354 | →→→𝜑𝜓→→¬¬→𝜓𝜒→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒→→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜓𝜒→𝜑𝜓, 𝜒↗→¬¬→𝜓𝜒→𝜑𝜒] into ax-2 | |
| 8355 | →→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒 | Modus ponens 8353, 8354 | |
| 8356 | →→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒 | Modus ponens 8345, 8355 | |
| 8357 | →→𝜑𝜒¬¬→𝜑𝜒 | Subs [𝜑↗→𝜑𝜒] into notnot | |
| 8358 | →→→𝜑𝜒¬¬→𝜑𝜒→¬¬→𝜓𝜒→→𝜑𝜒¬¬→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜒¬¬→𝜑𝜒, 𝜓↗¬¬→𝜓𝜒] into ax-1 | |
| 8359 | →¬¬→𝜓𝜒→→𝜑𝜒¬¬→𝜑𝜒 | Modus ponens 8357, 8358 | |
| 8360 | →→¬¬→𝜓𝜒→→𝜑𝜒¬¬→𝜑𝜒→→¬¬→𝜓𝜒→𝜑𝜒→¬¬→𝜓𝜒¬¬→𝜑𝜒 | Subs [𝜑↗¬¬→𝜓𝜒, 𝜓↗→𝜑𝜒, 𝜒↗¬¬→𝜑𝜒] into ax-2 | |
| 8361 | →→¬¬→𝜓𝜒→𝜑𝜒→¬¬→𝜓𝜒¬¬→𝜑𝜒 | Modus ponens 8359, 8360 | |
| 8362 | →→→¬¬→𝜓𝜒→𝜑𝜒→¬¬→𝜓𝜒¬¬→𝜑𝜒→→𝜑𝜓→→¬¬→𝜓𝜒→𝜑𝜒→¬¬→𝜓𝜒¬¬→𝜑𝜒 | Subs [𝜑↗→→¬¬→𝜓𝜒→𝜑𝜒→¬¬→𝜓𝜒¬¬→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 8363 | →→𝜑𝜓→→¬¬→𝜓𝜒→𝜑𝜒→¬¬→𝜓𝜒¬¬→𝜑𝜒 | Modus ponens 8361, 8362 | |
| 8364 | →→→𝜑𝜓→→¬¬→𝜓𝜒→𝜑𝜒→¬¬→𝜓𝜒¬¬→𝜑𝜒→→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒→→𝜑𝜓→¬¬→𝜓𝜒¬¬→𝜑𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜓𝜒→𝜑𝜒, 𝜒↗→¬¬→𝜓𝜒¬¬→𝜑𝜒] into ax-2 | |
| 8365 | →→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒→→𝜑𝜓→¬¬→𝜓𝜒¬¬→𝜑𝜒 | Modus ponens 8363, 8364 | |
| 8366 | →→𝜑𝜓→¬¬→𝜓𝜒¬¬→𝜑𝜒 | Modus ponens 8356, 8365 | |
| 8367 | →→¬¬→𝜓𝜒¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜓𝜒 | Subs [𝜑↗¬→𝜓𝜒, 𝜓↗¬→𝜑𝜒] into ax-3 | |
| 8368 | →→→¬¬→𝜓𝜒¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜓𝜒→→𝜑𝜓→→¬¬→𝜓𝜒¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜓𝜒 | Subs [𝜑↗→→¬¬→𝜓𝜒¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 8369 | →→𝜑𝜓→→¬¬→𝜓𝜒¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜓𝜒 | Modus ponens 8367, 8368 | |
| 8370 | →→→𝜑𝜓→→¬¬→𝜓𝜒¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜓𝜒→→→𝜑𝜓→¬¬→𝜓𝜒¬¬→𝜑𝜒→→𝜑𝜓→¬→𝜑𝜒¬→𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜓𝜒¬¬→𝜑𝜒, 𝜒↗→¬→𝜑𝜒¬→𝜓𝜒] into ax-2 | |
| 8371 | →→→𝜑𝜓→¬¬→𝜓𝜒¬¬→𝜑𝜒→→𝜑𝜓→¬→𝜑𝜒¬→𝜓𝜒 | Modus ponens 8369, 8370 | |
| 8372 | →→𝜑𝜓→¬→𝜑𝜒¬→𝜓𝜒 | Modus ponens 8366, 8371 | |
| 8373 | →¬→𝜑𝜒¬→𝜑𝜒 | Subs [𝜑↗¬→𝜑𝜒] into id | |
| 8374 | →¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 8375 | →→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒→¬→𝜑𝜒→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→𝜑𝜒] into ax-1 | |
| 8376 | →¬→𝜑𝜒→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒 | Modus ponens 8374, 8375 | |
| 8377 | →→¬→𝜑𝜒→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑𝜒¬→𝜑𝜒→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬→𝜑𝜒, 𝜒↗→→𝜑𝜓¬→𝜑𝜒] into ax-2 | |
| 8378 | →→¬→𝜑𝜒¬→𝜑𝜒→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒 | Modus ponens 8376, 8377 | |
| 8379 | →→→𝜑𝜓→¬→𝜑𝜒¬→𝜓𝜒→→→𝜑𝜓¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→𝜑𝜒, 𝜒↗¬→𝜓𝜒] into ax-2 | |
| 8380 | →→→𝜑𝜓¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒 | Modus ponens 8372, 8379 | |
| 8381 | →→→→𝜑𝜓¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒 | Subs [𝜑↗→→→𝜑𝜓¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬→𝜑𝜒] into ax-1 | |
| 8382 | →¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒 | Modus ponens 8380, 8381 | |
| 8383 | →→¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒→→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒→¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒 | Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→→𝜑𝜓¬→𝜑𝜒, 𝜒↗→→𝜑𝜓¬→𝜓𝜒] into ax-2 | |
| 8384 | →→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒→¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒 | Modus ponens 8382, 8383 | |
| 8385 | →¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒 | Modus ponens 8374, 8384 | |
| 8386 | →¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Subs [𝜑↗¬→→𝜑𝜓¬→𝜓𝜒] into id | |
| 8387 | →→¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒→¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬→𝜑𝜒] into ax-1 | |
| 8388 | →¬→𝜑𝜒→¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Modus ponens 8386, 8387 | |
| 8389 | →¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Subs [𝜑↗¬→→𝜑𝜓¬→𝜓𝜒] into notnotr | |
| 8390 | →¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Subs [𝜑↗¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬→𝜑𝜒] into ax-1 | |
| 8391 | →→¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜓𝜒] into ax-1 | |
| 8392 | →¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Modus ponens 8390, 8391 | |
| 8393 | →→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜒, 𝜒↗→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒] into ax-2 | |
| 8394 | →→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Modus ponens 8392, 8393 | |
| 8395 | →¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Modus ponens 8389, 8394 | |
| 8396 | →→¬→𝜑𝜒→¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜒, 𝜒↗¬→→𝜑𝜓¬→𝜓𝜒] into ax-2 | |
| 8397 | →→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Modus ponens 8388, 8396 | |
| 8398 | →→→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒→→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Subs [𝜑↗→→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜓𝜒] into ax-1 | |
| 8399 | →¬¬¬→→𝜑𝜓¬→𝜓𝜒→→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Modus ponens 8397, 8398 | |
| 8400 | →→¬¬¬→→𝜑𝜓¬→𝜓𝜒→→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒, 𝜒↗→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒] into ax-2 | |
| 8401 | →→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Modus ponens 8399, 8400 | |
| 8402 | →¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒 | Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜓𝜒] into ax-1 | |
| 8403 | →→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒 | Subs [𝜑↗→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒, 𝜓↗¬→𝜑𝜒] into ax-1 | |
| 8404 | →¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒 | Modus ponens 8402, 8403 | |
| 8405 | →→¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→→¬→𝜑𝜒¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒 | Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬→𝜑𝜒, 𝜒↗→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒] into ax-2 | |
| 8406 | →→¬→𝜑𝜒¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒 | Modus ponens 8404, 8405 | |
| 8407 | →→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬→𝜑𝜒, 𝜒↗¬→→𝜑𝜓¬→𝜓𝜒] into ax-2 | |
| 8408 | →→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Modus ponens 8395, 8407 | |
| 8409 | →→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬→𝜑𝜒] into ax-1 | |
| 8410 | →¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Modus ponens 8408, 8409 | |
| 8411 | →→¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒, 𝜒↗→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒] into ax-2 | |
| 8412 | →→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Modus ponens 8410, 8411 | |
| 8413 | →¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Modus ponens 8402, 8412 | |
| 8414 | →→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒 | Subs [𝜑↗¬¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗→→𝜑𝜓¬→𝜓𝜒] into ax-3 | |
| 8415 | →→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒 | Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬→𝜑𝜒] into ax-1 | |
| 8416 | →¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒 | Modus ponens 8414, 8415 | |
| 8417 | →→¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒→→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒 | Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒, 𝜒↗→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒] into ax-2 | |
| 8418 | →→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒 | Modus ponens 8416, 8417 | |
| 8419 | →¬→𝜑𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒 | Modus ponens 8413, 8418 | |
| 8420 | →→¬→𝜑𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒→→¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜓𝜒 | Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→→𝜑𝜓¬→𝜓𝜒, 𝜒↗¬¬→→𝜑𝜓¬→𝜓𝜒] into ax-2 | |
| 8421 | →→¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜓𝜒 | Modus ponens 8419, 8420 | |
| 8422 | →¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜓𝜒 | Modus ponens 8385, 8421 | |
| 8423 | →→¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜓𝜒→¬→→𝜑𝜓¬→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→𝜑𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜒] into ax-3 | |
| 8424 | →¬→→𝜑𝜓¬→𝜓𝜒→𝜑𝜒 | Modus ponens 8422, 8423 | |
| 8425 | →↔⋀→𝜑𝜓→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→⋀→𝜑𝜓→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Subs [𝜑↗⋀→𝜑𝜓→𝜓𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜒] into biimp | |
| 8426 | →⋀→𝜑𝜓→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒 | Modus ponens 8330, 8425 | |
| 8427 | →→¬→→𝜑𝜓¬→𝜓𝜒→𝜑𝜒→⋀→𝜑𝜓→𝜓𝜒→¬→→𝜑𝜓¬→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜒→𝜑𝜒, 𝜓↗⋀→𝜑𝜓→𝜓𝜒] into ax-1 | |
| 8428 | →⋀→𝜑𝜓→𝜓𝜒→¬→→𝜑𝜓¬→𝜓𝜒→𝜑𝜒 | Modus ponens 8424, 8427 | |
| 8429 | →→⋀→𝜑𝜓→𝜓𝜒→¬→→𝜑𝜓¬→𝜓𝜒→𝜑𝜒→→⋀→𝜑𝜓→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→⋀→𝜑𝜓→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗⋀→𝜑𝜓→𝜓𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜒, 𝜒↗→𝜑𝜒] into ax-2 | |
| 8430 | →→⋀→𝜑𝜓→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→⋀→𝜑𝜓→𝜓𝜒→𝜑𝜒 | Modus ponens 8428, 8429 | |
| 8431 | →⋀→𝜑𝜓→𝜓𝜒→𝜑𝜒 | Modus ponens 8426, 8430 | pm3.33 |
| 8432 | ↔⋀→𝜓𝜒→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓 | Subs [𝜑↗→𝜓𝜒, 𝜓↗→𝜑𝜓] into df-an | |
| 8433 | →→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→¬¬→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→→𝜓𝜒→𝜑𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1 | |
| 8434 | →¬¬→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓 | Modus ponens 63, 8433 | |
| 8435 | →→¬¬→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜓 | Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜓] into ax-2 | |
| 8436 | →→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜓 | Modus ponens 8434, 8435 | |
| 8437 | →¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜓 | Modus ponens 532, 8436 | |
| 8438 | →→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Modus ponens 68, 78 | |
| 8439 | →→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→¬¬→𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒, 𝜓↗¬¬→𝜑𝜓] into ax-1 | |
| 8440 | →¬¬→𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Modus ponens 8438, 8439 | |
| 8441 | →→¬¬→𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜓→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→→𝜓𝜒→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜒] into ax-2 | |
| 8442 | →→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜓→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Modus ponens 8440, 8441 | |
| 8443 | →¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜒 | Modus ponens 8437, 8442 | |
| 8444 | →→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒 | Subs [𝜑↗→𝜓𝜒, 𝜓↗¬¬→𝜑𝜓] into ax-1 | |
| 8445 | →→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒→→𝜓𝜒→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒 | Subs [𝜑↗→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒, 𝜓↗→𝜓𝜒] into ax-1 | |
| 8446 | →→𝜓𝜒→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒 | Modus ponens 8444, 8445 | |
| 8447 | →→→𝜓𝜒→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒 | Subs [𝜑↗→𝜓𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→¬¬→𝜑𝜓→𝜓𝜒] into ax-2 | |
| 8448 | →→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒 | Modus ponens 8446, 8447 | |
| 8449 | →→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→¬¬→𝜑𝜓→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜓𝜒, 𝜒↗→𝜑𝜒] into ax-2 | |
| 8450 | →→¬¬→𝜑𝜓→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒 | Modus ponens 8443, 8449 | |
| 8451 | →→→¬¬→𝜑𝜓→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒→→𝜓𝜒→→¬¬→𝜑𝜓→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→¬¬→𝜑𝜓→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜓𝜒] into ax-1 | |
| 8452 | →→𝜓𝜒→→¬¬→𝜑𝜓→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒 | Modus ponens 8450, 8451 | |
| 8453 | →→→𝜓𝜒→→¬¬→𝜑𝜓→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒→→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜓𝜒, 𝜓↗→¬¬→𝜑𝜓→𝜓𝜒, 𝜒↗→¬¬→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 8454 | →→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒→→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒 | Modus ponens 8452, 8453 | |
| 8455 | →→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒 | Modus ponens 8444, 8454 | |
| 8456 | →→→𝜑𝜒¬¬→𝜑𝜒→¬¬→𝜑𝜓→→𝜑𝜒¬¬→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜒¬¬→𝜑𝜒, 𝜓↗¬¬→𝜑𝜓] into ax-1 | |
| 8457 | →¬¬→𝜑𝜓→→𝜑𝜒¬¬→𝜑𝜒 | Modus ponens 8357, 8456 | |
| 8458 | →→¬¬→𝜑𝜓→→𝜑𝜒¬¬→𝜑𝜒→→¬¬→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒 | Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗¬¬→𝜑𝜒] into ax-2 | |
| 8459 | →→¬¬→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒 | Modus ponens 8457, 8458 | |
| 8460 | →→→¬¬→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒→→𝜓𝜒→→¬¬→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒 | Subs [𝜑↗→→¬¬→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒, 𝜓↗→𝜓𝜒] into ax-1 | |
| 8461 | →→𝜓𝜒→→¬¬→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒 | Modus ponens 8459, 8460 | |
| 8462 | →→→𝜓𝜒→→¬¬→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒→→→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒→→𝜓𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒 | Subs [𝜑↗→𝜓𝜒, 𝜓↗→¬¬→𝜑𝜓→𝜑𝜒, 𝜒↗→¬¬→𝜑𝜓¬¬→𝜑𝜒] into ax-2 | |
| 8463 | →→→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒→→𝜓𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒 | Modus ponens 8461, 8462 | |
| 8464 | →→𝜓𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒 | Modus ponens 8455, 8463 | |
| 8465 | →→¬¬→𝜑𝜓¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑𝜒] into ax-3 | |
| 8466 | →→→¬¬→𝜑𝜓¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜑𝜓→→𝜓𝜒→→¬¬→𝜑𝜓¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜑𝜓 | Subs [𝜑↗→→¬¬→𝜑𝜓¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜑𝜓, 𝜓↗→𝜓𝜒] into ax-1 | |
| 8467 | →→𝜓𝜒→→¬¬→𝜑𝜓¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜑𝜓 | Modus ponens 8465, 8466 | |
| 8468 | →→→𝜓𝜒→→¬¬→𝜑𝜓¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜑𝜓→→→𝜓𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒→→𝜓𝜒→¬→𝜑𝜒¬→𝜑𝜓 | Subs [𝜑↗→𝜓𝜒, 𝜓↗→¬¬→𝜑𝜓¬¬→𝜑𝜒, 𝜒↗→¬→𝜑𝜒¬→𝜑𝜓] into ax-2 | |
| 8469 | →→→𝜓𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒→→𝜓𝜒→¬→𝜑𝜒¬→𝜑𝜓 | Modus ponens 8467, 8468 | |
| 8470 | →→𝜓𝜒→¬→𝜑𝜒¬→𝜑𝜓 | Modus ponens 8464, 8469 | |
| 8471 | →¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒 | Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→𝜓𝜒] into ax-1 | |
| 8472 | →→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒→¬→𝜑𝜒→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒 | Subs [𝜑↗→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒, 𝜓↗¬→𝜑𝜒] into ax-1 | |
| 8473 | →¬→𝜑𝜒→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒 | Modus ponens 8471, 8472 | |
| 8474 | →→¬→𝜑𝜒→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒→→¬→𝜑𝜒¬→𝜑𝜒→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒 | Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬→𝜑𝜒, 𝜒↗→→𝜓𝜒¬→𝜑𝜒] into ax-2 | |
| 8475 | →→¬→𝜑𝜒¬→𝜑𝜒→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒 | Modus ponens 8473, 8474 | |
| 8476 | →→→𝜓𝜒→¬→𝜑𝜒¬→𝜑𝜓→→→𝜓𝜒¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓 | Subs [𝜑↗→𝜓𝜒, 𝜓↗¬→𝜑𝜒, 𝜒↗¬→𝜑𝜓] into ax-2 | |
| 8477 | →→→𝜓𝜒¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓 | Modus ponens 8470, 8476 | |
| 8478 | →→→→𝜓𝜒¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒→→→𝜓𝜒¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓 | Subs [𝜑↗→→→𝜓𝜒¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜒] into ax-1 | |
| 8479 | →¬→𝜑𝜒→→→𝜓𝜒¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓 | Modus ponens 8477, 8478 | |
| 8480 | →→¬→𝜑𝜒→→→𝜓𝜒¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓→→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→→𝜓𝜒¬→𝜑𝜒, 𝜒↗→→𝜓𝜒¬→𝜑𝜓] into ax-2 | |
| 8481 | →→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓 | Modus ponens 8479, 8480 | |
| 8482 | →¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓 | Modus ponens 8471, 8481 | |
| 8483 | →¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→→𝜓𝜒¬→𝜑𝜓] into id | |
| 8484 | →→¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒→¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓 | Subs [𝜑↗→¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜒] into ax-1 | |
| 8485 | →¬→𝜑𝜒→¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓 | Modus ponens 8483, 8484 | |
| 8486 | →¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→→𝜓𝜒¬→𝜑𝜓] into notnotr | |
| 8487 | →¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜒] into ax-1 | |
| 8488 | →→¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓 | Subs [𝜑↗→¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬¬¬→→𝜓𝜒¬→𝜑𝜓] into ax-1 | |
| 8489 | →¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓 | Modus ponens 8487, 8488 | |
| 8490 | →→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓 | Subs [𝜑↗¬¬¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬→→𝜓𝜒¬→𝜑𝜓, 𝜒↗→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓] into ax-2 | |
| 8491 | →→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓 | Modus ponens 8489, 8490 | |
| 8492 | →¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓 | Modus ponens 8486, 8491 | |
| 8493 | →→¬→𝜑𝜒→¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬→→𝜓𝜒¬→𝜑𝜓, 𝜒↗¬→→𝜓𝜒¬→𝜑𝜓] into ax-2 | |
| 8494 | →→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓 | Modus ponens 8485, 8493 | |
| 8495 | →→→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬¬¬→→𝜓𝜒¬→𝜑𝜓→→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓 | Subs [𝜑↗→→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬¬¬→→𝜓𝜒¬→𝜑𝜓] into ax-1 | |
| 8496 | →¬¬¬→→𝜓𝜒¬→𝜑𝜓→→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓 | Modus ponens 8494, 8495 | |
| 8497 | →→¬¬¬→→𝜓𝜒¬→𝜑𝜓→→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓 | Subs [𝜑↗¬¬¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓, 𝜒↗→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓] into ax-2 | |
| 8498 | →→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓 | Modus ponens 8496, 8497 | |
| 8499 | →¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬¬¬→→𝜓𝜒¬→𝜑𝜓] into ax-1 | |
| 8500 | →→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→𝜑𝜒] into ax-1 | |
| 8501 | →¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒 | Modus ponens 8499, 8500 | |
| 8502 | →→¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→→¬→𝜑𝜒¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒 | Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬→𝜑𝜒, 𝜒↗→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒] into ax-2 | |
| 8503 | →→¬→𝜑𝜒¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒 | Modus ponens 8501, 8502 | |
| 8504 | →→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓 | Subs [𝜑↗¬¬¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜒, 𝜒↗¬→→𝜓𝜒¬→𝜑𝜓] into ax-2 | |
| 8505 | →→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓 | Modus ponens 8492, 8504 | |
| 8506 | →→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓 | Subs [𝜑↗→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜒] into ax-1 | |
| 8507 | →¬→𝜑𝜒→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓 | Modus ponens 8505, 8506 | |
| 8508 | →→¬→𝜑𝜒→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒, 𝜒↗→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓] into ax-2 | |
| 8509 | →→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓 | Modus ponens 8507, 8508 | |
| 8510 | →¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓 | Modus ponens 8499, 8509 | |
| 8511 | →→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓 | Subs [𝜑↗¬¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗→→𝜓𝜒¬→𝜑𝜓] into ax-3 | |
| 8512 | →→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓 | Subs [𝜑↗→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜒] into ax-1 | |
| 8513 | →¬→𝜑𝜒→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓 | Modus ponens 8511, 8512 | |
| 8514 | →→¬→𝜑𝜒→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓→→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓, 𝜒↗→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓] into ax-2 | |
| 8515 | →→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓 | Modus ponens 8513, 8514 | |
| 8516 | →¬→𝜑𝜒→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓 | Modus ponens 8510, 8515 | |
| 8517 | →→¬→𝜑𝜒→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓→→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬¬→→𝜓𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→→𝜓𝜒¬→𝜑𝜓, 𝜒↗¬¬→→𝜓𝜒¬→𝜑𝜓] into ax-2 | |
| 8518 | →→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬¬→→𝜓𝜒¬→𝜑𝜓 | Modus ponens 8516, 8517 | |
| 8519 | →¬→𝜑𝜒¬¬→→𝜓𝜒¬→𝜑𝜓 | Modus ponens 8482, 8518 | |
| 8520 | →→¬→𝜑𝜒¬¬→→𝜓𝜒¬→𝜑𝜓→¬→→𝜓𝜒¬→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑𝜒, 𝜓↗¬→→𝜓𝜒¬→𝜑𝜓] into ax-3 | |
| 8521 | →¬→→𝜓𝜒¬→𝜑𝜓→𝜑𝜒 | Modus ponens 8519, 8520 | |
| 8522 | →↔⋀→𝜓𝜒→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→⋀→𝜓𝜒→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓 | Subs [𝜑↗⋀→𝜓𝜒→𝜑𝜓, 𝜓↗¬→→𝜓𝜒¬→𝜑𝜓] into biimp | |
| 8523 | →⋀→𝜓𝜒→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓 | Modus ponens 8432, 8522 | |
| 8524 | →→¬→→𝜓𝜒¬→𝜑𝜓→𝜑𝜒→⋀→𝜓𝜒→𝜑𝜓→¬→→𝜓𝜒¬→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→¬→→𝜓𝜒¬→𝜑𝜓→𝜑𝜒, 𝜓↗⋀→𝜓𝜒→𝜑𝜓] into ax-1 | |
| 8525 | →⋀→𝜓𝜒→𝜑𝜓→¬→→𝜓𝜒¬→𝜑𝜓→𝜑𝜒 | Modus ponens 8521, 8524 | |
| 8526 | →→⋀→𝜓𝜒→𝜑𝜓→¬→→𝜓𝜒¬→𝜑𝜓→𝜑𝜒→→⋀→𝜓𝜒→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→⋀→𝜓𝜒→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗⋀→𝜓𝜒→𝜑𝜓, 𝜓↗¬→→𝜓𝜒¬→𝜑𝜓, 𝜒↗→𝜑𝜒] into ax-2 | |
| 8527 | →→⋀→𝜓𝜒→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→⋀→𝜓𝜒→𝜑𝜓→𝜑𝜒 | Modus ponens 8525, 8526 | |
| 8528 | →⋀→𝜓𝜒→𝜑𝜓→𝜑𝜒 | Modus ponens 8523, 8527 | pm3.34 |
| 8529 | →→𝜑→𝜒𝜑→→𝜑𝜒→𝜑𝜑 | Subs [𝜓↗𝜒, 𝜒↗𝜑] into ax-2 | |
| 8530 | →→𝜑𝜒→𝜑𝜑 | Modus ponens 13, 8529 | |
| 8531 | →→→𝜑𝜒→𝜑𝜑→¬¬𝜒→→𝜑𝜒→𝜑𝜑 | Subs [𝜑↗→→𝜑𝜒→𝜑𝜑, 𝜓↗¬¬𝜒] into ax-1 | |
| 8532 | →¬¬𝜒→→𝜑𝜒→𝜑𝜑 | Modus ponens 8530, 8531 | |
| 8533 | →→¬¬𝜒→→𝜑𝜒→𝜑𝜑→→¬¬𝜒→𝜑𝜒→¬¬𝜒→𝜑𝜑 | Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑𝜑] into ax-2 | |
| 8534 | →→¬¬𝜒→𝜑𝜒→¬¬𝜒→𝜑𝜑 | Modus ponens 8532, 8533 | |
| 8535 | →¬¬𝜒→𝜑𝜑 | Modus ponens 7398, 8534 | |
| 8536 | →→¬¬𝜒→𝜑𝜑→→¬¬𝜒𝜑→¬¬𝜒𝜑 | Subs [𝜑↗¬¬𝜒, 𝜓↗𝜑, 𝜒↗𝜑] into ax-2 | |
| 8537 | →→¬¬𝜒𝜑→¬¬𝜒𝜑 | Modus ponens 8535, 8536 | |
| 8538 | →→→¬¬𝜒𝜑→¬¬𝜒𝜑→𝜑→→¬¬𝜒𝜑→¬¬𝜒𝜑 | Subs [𝜑↗→→¬¬𝜒𝜑→¬¬𝜒𝜑, 𝜓↗𝜑] into ax-1 | |
| 8539 | →𝜑→→¬¬𝜒𝜑→¬¬𝜒𝜑 | Modus ponens 8537, 8538 | |
| 8540 | →→𝜑→→¬¬𝜒𝜑→¬¬𝜒𝜑→→𝜑→¬¬𝜒𝜑→𝜑→¬¬𝜒𝜑 | Subs [𝜓↗→¬¬𝜒𝜑, 𝜒↗→¬¬𝜒𝜑] into ax-2 | |
| 8541 | →→𝜑→¬¬𝜒𝜑→𝜑→¬¬𝜒𝜑 | Modus ponens 8539, 8540 | |
| 8542 | →→𝜑¬¬𝜑→¬¬𝜒→𝜑¬¬𝜑 | Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜒] into ax-1 | |
| 8543 | →¬¬𝜒→𝜑¬¬𝜑 | Modus ponens notnot, 8542 | |
| 8544 | →→¬¬𝜒→𝜑¬¬𝜑→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑 | Subs [𝜑↗¬¬𝜒, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2 | |
| 8545 | →→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑 | Modus ponens 8543, 8544 | |
| 8546 | →→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑→𝜑→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑 | Subs [𝜑↗→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑, 𝜓↗𝜑] into ax-1 | |
| 8547 | →𝜑→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑 | Modus ponens 8545, 8546 | |
| 8548 | →→𝜑→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑→→𝜑→¬¬𝜒𝜑→𝜑→¬¬𝜒¬¬𝜑 | Subs [𝜓↗→¬¬𝜒𝜑, 𝜒↗→¬¬𝜒¬¬𝜑] into ax-2 | |
| 8549 | →→𝜑→¬¬𝜒𝜑→𝜑→¬¬𝜒¬¬𝜑 | Modus ponens 8547, 8548 | |
| 8550 | →𝜑→¬¬𝜒¬¬𝜑 | Modus ponens 7406, 8549 | |
| 8551 | →→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬𝜑] into ax-3 | |
| 8552 | →→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒→𝜑→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒 | Subs [𝜑↗→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒, 𝜓↗𝜑] into ax-1 | |
| 8553 | →𝜑→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒 | Modus ponens 8551, 8552 | |
| 8554 | →→𝜑→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒→→𝜑→¬¬𝜒¬¬𝜑→𝜑→¬𝜑¬𝜒 | Subs [𝜓↗→¬¬𝜒¬¬𝜑, 𝜒↗→¬𝜑¬𝜒] into ax-2 | |
| 8555 | →→𝜑→¬¬𝜒¬¬𝜑→𝜑→¬𝜑¬𝜒 | Modus ponens 8553, 8554 | |
| 8556 | →𝜑→¬𝜑¬𝜒 | Modus ponens 8550, 8555 | |
| 8557 | →→𝜑→¬𝜑¬𝜒→→𝜑¬𝜑→𝜑¬𝜒 | Subs [𝜓↗¬𝜑, 𝜒↗¬𝜒] into ax-2 | |
| 8558 | →→𝜑¬𝜑→𝜑¬𝜒 | Modus ponens 8556, 8557 | |
| 8559 | →→→𝜑¬𝜑→𝜑¬𝜒→¬𝜑→→𝜑¬𝜑→𝜑¬𝜒 | Subs [𝜑↗→→𝜑¬𝜑→𝜑¬𝜒, 𝜓↗¬𝜑] into ax-1 | |
| 8560 | →¬𝜑→→𝜑¬𝜑→𝜑¬𝜒 | Modus ponens 8558, 8559 | |
| 8561 | →→¬𝜑→→𝜑¬𝜑→𝜑¬𝜒→→¬𝜑→𝜑¬𝜑→¬𝜑→𝜑¬𝜒 | Subs [𝜑↗¬𝜑, 𝜓↗→𝜑¬𝜑, 𝜒↗→𝜑¬𝜒] into ax-2 | |
| 8562 | →→¬𝜑→𝜑¬𝜑→¬𝜑→𝜑¬𝜒 | Modus ponens 8560, 8561 | |
| 8563 | →¬𝜑→𝜑¬𝜒 | Modus ponens 414, 8562 | |
| 8564 | →→¬→𝜑¬𝜒¬→𝜑¬𝜒→¬𝜑→¬→𝜑¬𝜒¬→𝜑¬𝜒 | Subs [𝜑↗→¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜓↗¬𝜑] into ax-1 | |
| 8565 | →¬𝜑→¬→𝜑¬𝜒¬→𝜑¬𝜒 | Modus ponens 7440, 8564 | |
| 8566 | →¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒 | Subs [𝜑↗¬→𝜑¬𝜒, 𝜓↗¬𝜑] into ax-1 | |
| 8567 | →→¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒 | Subs [𝜑↗→¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒, 𝜓↗¬¬¬→𝜑¬𝜒] into ax-1 | |
| 8568 | →¬¬¬→𝜑¬𝜒→¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒 | Modus ponens 8566, 8567 | |
| 8569 | →→¬¬¬→𝜑¬𝜒→¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒 | Subs [𝜑↗¬¬¬→𝜑¬𝜒, 𝜓↗¬→𝜑¬𝜒, 𝜒↗→¬𝜑¬→𝜑¬𝜒] into ax-2 | |
| 8570 | →→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒 | Modus ponens 8568, 8569 | |
| 8571 | →¬¬¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒 | Modus ponens 7443, 8570 | |
| 8572 | →→¬𝜑→¬→𝜑¬𝜒¬→𝜑¬𝜒→→¬𝜑¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒 | Subs [𝜑↗¬𝜑, 𝜓↗¬→𝜑¬𝜒, 𝜒↗¬→𝜑¬𝜒] into ax-2 | |
| 8573 | →→¬𝜑¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒 | Modus ponens 8565, 8572 | |
| 8574 | →→→¬𝜑¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→→¬𝜑¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒 | Subs [𝜑↗→→¬𝜑¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒, 𝜓↗¬¬¬→𝜑¬𝜒] into ax-1 | |
| 8575 | →¬¬¬→𝜑¬𝜒→→¬𝜑¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒 | Modus ponens 8573, 8574 | |
| 8576 | →→¬¬¬→𝜑¬𝜒→→¬𝜑¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒→→¬¬¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒 | Subs [𝜑↗¬¬¬→𝜑¬𝜒, 𝜓↗→¬𝜑¬→𝜑¬𝜒, 𝜒↗→¬𝜑¬→𝜑¬𝜒] into ax-2 | |
| 8577 | →→¬¬¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒 | Modus ponens 8575, 8576 | |
| 8578 | →¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→𝜑¬𝜒] into ax-1 | |
| 8579 | →→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑→¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 8580 | →¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑 | Modus ponens 8578, 8579 | |
| 8581 | →→¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→𝜑¬𝜒¬𝜑] into ax-2 | |
| 8582 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑 | Modus ponens 8580, 8581 | |
| 8583 | →→¬¬¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒→→¬¬¬→𝜑¬𝜒¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒 | Subs [𝜑↗¬¬¬→𝜑¬𝜒, 𝜓↗¬𝜑, 𝜒↗¬→𝜑¬𝜒] into ax-2 | |
| 8584 | →→¬¬¬→𝜑¬𝜒¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒 | Modus ponens 8571, 8583 | |
| 8585 | →→→¬¬¬→𝜑¬𝜒¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬𝜑→→¬¬¬→𝜑¬𝜒¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒 | Subs [𝜑↗→→¬¬¬→𝜑¬𝜒¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜓↗¬𝜑] into ax-1 | |
| 8586 | →¬𝜑→→¬¬¬→𝜑¬𝜒¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒 | Modus ponens 8584, 8585 | |
| 8587 | →→¬𝜑→→¬¬¬→𝜑¬𝜒¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→𝜑¬𝜒¬𝜑, 𝜒↗→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒] into ax-2 | |
| 8588 | →→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒 | Modus ponens 8586, 8587 | |
| 8589 | →¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒 | Modus ponens 8578, 8588 | |
| 8590 | →→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒→¬𝜑→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒 | Subs [𝜑↗→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒, 𝜓↗¬𝜑] into ax-1 | |
| 8591 | →¬𝜑→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒 | Modus ponens 7468, 8590 | |
| 8592 | →→¬𝜑→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒→→¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬𝜑→→𝜑¬𝜒¬¬→𝜑¬𝜒 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜒↗→→𝜑¬𝜒¬¬→𝜑¬𝜒] into ax-2 | |
| 8593 | →→¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬𝜑→→𝜑¬𝜒¬¬→𝜑¬𝜒 | Modus ponens 8591, 8592 | |
| 8594 | →¬𝜑→→𝜑¬𝜒¬¬→𝜑¬𝜒 | Modus ponens 8589, 8593 | |
| 8595 | →→¬𝜑→→𝜑¬𝜒¬¬→𝜑¬𝜒→→¬𝜑→𝜑¬𝜒→¬𝜑¬¬→𝜑¬𝜒 | Subs [𝜑↗¬𝜑, 𝜓↗→𝜑¬𝜒, 𝜒↗¬¬→𝜑¬𝜒] into ax-2 | |
| 8596 | →→¬𝜑→𝜑¬𝜒→¬𝜑¬¬→𝜑¬𝜒 | Modus ponens 8594, 8595 | |
| 8597 | →¬𝜑¬¬→𝜑¬𝜒 | Modus ponens 8563, 8596 | |
| 8598 | →→¬𝜑¬¬→𝜑¬𝜒→¬→𝜑¬𝜒𝜑 | Subs [𝜓↗¬→𝜑¬𝜒] into ax-3 | |
| 8599 | →¬→𝜑¬𝜒𝜑 | Modus ponens 8597, 8598 | |
| 8600 | →→¬→𝜑¬𝜒𝜑→⋀𝜑𝜒→¬→𝜑¬𝜒𝜑 | Subs [𝜑↗→¬→𝜑¬𝜒𝜑, 𝜓↗⋀𝜑𝜒] into ax-1 | |
| 8601 | →⋀𝜑𝜒→¬→𝜑¬𝜒𝜑 | Modus ponens 8599, 8600 | |
| 8602 | →→⋀𝜑𝜒→¬→𝜑¬𝜒𝜑→→⋀𝜑𝜒¬→𝜑¬𝜒→⋀𝜑𝜒𝜑 | Subs [𝜑↗⋀𝜑𝜒, 𝜓↗¬→𝜑¬𝜒, 𝜒↗𝜑] into ax-2 | |
| 8603 | →→⋀𝜑𝜒¬→𝜑¬𝜒→⋀𝜑𝜒𝜑 | Modus ponens 8601, 8602 | |
| 8604 | →⋀𝜑𝜒𝜑 | Modus ponens 7480, 8603 | |
| 8605 | →↔¬→𝜑¬𝜒⋀𝜑𝜒→¬→𝜑¬𝜒⋀𝜑𝜒 | Subs [𝜑↗¬→𝜑¬𝜒, 𝜓↗⋀𝜑𝜒] into biimp | |
| 8606 | →¬→𝜑¬𝜒⋀𝜑𝜒 | Modus ponens 6605, 8605 | |
| 8607 | →→⋀𝜑𝜒𝜑→¬→𝜑¬𝜒→⋀𝜑𝜒𝜑 | Subs [𝜑↗→⋀𝜑𝜒𝜑, 𝜓↗¬→𝜑¬𝜒] into ax-1 | |
| 8608 | →¬→𝜑¬𝜒→⋀𝜑𝜒𝜑 | Modus ponens 8604, 8607 | |
| 8609 | →→¬→𝜑¬𝜒→⋀𝜑𝜒𝜑→→¬→𝜑¬𝜒⋀𝜑𝜒→¬→𝜑¬𝜒𝜑 | Subs [𝜑↗¬→𝜑¬𝜒, 𝜓↗⋀𝜑𝜒, 𝜒↗𝜑] into ax-2 | |
| 8610 | →→¬→𝜑¬𝜒⋀𝜑𝜒→¬→𝜑¬𝜒𝜑 | Modus ponens 8608, 8609 | |
| 8611 | →𝜑→𝜒¬→𝜑¬𝜒 | Subs [𝜓↗𝜒] into pm3.2im | |
| 8612 | →→¬→𝜑¬𝜒𝜑→𝜒→¬→𝜑¬𝜒𝜑 | Subs [𝜑↗→¬→𝜑¬𝜒𝜑, 𝜓↗𝜒] into ax-1 | |
| 8613 | →𝜒→¬→𝜑¬𝜒𝜑 | Modus ponens 8599, 8612 | |
| 8614 | →→𝜒→¬→𝜑¬𝜒𝜑→→𝜒¬→𝜑¬𝜒→𝜒𝜑 | Subs [𝜑↗𝜒, 𝜓↗¬→𝜑¬𝜒, 𝜒↗𝜑] into ax-2 | |
| 8615 | →→𝜒¬→𝜑¬𝜒→𝜒𝜑 | Modus ponens 8613, 8614 | |
| 8616 | →→→𝜒¬→𝜑¬𝜒→𝜒𝜑→𝜑→→𝜒¬→𝜑¬𝜒→𝜒𝜑 | Subs [𝜑↗→→𝜒¬→𝜑¬𝜒→𝜒𝜑, 𝜓↗𝜑] into ax-1 | |
| 8617 | →𝜑→→𝜒¬→𝜑¬𝜒→𝜒𝜑 | Modus ponens 8615, 8616 | |
| 8618 | →→𝜑→→𝜒¬→𝜑¬𝜒→𝜒𝜑→→𝜑→𝜒¬→𝜑¬𝜒→𝜑→𝜒𝜑 | Subs [𝜓↗→𝜒¬→𝜑¬𝜒, 𝜒↗→𝜒𝜑] into ax-2 | |
| 8619 | →→𝜑→𝜒¬→𝜑¬𝜒→𝜑→𝜒𝜑 | Modus ponens 8617, 8618 | |
| 8620 | →→→𝜑𝜒→𝜑𝜑→𝜒→→𝜑𝜒→𝜑𝜑 | Subs [𝜑↗→→𝜑𝜒→𝜑𝜑, 𝜓↗𝜒] into ax-1 | |
| 8621 | →𝜒→→𝜑𝜒→𝜑𝜑 | Modus ponens 8530, 8620 | |
| 8622 | →→𝜒→→𝜑𝜒→𝜑𝜑→→𝜒→𝜑𝜒→𝜒→𝜑𝜑 | Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑𝜑] into ax-2 | |
| 8623 | →→𝜒→𝜑𝜒→𝜒→𝜑𝜑 | Modus ponens 8621, 8622 | |
| 8624 | →𝜒→𝜑𝜑 | Modus ponens 1834, 8623 | |
| 8625 | →→𝜑→𝜒𝜑→⋀𝜑𝜓→𝜑→𝜒𝜑 | Subs [𝜑↗→𝜑→𝜒𝜑, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 8626 | →⋀𝜑𝜓→𝜑→𝜒𝜑 | Modus ponens 13, 8625 | |
| 8627 | →→⋀𝜑𝜓→𝜑→𝜒𝜑→→⋀𝜑𝜓𝜑→⋀𝜑𝜓→𝜒𝜑 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜑, 𝜒↗→𝜒𝜑] into ax-2 | |
| 8628 | →→⋀𝜑𝜓𝜑→⋀𝜑𝜓→𝜒𝜑 | Modus ponens 8626, 8627 | |
| 8629 | →⋀𝜑𝜓→𝜒𝜑 | Modus ponens simpl, 8628 | |
| 8630 | →→𝜒→𝜑𝜑→→𝜒𝜑→𝜒𝜑 | Subs [𝜑↗𝜒, 𝜓↗𝜑, 𝜒↗𝜑] into ax-2 | |
| 8631 | →→𝜒𝜑→𝜒𝜑 | Modus ponens 8624, 8630 | |
| 8632 | →→→𝜒𝜑→𝜒𝜑→⋀𝜑𝜓→→𝜒𝜑→𝜒𝜑 | Subs [𝜑↗→→𝜒𝜑→𝜒𝜑, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 8633 | →⋀𝜑𝜓→→𝜒𝜑→𝜒𝜑 | Modus ponens 8631, 8632 | |
| 8634 | →→⋀𝜑𝜓→→𝜒𝜑→𝜒𝜑→→⋀𝜑𝜓→𝜒𝜑→⋀𝜑𝜓→𝜒𝜑 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜒𝜑, 𝜒↗→𝜒𝜑] into ax-2 | |
| 8635 | →→⋀𝜑𝜓→𝜒𝜑→⋀𝜑𝜓→𝜒𝜑 | Modus ponens 8633, 8634 | |
| 8636 | →→𝜒→⋀𝜑𝜓𝜒→𝜒→𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→𝜒→⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 8637 | →𝜒→𝜒→⋀𝜑𝜓𝜒 | Modus ponens 5154, 8636 | |
| 8638 | →→𝜒→𝜒→⋀𝜑𝜓𝜒→→𝜒𝜒→𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗𝜒, 𝜒↗→⋀𝜑𝜓𝜒] into ax-2 | |
| 8639 | →→𝜒𝜒→𝜒→⋀𝜑𝜓𝜒 | Modus ponens 8637, 8638 | |
| 8640 | →→⋀𝜑𝜓→𝜒𝜑→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒, 𝜒↗𝜑] into ax-2 | |
| 8641 | →→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑 | Modus ponens 8629, 8640 | |
| 8642 | →→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑→𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑 | Subs [𝜑↗→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑, 𝜓↗𝜒] into ax-1 | |
| 8643 | →𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑 | Modus ponens 8641, 8642 | |
| 8644 | →→𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑→→𝜒→⋀𝜑𝜓𝜒→𝜒→⋀𝜑𝜓𝜑 | Subs [𝜑↗𝜒, 𝜓↗→⋀𝜑𝜓𝜒, 𝜒↗→⋀𝜑𝜓𝜑] into ax-2 | |
| 8645 | →→𝜒→⋀𝜑𝜓𝜒→𝜒→⋀𝜑𝜓𝜑 | Modus ponens 8643, 8644 | |
| 8646 | →𝜒→⋀𝜑𝜓𝜑 | Modus ponens 5154, 8645 | |
| 8647 | →⋀𝜑𝜓→𝜒⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒] into ax-1 | |
| 8648 | →→⋀𝜑𝜓→𝜒⋀𝜑𝜓→⋀𝜑𝜓→⋀𝜑𝜓→𝜒⋀𝜑𝜓 | Subs [𝜑↗→⋀𝜑𝜓→𝜒⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 8649 | →⋀𝜑𝜓→⋀𝜑𝜓→𝜒⋀𝜑𝜓 | Modus ponens 8647, 8648 | |
| 8650 | →→⋀𝜑𝜓→⋀𝜑𝜓→𝜒⋀𝜑𝜓→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→𝜒⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗→𝜒⋀𝜑𝜓] into ax-2 | |
| 8651 | →→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→𝜒⋀𝜑𝜓 | Modus ponens 8649, 8650 | |
| 8652 | →→𝜒→⋀𝜑𝜓𝜑→→𝜒⋀𝜑𝜓→𝜒𝜑 | Subs [𝜑↗𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜑] into ax-2 | |
| 8653 | →→𝜒⋀𝜑𝜓→𝜒𝜑 | Modus ponens 8646, 8652 | |
| 8654 | →→→𝜒⋀𝜑𝜓→𝜒𝜑→⋀𝜑𝜓→→𝜒⋀𝜑𝜓→𝜒𝜑 | Subs [𝜑↗→→𝜒⋀𝜑𝜓→𝜒𝜑, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 8655 | →⋀𝜑𝜓→→𝜒⋀𝜑𝜓→𝜒𝜑 | Modus ponens 8653, 8654 | |
| 8656 | →→⋀𝜑𝜓→→𝜒⋀𝜑𝜓→𝜒𝜑→→⋀𝜑𝜓→𝜒⋀𝜑𝜓→⋀𝜑𝜓→𝜒𝜑 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜒⋀𝜑𝜓, 𝜒↗→𝜒𝜑] into ax-2 | |
| 8657 | →→⋀𝜑𝜓→𝜒⋀𝜑𝜓→⋀𝜑𝜓→𝜒𝜑 | Modus ponens 8655, 8656 | |
| 8658 | →→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑→¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑 | Subs [𝜑↗→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑, 𝜓↗¬¬𝜒] into ax-1 | |
| 8659 | →¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑 | Modus ponens 8641, 8658 | |
| 8660 | →→¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑→→¬¬𝜒→⋀𝜑𝜓𝜒→¬¬𝜒→⋀𝜑𝜓𝜑 | Subs [𝜑↗¬¬𝜒, 𝜓↗→⋀𝜑𝜓𝜒, 𝜒↗→⋀𝜑𝜓𝜑] into ax-2 | |
| 8661 | →→¬¬𝜒→⋀𝜑𝜓𝜒→¬¬𝜒→⋀𝜑𝜓𝜑 | Modus ponens 8659, 8660 | |
| 8662 | →¬¬𝜒→⋀𝜑𝜓𝜑 | Modus ponens 5159, 8661 | |
| 8663 | →→¬¬𝜒→⋀𝜑𝜓𝜑→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜑 | Subs [𝜑↗¬¬𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜑] into ax-2 | |
| 8664 | →→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜑 | Modus ponens 8662, 8663 | |
| 8665 | →→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜑→⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜑 | Subs [𝜑↗→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜑, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 8666 | →⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜑 | Modus ponens 8664, 8665 | |
| 8667 | →→⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜑→→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒𝜑 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒⋀𝜑𝜓, 𝜒↗→¬¬𝜒𝜑] into ax-2 | |
| 8668 | →→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒𝜑 | Modus ponens 8666, 8667 | |
| 8669 | →⋀𝜑𝜓→¬¬𝜒𝜑 | Modus ponens 5167, 8668 | |
| 8670 | →→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑→⋀𝜑𝜓→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑 | Subs [𝜑↗→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 8671 | →⋀𝜑𝜓→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑 | Modus ponens 8545, 8670 | |
| 8672 | →→⋀𝜑𝜓→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑→→⋀𝜑𝜓→¬¬𝜒𝜑→⋀𝜑𝜓→¬¬𝜒¬¬𝜑 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒𝜑, 𝜒↗→¬¬𝜒¬¬𝜑] into ax-2 | |
| 8673 | →→⋀𝜑𝜓→¬¬𝜒𝜑→⋀𝜑𝜓→¬¬𝜒¬¬𝜑 | Modus ponens 8671, 8672 | |
| 8674 | →⋀𝜑𝜓→¬¬𝜒¬¬𝜑 | Modus ponens 8669, 8673 | |
| 8675 | →→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒→⋀𝜑𝜓→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒 | Subs [𝜑↗→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 8676 | →⋀𝜑𝜓→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒 | Modus ponens 8551, 8675 | |
| 8677 | →→⋀𝜑𝜓→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒→→⋀𝜑𝜓→¬¬𝜒¬¬𝜑→⋀𝜑𝜓→¬𝜑¬𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒¬¬𝜑, 𝜒↗→¬𝜑¬𝜒] into ax-2 | |
| 8678 | →→⋀𝜑𝜓→¬¬𝜒¬¬𝜑→⋀𝜑𝜓→¬𝜑¬𝜒 | Modus ponens 8676, 8677 | |
| 8679 | →⋀𝜑𝜓→¬𝜑¬𝜒 | Modus ponens 8674, 8678 | |
| 8680 | →¬𝜑→⋀𝜑𝜓¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 8681 | →→¬𝜑→⋀𝜑𝜓¬𝜑→¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜑 | Subs [𝜑↗→¬𝜑→⋀𝜑𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 8682 | →¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜑 | Modus ponens 8680, 8681 | |
| 8683 | →→¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀𝜑𝜓¬𝜑] into ax-2 | |
| 8684 | →→¬𝜑¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜑 | Modus ponens 8682, 8683 | |
| 8685 | →→⋀𝜑𝜓→¬𝜑¬𝜒→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬𝜑, 𝜒↗¬𝜒] into ax-2 | |
| 8686 | →→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜒 | Modus ponens 8679, 8685 | |
| 8687 | →→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜒→¬𝜑→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜑] into ax-1 | |
| 8688 | →¬𝜑→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜒 | Modus ponens 8686, 8687 | |
| 8689 | →→¬𝜑→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜒→→¬𝜑→⋀𝜑𝜓¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀𝜑𝜓¬𝜑, 𝜒↗→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 8690 | →→¬𝜑→⋀𝜑𝜓¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜒 | Modus ponens 8688, 8689 | |
| 8691 | →¬𝜑→⋀𝜑𝜓¬𝜒 | Modus ponens 8680, 8690 | |
| 8692 | →→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬𝜑→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜑] into ax-1 | |
| 8693 | →¬𝜑→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Modus ponens 5208, 8692 | |
| 8694 | →¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜑] into ax-1 | |
| 8695 | →→¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1 | |
| 8696 | →¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8694, 8695 | |
| 8697 | →→¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗→¬𝜑¬→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 8698 | →→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8696, 8697 | |
| 8699 | →¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒 | Modus ponens 5211, 8698 | |
| 8700 | →→¬𝜑→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗¬→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 8701 | →→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8693, 8700 | |
| 8702 | →→→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1 | |
| 8703 | →¬¬¬→⋀𝜑𝜓¬𝜒→→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8701, 8702 | |
| 8704 | →→¬¬¬→⋀𝜑𝜓¬𝜒→→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗→¬𝜑¬→⋀𝜑𝜓¬𝜒, 𝜒↗→¬𝜑¬→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 8705 | →→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8703, 8704 | |
| 8706 | →¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1 | |
| 8707 | →→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 8708 | →¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑 | Modus ponens 8706, 8707 | |
| 8709 | →→¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑] into ax-2 | |
| 8710 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑 | Modus ponens 8708, 8709 | |
| 8711 | →→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜑, 𝜒↗¬→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 8712 | →→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8699, 8711 | |
| 8713 | →→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜑] into ax-1 | |
| 8714 | →¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8712, 8713 | |
| 8715 | →→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 8716 | →→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8714, 8715 | |
| 8717 | →¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8706, 8716 | |
| 8718 | →→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜑] into ax-1 | |
| 8719 | →¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒 | Modus ponens 5236, 8718 | |
| 8720 | →→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬𝜑→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜒↗→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 8721 | →→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬𝜑→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8719, 8720 | |
| 8722 | →¬𝜑→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8717, 8721 | |
| 8723 | →→¬𝜑→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→→¬𝜑→⋀𝜑𝜓¬𝜒→¬𝜑¬¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀𝜑𝜓¬𝜒, 𝜒↗¬¬→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 8724 | →→¬𝜑→⋀𝜑𝜓¬𝜒→¬𝜑¬¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8722, 8723 | |
| 8725 | →¬𝜑¬¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8691, 8724 | |
| 8726 | →→¬𝜑¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒𝜑 | Subs [𝜓↗¬→⋀𝜑𝜓¬𝜒] into ax-3 | |
| 8727 | →¬→⋀𝜑𝜓¬𝜒𝜑 | Modus ponens 8725, 8726 | |
| 8728 | →→¬→⋀𝜑𝜓¬𝜒𝜑→⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒𝜑 | Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 8729 | →⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒𝜑 | Modus ponens 8727, 8728 | |
| 8730 | →→⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒𝜑→→⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒𝜑 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗𝜑] into ax-2 | |
| 8731 | →→⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒𝜑 | Modus ponens 8729, 8730 | |
| 8732 | →⋀⋀𝜑𝜓𝜒𝜑 | Modus ponens 5248, 8731 | simpll |
| 8733 | →→𝜓→𝜒𝜓→→𝜓𝜒→𝜓𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗𝜓] into ax-2 | |
| 8734 | →→𝜓𝜒→𝜓𝜓 | Modus ponens 5350, 8733 | |
| 8735 | →→→𝜓𝜒→𝜓𝜓→¬¬𝜒→→𝜓𝜒→𝜓𝜓 | Subs [𝜑↗→→𝜓𝜒→𝜓𝜓, 𝜓↗¬¬𝜒] into ax-1 | |
| 8736 | →¬¬𝜒→→𝜓𝜒→𝜓𝜓 | Modus ponens 8734, 8735 | |
| 8737 | →→¬¬𝜒→→𝜓𝜒→𝜓𝜓→→¬¬𝜒→𝜓𝜒→¬¬𝜒→𝜓𝜓 | Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→𝜓𝜓] into ax-2 | |
| 8738 | →→¬¬𝜒→𝜓𝜒→¬¬𝜒→𝜓𝜓 | Modus ponens 8736, 8737 | |
| 8739 | →¬¬𝜒→𝜓𝜓 | Modus ponens 5367, 8738 | |
| 8740 | →→¬¬𝜒→𝜓𝜓→→¬¬𝜒𝜓→¬¬𝜒𝜓 | Subs [𝜑↗¬¬𝜒, 𝜒↗𝜓] into ax-2 | |
| 8741 | →→¬¬𝜒𝜓→¬¬𝜒𝜓 | Modus ponens 8739, 8740 | |
| 8742 | →→→¬¬𝜒𝜓→¬¬𝜒𝜓→𝜓→→¬¬𝜒𝜓→¬¬𝜒𝜓 | Subs [𝜑↗→→¬¬𝜒𝜓→¬¬𝜒𝜓] into ax-1 | |
| 8743 | →𝜓→→¬¬𝜒𝜓→¬¬𝜒𝜓 | Modus ponens 8741, 8742 | |
| 8744 | →→𝜓→→¬¬𝜒𝜓→¬¬𝜒𝜓→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒𝜓 | Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒𝜓, 𝜒↗→¬¬𝜒𝜓] into ax-2 | |
| 8745 | →→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒𝜓 | Modus ponens 8743, 8744 | |
| 8746 | →→𝜓¬¬𝜓→¬¬𝜒→𝜓¬¬𝜓 | Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜒] into ax-1 | |
| 8747 | →¬¬𝜒→𝜓¬¬𝜓 | Modus ponens 448, 8746 | |
| 8748 | →→¬¬𝜒→𝜓¬¬𝜓→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓 | Subs [𝜑↗¬¬𝜒, 𝜒↗¬¬𝜓] into ax-2 | |
| 8749 | →→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓 | Modus ponens 8747, 8748 | |
| 8750 | →→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓→𝜓→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓 | Subs [𝜑↗→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓] into ax-1 | |
| 8751 | →𝜓→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓 | Modus ponens 8749, 8750 | |
| 8752 | →→𝜓→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒¬¬𝜓 | Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒𝜓, 𝜒↗→¬¬𝜒¬¬𝜓] into ax-2 | |
| 8753 | →→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒¬¬𝜓 | Modus ponens 8751, 8752 | |
| 8754 | →𝜓→¬¬𝜒¬¬𝜓 | Modus ponens 5375, 8753 | |
| 8755 | →→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬𝜓] into ax-3 | |
| 8756 | →→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒→𝜓→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒 | Subs [𝜑↗→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒] into ax-1 | |
| 8757 | →𝜓→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒 | Modus ponens 8755, 8756 | |
| 8758 | →→𝜓→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒→→𝜓→¬¬𝜒¬¬𝜓→𝜓→¬𝜓¬𝜒 | Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒¬¬𝜓, 𝜒↗→¬𝜓¬𝜒] into ax-2 | |
| 8759 | →→𝜓→¬¬𝜒¬¬𝜓→𝜓→¬𝜓¬𝜒 | Modus ponens 8757, 8758 | |
| 8760 | →𝜓→¬𝜓¬𝜒 | Modus ponens 8754, 8759 | |
| 8761 | →→𝜓→¬𝜓¬𝜒→→𝜓¬𝜓→𝜓¬𝜒 | Subs [𝜑↗𝜓, 𝜓↗¬𝜓, 𝜒↗¬𝜒] into ax-2 | |
| 8762 | →→𝜓¬𝜓→𝜓¬𝜒 | Modus ponens 8760, 8761 | |
| 8763 | →→→𝜓¬𝜓→𝜓¬𝜒→¬𝜓→→𝜓¬𝜓→𝜓¬𝜒 | Subs [𝜑↗→→𝜓¬𝜓→𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1 | |
| 8764 | →¬𝜓→→𝜓¬𝜓→𝜓¬𝜒 | Modus ponens 8762, 8763 | |
| 8765 | →→¬𝜓→→𝜓¬𝜓→𝜓¬𝜒→→¬𝜓→𝜓¬𝜓→¬𝜓→𝜓¬𝜒 | Subs [𝜑↗¬𝜓, 𝜓↗→𝜓¬𝜓, 𝜒↗→𝜓¬𝜒] into ax-2 | |
| 8766 | →→¬𝜓→𝜓¬𝜓→¬𝜓→𝜓¬𝜒 | Modus ponens 8764, 8765 | |
| 8767 | →¬𝜓→𝜓¬𝜒 | Modus ponens 5845, 8766 | |
| 8768 | →→¬→𝜓¬𝜒¬→𝜓¬𝜒→¬𝜓→¬→𝜓¬𝜒¬→𝜓¬𝜒 | Subs [𝜑↗→¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1 | |
| 8769 | →¬𝜓→¬→𝜓¬𝜒¬→𝜓¬𝜒 | Modus ponens 5416, 8768 | |
| 8770 | →¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒 | Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1 | |
| 8771 | →→¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒 | Subs [𝜑↗→¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1 | |
| 8772 | →¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒 | Modus ponens 8770, 8771 | |
| 8773 | →→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒 | Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→¬𝜓¬→𝜓¬𝜒] into ax-2 | |
| 8774 | →→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒 | Modus ponens 8772, 8773 | |
| 8775 | →¬¬¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒 | Modus ponens 5419, 8774 | |
| 8776 | →→¬𝜓→¬→𝜓¬𝜒¬→𝜓¬𝜒→→¬𝜓¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒 | Subs [𝜑↗¬𝜓, 𝜓↗¬→𝜓¬𝜒, 𝜒↗¬→𝜓¬𝜒] into ax-2 | |
| 8777 | →→¬𝜓¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒 | Modus ponens 8769, 8776 | |
| 8778 | →→→¬𝜓¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→→¬𝜓¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒 | Subs [𝜑↗→→¬𝜓¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1 | |
| 8779 | →¬¬¬→𝜓¬𝜒→→¬𝜓¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒 | Modus ponens 8777, 8778 | |
| 8780 | →→¬¬¬→𝜓¬𝜒→→¬𝜓¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒 | Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗→¬𝜓¬→𝜓¬𝜒, 𝜒↗→¬𝜓¬→𝜓¬𝜒] into ax-2 | |
| 8781 | →→¬¬¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒 | Modus ponens 8779, 8780 | |
| 8782 | →¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1 | |
| 8783 | →→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓→¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 8784 | →¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓 | Modus ponens 8782, 8783 | |
| 8785 | →→¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→𝜓¬𝜒¬𝜓] into ax-2 | |
| 8786 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓 | Modus ponens 8784, 8785 | |
| 8787 | →→¬¬¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗¬𝜓, 𝜒↗¬→𝜓¬𝜒] into ax-2 | |
| 8788 | →→¬¬¬→𝜓¬𝜒¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Modus ponens 8775, 8787 | |
| 8789 | →→→¬¬¬→𝜓¬𝜒¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬𝜓→→¬¬¬→𝜓¬𝜒¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Subs [𝜑↗→→¬¬¬→𝜓¬𝜒¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1 | |
| 8790 | →¬𝜓→→¬¬¬→𝜓¬𝜒¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Modus ponens 8788, 8789 | |
| 8791 | →→¬𝜓→→¬¬¬→𝜓¬𝜒¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜓¬𝜒¬𝜓, 𝜒↗→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒] into ax-2 | |
| 8792 | →→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Modus ponens 8790, 8791 | |
| 8793 | →¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Modus ponens 8782, 8792 | |
| 8794 | →→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→¬𝜓→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒 | Subs [𝜑↗→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1 | |
| 8795 | →¬𝜓→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒 | Modus ponens 5444, 8794 | |
| 8796 | →→¬𝜓→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→→¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬𝜓→→𝜓¬𝜒¬¬→𝜓¬𝜒 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜒↗→→𝜓¬𝜒¬¬→𝜓¬𝜒] into ax-2 | |
| 8797 | →→¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬𝜓→→𝜓¬𝜒¬¬→𝜓¬𝜒 | Modus ponens 8795, 8796 | |
| 8798 | →¬𝜓→→𝜓¬𝜒¬¬→𝜓¬𝜒 | Modus ponens 8793, 8797 | |
| 8799 | →→¬𝜓→→𝜓¬𝜒¬¬→𝜓¬𝜒→→¬𝜓→𝜓¬𝜒→¬𝜓¬¬→𝜓¬𝜒 | Subs [𝜑↗¬𝜓, 𝜓↗→𝜓¬𝜒, 𝜒↗¬¬→𝜓¬𝜒] into ax-2 | |
| 8800 | →→¬𝜓→𝜓¬𝜒→¬𝜓¬¬→𝜓¬𝜒 | Modus ponens 8798, 8799 | |
| 8801 | →¬𝜓¬¬→𝜓¬𝜒 | Modus ponens 8767, 8800 | |
| 8802 | →→¬𝜓¬¬→𝜓¬𝜒→¬→𝜓¬𝜒𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→𝜓¬𝜒] into ax-3 | |
| 8803 | →¬→𝜓¬𝜒𝜓 | Modus ponens 8801, 8802 | |
| 8804 | →→¬→𝜓¬𝜒𝜓→⋀𝜓𝜒→¬→𝜓¬𝜒𝜓 | Subs [𝜑↗→¬→𝜓¬𝜒𝜓, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 8805 | →⋀𝜓𝜒→¬→𝜓¬𝜒𝜓 | Modus ponens 8803, 8804 | |
| 8806 | →→⋀𝜓𝜒→¬→𝜓¬𝜒𝜓→→⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒𝜓 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗𝜓] into ax-2 | |
| 8807 | →→⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒𝜓 | Modus ponens 8805, 8806 | |
| 8808 | →→⋀𝜓𝜒𝜓→¬→𝜓¬𝜒→⋀𝜓𝜒𝜓 | Subs [𝜑↗→⋀𝜓𝜒𝜓, 𝜓↗¬→𝜓¬𝜒] into ax-1 | |
| 8809 | →¬→𝜓¬𝜒→⋀𝜓𝜒𝜓 | Modus ponens 6072, 8808 | |
| 8810 | →→¬→𝜓¬𝜒→⋀𝜓𝜒𝜓→→¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒𝜓 | Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗𝜓] into ax-2 | |
| 8811 | →→¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒𝜓 | Modus ponens 8809, 8810 | |
| 8812 | →→¬→𝜓¬𝜒𝜓→𝜒→¬→𝜓¬𝜒𝜓 | Subs [𝜑↗→¬→𝜓¬𝜒𝜓, 𝜓↗𝜒] into ax-1 | |
| 8813 | →𝜒→¬→𝜓¬𝜒𝜓 | Modus ponens 8803, 8812 | |
| 8814 | →→𝜒→¬→𝜓¬𝜒𝜓→→𝜒¬→𝜓¬𝜒→𝜒𝜓 | Subs [𝜑↗𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗𝜓] into ax-2 | |
| 8815 | →→𝜒¬→𝜓¬𝜒→𝜒𝜓 | Modus ponens 8813, 8814 | |
| 8816 | →→→𝜒¬→𝜓¬𝜒→𝜒𝜓→𝜓→→𝜒¬→𝜓¬𝜒→𝜒𝜓 | Subs [𝜑↗→→𝜒¬→𝜓¬𝜒→𝜒𝜓] into ax-1 | |
| 8817 | →𝜓→→𝜒¬→𝜓¬𝜒→𝜒𝜓 | Modus ponens 8815, 8816 | |
| 8818 | →→𝜓→→𝜒¬→𝜓¬𝜒→𝜒𝜓→→𝜓→𝜒¬→𝜓¬𝜒→𝜓→𝜒𝜓 | Subs [𝜑↗𝜓, 𝜓↗→𝜒¬→𝜓¬𝜒, 𝜒↗→𝜒𝜓] into ax-2 | |
| 8819 | →→𝜓→𝜒¬→𝜓¬𝜒→𝜓→𝜒𝜓 | Modus ponens 8817, 8818 | |
| 8820 | →→→𝜓𝜒→𝜓𝜓→𝜒→→𝜓𝜒→𝜓𝜓 | Subs [𝜑↗→→𝜓𝜒→𝜓𝜓, 𝜓↗𝜒] into ax-1 | |
| 8821 | →𝜒→→𝜓𝜒→𝜓𝜓 | Modus ponens 8734, 8820 | |
| 8822 | →→𝜒→→𝜓𝜒→𝜓𝜓→→𝜒→𝜓𝜒→𝜒→𝜓𝜓 | Subs [𝜑↗𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→𝜓𝜓] into ax-2 | |
| 8823 | →→𝜒→𝜓𝜒→𝜒→𝜓𝜓 | Modus ponens 8821, 8822 | |
| 8824 | →𝜒→𝜓𝜓 | Modus ponens 5362, 8823 | |
| 8825 | →→𝜓→𝜒𝜓→⋀𝜑𝜓→𝜓→𝜒𝜓 | Subs [𝜑↗→𝜓→𝜒𝜓, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 8826 | →⋀𝜑𝜓→𝜓→𝜒𝜓 | Modus ponens 5350, 8825 | |
| 8827 | →→⋀𝜑𝜓→𝜓→𝜒𝜓→→⋀𝜑𝜓𝜓→⋀𝜑𝜓→𝜒𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜒↗→𝜒𝜓] into ax-2 | |
| 8828 | →→⋀𝜑𝜓𝜓→⋀𝜑𝜓→𝜒𝜓 | Modus ponens 8826, 8827 | |
| 8829 | →⋀𝜑𝜓→𝜒𝜓 | Modus ponens simpr, 8828 | |
| 8830 | →→𝜒→𝜓𝜓→→𝜒𝜓→𝜒𝜓 | Subs [𝜑↗𝜒, 𝜒↗𝜓] into ax-2 | |
| 8831 | →→𝜒𝜓→𝜒𝜓 | Modus ponens 8824, 8830 | |
| 8832 | →→→𝜒𝜓→𝜒𝜓→⋀𝜑𝜓→→𝜒𝜓→𝜒𝜓 | Subs [𝜑↗→→𝜒𝜓→𝜒𝜓, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 8833 | →⋀𝜑𝜓→→𝜒𝜓→𝜒𝜓 | Modus ponens 8831, 8832 | |
| 8834 | →→⋀𝜑𝜓→→𝜒𝜓→𝜒𝜓→→⋀𝜑𝜓→𝜒𝜓→⋀𝜑𝜓→𝜒𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜒𝜓, 𝜒↗→𝜒𝜓] into ax-2 | |
| 8835 | →→⋀𝜑𝜓→𝜒𝜓→⋀𝜑𝜓→𝜒𝜓 | Modus ponens 8833, 8834 | |
| 8836 | →→⋀𝜑𝜓→𝜒𝜓→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒, 𝜒↗𝜓] into ax-2 | |
| 8837 | →→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓 | Modus ponens 8829, 8836 | |
| 8838 | →→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓→𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓 | Subs [𝜑↗→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓, 𝜓↗𝜒] into ax-1 | |
| 8839 | →𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓 | Modus ponens 8837, 8838 | |
| 8840 | →→𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓→→𝜒→⋀𝜑𝜓𝜒→𝜒→⋀𝜑𝜓𝜓 | Subs [𝜑↗𝜒, 𝜓↗→⋀𝜑𝜓𝜒, 𝜒↗→⋀𝜑𝜓𝜓] into ax-2 | |
| 8841 | →→𝜒→⋀𝜑𝜓𝜒→𝜒→⋀𝜑𝜓𝜓 | Modus ponens 8839, 8840 | |
| 8842 | →𝜒→⋀𝜑𝜓𝜓 | Modus ponens 5154, 8841 | |
| 8843 | →→𝜒→⋀𝜑𝜓𝜓→→𝜒⋀𝜑𝜓→𝜒𝜓 | Subs [𝜑↗𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜓] into ax-2 | |
| 8844 | →→𝜒⋀𝜑𝜓→𝜒𝜓 | Modus ponens 8842, 8843 | |
| 8845 | →→→𝜒⋀𝜑𝜓→𝜒𝜓→⋀𝜑𝜓→→𝜒⋀𝜑𝜓→𝜒𝜓 | Subs [𝜑↗→→𝜒⋀𝜑𝜓→𝜒𝜓, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 8846 | →⋀𝜑𝜓→→𝜒⋀𝜑𝜓→𝜒𝜓 | Modus ponens 8844, 8845 | |
| 8847 | →→⋀𝜑𝜓→→𝜒⋀𝜑𝜓→𝜒𝜓→→⋀𝜑𝜓→𝜒⋀𝜑𝜓→⋀𝜑𝜓→𝜒𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜒⋀𝜑𝜓, 𝜒↗→𝜒𝜓] into ax-2 | |
| 8848 | →→⋀𝜑𝜓→𝜒⋀𝜑𝜓→⋀𝜑𝜓→𝜒𝜓 | Modus ponens 8846, 8847 | |
| 8849 | →→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓→¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓 | Subs [𝜑↗→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓, 𝜓↗¬¬𝜒] into ax-1 | |
| 8850 | →¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓 | Modus ponens 8837, 8849 | |
| 8851 | →→¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓→→¬¬𝜒→⋀𝜑𝜓𝜒→¬¬𝜒→⋀𝜑𝜓𝜓 | Subs [𝜑↗¬¬𝜒, 𝜓↗→⋀𝜑𝜓𝜒, 𝜒↗→⋀𝜑𝜓𝜓] into ax-2 | |
| 8852 | →→¬¬𝜒→⋀𝜑𝜓𝜒→¬¬𝜒→⋀𝜑𝜓𝜓 | Modus ponens 8850, 8851 | |
| 8853 | →¬¬𝜒→⋀𝜑𝜓𝜓 | Modus ponens 5159, 8852 | |
| 8854 | →→¬¬𝜒→⋀𝜑𝜓𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜓 | Subs [𝜑↗¬¬𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜓] into ax-2 | |
| 8855 | →→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜓 | Modus ponens 8853, 8854 | |
| 8856 | →→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜓→⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜓 | Subs [𝜑↗→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜓, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 8857 | →⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜓 | Modus ponens 8855, 8856 | |
| 8858 | →→⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜓→→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒⋀𝜑𝜓, 𝜒↗→¬¬𝜒𝜓] into ax-2 | |
| 8859 | →→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒𝜓 | Modus ponens 8857, 8858 | |
| 8860 | →⋀𝜑𝜓→¬¬𝜒𝜓 | Modus ponens 5167, 8859 | |
| 8861 | →→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓→⋀𝜑𝜓→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓 | Subs [𝜑↗→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 8862 | →⋀𝜑𝜓→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓 | Modus ponens 8749, 8861 | |
| 8863 | →→⋀𝜑𝜓→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓→→⋀𝜑𝜓→¬¬𝜒𝜓→⋀𝜑𝜓→¬¬𝜒¬¬𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒𝜓, 𝜒↗→¬¬𝜒¬¬𝜓] into ax-2 | |
| 8864 | →→⋀𝜑𝜓→¬¬𝜒𝜓→⋀𝜑𝜓→¬¬𝜒¬¬𝜓 | Modus ponens 8862, 8863 | |
| 8865 | →⋀𝜑𝜓→¬¬𝜒¬¬𝜓 | Modus ponens 8860, 8864 | |
| 8866 | →→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒→⋀𝜑𝜓→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒 | Subs [𝜑↗→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 8867 | →⋀𝜑𝜓→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒 | Modus ponens 8755, 8866 | |
| 8868 | →→⋀𝜑𝜓→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒→→⋀𝜑𝜓→¬¬𝜒¬¬𝜓→⋀𝜑𝜓→¬𝜓¬𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒¬¬𝜓, 𝜒↗→¬𝜓¬𝜒] into ax-2 | |
| 8869 | →→⋀𝜑𝜓→¬¬𝜒¬¬𝜓→⋀𝜑𝜓→¬𝜓¬𝜒 | Modus ponens 8867, 8868 | |
| 8870 | →⋀𝜑𝜓→¬𝜓¬𝜒 | Modus ponens 8865, 8869 | |
| 8871 | →¬𝜓→⋀𝜑𝜓¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 8872 | →→¬𝜓→⋀𝜑𝜓¬𝜓→¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜓 | Subs [𝜑↗→¬𝜓→⋀𝜑𝜓¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 8873 | →¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜓 | Modus ponens 8871, 8872 | |
| 8874 | →→¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀𝜑𝜓¬𝜓] into ax-2 | |
| 8875 | →→¬𝜓¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜓 | Modus ponens 8873, 8874 | |
| 8876 | →→⋀𝜑𝜓→¬𝜓¬𝜒→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬𝜓, 𝜒↗¬𝜒] into ax-2 | |
| 8877 | →→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜒 | Modus ponens 8870, 8876 | |
| 8878 | →→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜒→¬𝜓→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1 | |
| 8879 | →¬𝜓→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜒 | Modus ponens 8877, 8878 | |
| 8880 | →→¬𝜓→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜒→→¬𝜓→⋀𝜑𝜓¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜑𝜓¬𝜓, 𝜒↗→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 8881 | →→¬𝜓→⋀𝜑𝜓¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜒 | Modus ponens 8879, 8880 | |
| 8882 | →¬𝜓→⋀𝜑𝜓¬𝜒 | Modus ponens 8871, 8881 | |
| 8883 | →→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬𝜓→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1 | |
| 8884 | →¬𝜓→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Modus ponens 5208, 8883 | |
| 8885 | →¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1 | |
| 8886 | →→¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1 | |
| 8887 | →¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8885, 8886 | |
| 8888 | →→¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗→¬𝜓¬→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 8889 | →→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8887, 8888 | |
| 8890 | →¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒 | Modus ponens 5211, 8889 | |
| 8891 | →→¬𝜓→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗¬→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 8892 | →→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8884, 8891 | |
| 8893 | →→→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1 | |
| 8894 | →¬¬¬→⋀𝜑𝜓¬𝜒→→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8892, 8893 | |
| 8895 | →→¬¬¬→⋀𝜑𝜓¬𝜒→→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗→¬𝜓¬→⋀𝜑𝜓¬𝜒, 𝜒↗→¬𝜓¬→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 8896 | →→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8894, 8895 | |
| 8897 | →¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1 | |
| 8898 | →→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 8899 | →¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓 | Modus ponens 8897, 8898 | |
| 8900 | →→¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓] into ax-2 | |
| 8901 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓 | Modus ponens 8899, 8900 | |
| 8902 | →→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜓, 𝜒↗¬→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 8903 | →→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8890, 8902 | |
| 8904 | →→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1 | |
| 8905 | →¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8903, 8904 | |
| 8906 | →→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 8907 | →→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8905, 8906 | |
| 8908 | →¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8897, 8907 | |
| 8909 | →→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1 | |
| 8910 | →¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒 | Modus ponens 5236, 8909 | |
| 8911 | →→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬𝜓→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜒↗→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 8912 | →→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬𝜓→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8910, 8911 | |
| 8913 | →¬𝜓→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8908, 8912 | |
| 8914 | →→¬𝜓→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→→¬𝜓→⋀𝜑𝜓¬𝜒→¬𝜓¬¬→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜑𝜓¬𝜒, 𝜒↗¬¬→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 8915 | →→¬𝜓→⋀𝜑𝜓¬𝜒→¬𝜓¬¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8913, 8914 | |
| 8916 | →¬𝜓¬¬→⋀𝜑𝜓¬𝜒 | Modus ponens 8882, 8915 | |
| 8917 | →→¬𝜓¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→⋀𝜑𝜓¬𝜒] into ax-3 | |
| 8918 | →¬→⋀𝜑𝜓¬𝜒𝜓 | Modus ponens 8916, 8917 | |
| 8919 | →→¬→⋀𝜑𝜓¬𝜒𝜓→⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒𝜓 | Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 8920 | →⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒𝜓 | Modus ponens 8918, 8919 | |
| 8921 | →→⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒𝜓→→⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒𝜓 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗𝜓] into ax-2 | |
| 8922 | →→⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒𝜓 | Modus ponens 8920, 8921 | |
| 8923 | →⋀⋀𝜑𝜓𝜒𝜓 | Modus ponens 5248, 8922 | simplr |
| 8924 | →→𝜓→𝜑𝜓→⋀𝜓𝜒→𝜓→𝜑𝜓 | Subs [𝜑↗→𝜓→𝜑𝜓, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 8925 | →⋀𝜓𝜒→𝜓→𝜑𝜓 | Modus ponens 208, 8924 | |
| 8926 | →→⋀𝜓𝜒→𝜓→𝜑𝜓→→⋀𝜓𝜒𝜓→⋀𝜓𝜒→𝜑𝜓 | Subs [𝜑↗⋀𝜓𝜒, 𝜒↗→𝜑𝜓] into ax-2 | |
| 8927 | →→⋀𝜓𝜒𝜓→⋀𝜓𝜒→𝜑𝜓 | Modus ponens 8925, 8926 | |
| 8928 | →⋀𝜓𝜒→𝜑𝜓 | Modus ponens 6072, 8927 | |
| 8929 | ↔⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜑] into df-an | |
| 8930 | →→𝜑→⋀𝜓𝜒𝜑→¬¬𝜑→𝜑→⋀𝜓𝜒𝜑 | Subs [𝜑↗→𝜑→⋀𝜓𝜒𝜑, 𝜓↗¬¬𝜑] into ax-1 | |
| 8931 | →¬¬𝜑→𝜑→⋀𝜓𝜒𝜑 | Modus ponens 5462, 8930 | |
| 8932 | →→¬¬𝜑→𝜑→⋀𝜓𝜒𝜑→→¬¬𝜑𝜑→¬¬𝜑→⋀𝜓𝜒𝜑 | Subs [𝜑↗¬¬𝜑, 𝜓↗𝜑, 𝜒↗→⋀𝜓𝜒𝜑] into ax-2 | |
| 8933 | →→¬¬𝜑𝜑→¬¬𝜑→⋀𝜓𝜒𝜑 | Modus ponens 8931, 8932 | |
| 8934 | →¬¬𝜑→⋀𝜓𝜒𝜑 | Modus ponens notnotr, 8933 | |
| 8935 | →→⋀𝜓𝜒→𝜑𝜓→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2 | |
| 8936 | →→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓 | Modus ponens 8928, 8935 | |
| 8937 | →→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓→¬¬𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓 | Subs [𝜑↗→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓, 𝜓↗¬¬𝜑] into ax-1 | |
| 8938 | →¬¬𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓 | Modus ponens 8936, 8937 | |
| 8939 | →→¬¬𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓→→¬¬𝜑→⋀𝜓𝜒𝜑→¬¬𝜑→⋀𝜓𝜒𝜓 | Subs [𝜑↗¬¬𝜑, 𝜓↗→⋀𝜓𝜒𝜑, 𝜒↗→⋀𝜓𝜒𝜓] into ax-2 | |
| 8940 | →→¬¬𝜑→⋀𝜓𝜒𝜑→¬¬𝜑→⋀𝜓𝜒𝜓 | Modus ponens 8938, 8939 | |
| 8941 | →¬¬𝜑→⋀𝜓𝜒𝜓 | Modus ponens 8934, 8940 | |
| 8942 | →⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬¬𝜑] into ax-1 | |
| 8943 | →→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒→⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒 | Subs [𝜑↗→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 8944 | →⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒 | Modus ponens 8942, 8943 | |
| 8945 | →→⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→¬¬𝜑⋀𝜓𝜒] into ax-2 | |
| 8946 | →→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒 | Modus ponens 8944, 8945 | |
| 8947 | →→¬¬𝜑→⋀𝜓𝜒𝜓→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜓 | Subs [𝜑↗¬¬𝜑, 𝜓↗⋀𝜓𝜒, 𝜒↗𝜓] into ax-2 | |
| 8948 | →→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜓 | Modus ponens 8941, 8947 | |
| 8949 | →→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜓→⋀𝜓𝜒→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜓 | Subs [𝜑↗→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜓, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 8950 | →⋀𝜓𝜒→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜓 | Modus ponens 8948, 8949 | |
| 8951 | →→⋀𝜓𝜒→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜓→→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑𝜓 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜑⋀𝜓𝜒, 𝜒↗→¬¬𝜑𝜓] into ax-2 | |
| 8952 | →→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑𝜓 | Modus ponens 8950, 8951 | |
| 8953 | →⋀𝜓𝜒→¬¬𝜑𝜓 | Modus ponens 8942, 8952 | |
| 8954 | →→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓→⋀𝜓𝜒→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓 | Subs [𝜑↗→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 8955 | →⋀𝜓𝜒→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓 | Modus ponens 488, 8954 | |
| 8956 | →→⋀𝜓𝜒→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓→→⋀𝜓𝜒→¬¬𝜑𝜓→⋀𝜓𝜒→¬¬𝜑¬¬𝜓 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜑𝜓, 𝜒↗→¬¬𝜑¬¬𝜓] into ax-2 | |
| 8957 | →→⋀𝜓𝜒→¬¬𝜑𝜓→⋀𝜓𝜒→¬¬𝜑¬¬𝜓 | Modus ponens 8955, 8956 | |
| 8958 | →⋀𝜓𝜒→¬¬𝜑¬¬𝜓 | Modus ponens 8953, 8957 | |
| 8959 | →→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑→⋀𝜓𝜒→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑 | Subs [𝜑↗→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 8960 | →⋀𝜓𝜒→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑 | Modus ponens 494, 8959 | |
| 8961 | →→⋀𝜓𝜒→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑→→⋀𝜓𝜒→¬¬𝜑¬¬𝜓→⋀𝜓𝜒→¬𝜓¬𝜑 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜑¬¬𝜓, 𝜒↗→¬𝜓¬𝜑] into ax-2 | |
| 8962 | →→⋀𝜓𝜒→¬¬𝜑¬¬𝜓→⋀𝜓𝜒→¬𝜓¬𝜑 | Modus ponens 8960, 8961 | |
| 8963 | →⋀𝜓𝜒→¬𝜓¬𝜑 | Modus ponens 8958, 8962 | |
| 8964 | →¬𝜓→⋀𝜓𝜒¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 8965 | →→¬𝜓→⋀𝜓𝜒¬𝜓→¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜓 | Subs [𝜑↗→¬𝜓→⋀𝜓𝜒¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 8966 | →¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜓 | Modus ponens 8964, 8965 | |
| 8967 | →→¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀𝜓𝜒¬𝜓] into ax-2 | |
| 8968 | →→¬𝜓¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜓 | Modus ponens 8966, 8967 | |
| 8969 | →→⋀𝜓𝜒→¬𝜓¬𝜑→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬𝜓, 𝜒↗¬𝜑] into ax-2 | |
| 8970 | →→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜑 | Modus ponens 8963, 8969 | |
| 8971 | →→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜑→¬𝜓→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜓] into ax-1 | |
| 8972 | →¬𝜓→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜑 | Modus ponens 8970, 8971 | |
| 8973 | →→¬𝜓→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜑→→¬𝜓→⋀𝜓𝜒¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜓𝜒¬𝜓, 𝜒↗→⋀𝜓𝜒¬𝜑] into ax-2 | |
| 8974 | →→¬𝜓→⋀𝜓𝜒¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜑 | Modus ponens 8972, 8973 | |
| 8975 | →¬𝜓→⋀𝜓𝜒¬𝜑 | Modus ponens 8964, 8974 | |
| 8976 | →¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗¬→⋀𝜓𝜒¬𝜑] into id | |
| 8977 | →→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬𝜓→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜓] into ax-1 | |
| 8978 | →¬𝜓→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑 | Modus ponens 8976, 8977 | |
| 8979 | →¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗¬→⋀𝜓𝜒¬𝜑] into notnotr | |
| 8980 | →¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜓] into ax-1 | |
| 8981 | →→¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜑] into ax-1 | |
| 8982 | →¬¬¬→⋀𝜓𝜒¬𝜑→¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑 | Modus ponens 8980, 8981 | |
| 8983 | →→¬¬¬→⋀𝜓𝜒¬𝜑→¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬→⋀𝜓𝜒¬𝜑, 𝜒↗→¬𝜓¬→⋀𝜓𝜒¬𝜑] into ax-2 | |
| 8984 | →→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑 | Modus ponens 8982, 8983 | |
| 8985 | →¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑 | Modus ponens 8979, 8984 | |
| 8986 | →→¬𝜓→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀𝜓𝜒¬𝜑, 𝜒↗¬→⋀𝜓𝜒¬𝜑] into ax-2 | |
| 8987 | →→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑 | Modus ponens 8978, 8986 | |
| 8988 | →→→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗→→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜑] into ax-1 | |
| 8989 | →¬¬¬→⋀𝜓𝜒¬𝜑→→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑 | Modus ponens 8987, 8988 | |
| 8990 | →→¬¬¬→⋀𝜓𝜒¬𝜑→→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑→→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗→¬𝜓¬→⋀𝜓𝜒¬𝜑, 𝜒↗→¬𝜓¬→⋀𝜓𝜒¬𝜑] into ax-2 | |
| 8991 | →→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑 | Modus ponens 8989, 8990 | |
| 8992 | →¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜑] into ax-1 | |
| 8993 | →→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 8994 | →¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓 | Modus ponens 8992, 8993 | |
| 8995 | →→¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓] into ax-2 | |
| 8996 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓 | Modus ponens 8994, 8995 | |
| 8997 | →→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜓, 𝜒↗¬→⋀𝜓𝜒¬𝜑] into ax-2 | |
| 8998 | →→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑 | Modus ponens 8985, 8997 | |
| 8999 | →→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜓] into ax-1 | |
| 9000 | →¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑 | Modus ponens 8998, 8999 | |
| 9001 | →→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓, 𝜒↗→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑] into ax-2 | |
| 9002 | →→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑 | Modus ponens 9000, 9001 | |
| 9003 | →¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑 | Modus ponens 8992, 9002 | |
| 9004 | →→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗→⋀𝜓𝜒¬𝜑] into ax-3 | |
| 9005 | →→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜓] into ax-1 | |
| 9006 | →¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑 | Modus ponens 9004, 9005 | |
| 9007 | →→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑→→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬𝜓→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑, 𝜒↗→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑] into ax-2 | |
| 9008 | →→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬𝜓→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑 | Modus ponens 9006, 9007 | |
| 9009 | →¬𝜓→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑 | Modus ponens 9003, 9008 | |
| 9010 | →→¬𝜓→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑→→¬𝜓→⋀𝜓𝜒¬𝜑→¬𝜓¬¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜓𝜒¬𝜑, 𝜒↗¬¬→⋀𝜓𝜒¬𝜑] into ax-2 | |
| 9011 | →→¬𝜓→⋀𝜓𝜒¬𝜑→¬𝜓¬¬→⋀𝜓𝜒¬𝜑 | Modus ponens 9009, 9010 | |
| 9012 | →¬𝜓¬¬→⋀𝜓𝜒¬𝜑 | Modus ponens 8975, 9011 | |
| 9013 | →→¬𝜓¬¬→⋀𝜓𝜒¬𝜑→¬→⋀𝜓𝜒¬𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→⋀𝜓𝜒¬𝜑] into ax-3 | |
| 9014 | →¬→⋀𝜓𝜒¬𝜑𝜓 | Modus ponens 9012, 9013 | |
| 9015 | →↔⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗⋀⋀𝜓𝜒𝜑, 𝜓↗¬→⋀𝜓𝜒¬𝜑] into biimp | |
| 9016 | →⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑 | Modus ponens 8929, 9015 | |
| 9017 | →→¬→⋀𝜓𝜒¬𝜑𝜓→⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜓 | Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜑𝜓, 𝜓↗⋀⋀𝜓𝜒𝜑] into ax-1 | |
| 9018 | →⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜓 | Modus ponens 9014, 9017 | |
| 9019 | →→⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜓→→⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜓 | Subs [𝜑↗⋀⋀𝜓𝜒𝜑, 𝜓↗¬→⋀𝜓𝜒¬𝜑, 𝜒↗𝜓] into ax-2 | |
| 9020 | →→⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜓 | Modus ponens 9018, 9019 | |
| 9021 | →⋀⋀𝜓𝜒𝜑𝜓 | Modus ponens 9016, 9020 | |
| 9022 | →↔⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑↔¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑 | Subs [𝜑↗⋀⋀𝜓𝜒𝜑, 𝜓↗¬→⋀𝜓𝜒¬𝜑] into bicom1 | |
| 9023 | ↔¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑 | Modus ponens 8929, 9022 | |
| 9024 | →↔¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑 | Subs [𝜑↗¬→⋀𝜓𝜒¬𝜑, 𝜓↗⋀⋀𝜓𝜒𝜑] into biimp | |
| 9025 | →¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑 | Modus ponens 9023, 9024 | |
| 9026 | →→⋀⋀𝜓𝜒𝜑𝜓→¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜓 | Subs [𝜑↗→⋀⋀𝜓𝜒𝜑𝜓, 𝜓↗¬→⋀𝜓𝜒¬𝜑] into ax-1 | |
| 9027 | →¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜓 | Modus ponens 9021, 9026 | |
| 9028 | →→¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜓→→¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜓 | Subs [𝜑↗¬→⋀𝜓𝜒¬𝜑, 𝜓↗⋀⋀𝜓𝜒𝜑, 𝜒↗𝜓] into ax-2 | |
| 9029 | →→¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜓 | Modus ponens 9027, 9028 | |
| 9030 | →⋀𝜓𝜒→𝜑¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜑] into pm3.2im | |
| 9031 | →→¬→⋀𝜓𝜒¬𝜑𝜓→𝜑→¬→⋀𝜓𝜒¬𝜑𝜓 | Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 9032 | →𝜑→¬→⋀𝜓𝜒¬𝜑𝜓 | Modus ponens 9014, 9031 | |
| 9033 | →→𝜑→¬→⋀𝜓𝜒¬𝜑𝜓→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜓 | Subs [𝜓↗¬→⋀𝜓𝜒¬𝜑, 𝜒↗𝜓] into ax-2 | |
| 9034 | →→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜓 | Modus ponens 9032, 9033 | |
| 9035 | →→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜓→⋀𝜓𝜒→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜓 | Subs [𝜑↗→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜓, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 9036 | →⋀𝜓𝜒→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜓 | Modus ponens 9034, 9035 | |
| 9037 | →→⋀𝜓𝜒→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜓→→⋀𝜓𝜒→𝜑¬→⋀𝜓𝜒¬𝜑→⋀𝜓𝜒→𝜑𝜓 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→𝜑¬→⋀𝜓𝜒¬𝜑, 𝜒↗→𝜑𝜓] into ax-2 | |
| 9038 | →→⋀𝜓𝜒→𝜑¬→⋀𝜓𝜒¬𝜑→⋀𝜓𝜒→𝜑𝜓 | Modus ponens 9036, 9037 | |
| 9039 | →→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓→𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓 | Subs [𝜑↗→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓, 𝜓↗𝜑] into ax-1 | |
| 9040 | →𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓 | Modus ponens 8936, 9039 | |
| 9041 | →→𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓→→𝜑→⋀𝜓𝜒𝜑→𝜑→⋀𝜓𝜒𝜓 | Subs [𝜓↗→⋀𝜓𝜒𝜑, 𝜒↗→⋀𝜓𝜒𝜓] into ax-2 | |
| 9042 | →→𝜑→⋀𝜓𝜒𝜑→𝜑→⋀𝜓𝜒𝜓 | Modus ponens 9040, 9041 | |
| 9043 | →→→𝜑⋀𝜓𝜒→𝜑𝜓→¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜑⋀𝜓𝜒→𝜑𝜓, 𝜓↗¬¬⋀𝜓𝜒] into ax-1 | |
| 9044 | →¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑𝜓 | Modus ponens 6076, 9043 | |
| 9045 | →→¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑𝜓→→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒→¬¬⋀𝜓𝜒→𝜑𝜓 | Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗→𝜑⋀𝜓𝜒, 𝜒↗→𝜑𝜓] into ax-2 | |
| 9046 | →→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒→¬¬⋀𝜓𝜒→𝜑𝜓 | Modus ponens 9044, 9045 | |
| 9047 | →¬¬⋀𝜓𝜒→𝜑𝜓 | Modus ponens 5479, 9046 | |
| 9048 | →→¬¬⋀𝜓𝜒→𝜑𝜓→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜓 | Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2 | |
| 9049 | →→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜓 | Modus ponens 9047, 9048 | |
| 9050 | →→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜓→𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜓 | Subs [𝜑↗→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜓, 𝜓↗𝜑] into ax-1 | |
| 9051 | →𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜓 | Modus ponens 9049, 9050 | |
| 9052 | →→𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜓→→𝜑→¬¬⋀𝜓𝜒𝜑→𝜑→¬¬⋀𝜓𝜒𝜓 | Subs [𝜓↗→¬¬⋀𝜓𝜒𝜑, 𝜒↗→¬¬⋀𝜓𝜒𝜓] into ax-2 | |
| 9053 | →→𝜑→¬¬⋀𝜓𝜒𝜑→𝜑→¬¬⋀𝜓𝜒𝜓 | Modus ponens 9051, 9052 | |
| 9054 | →𝜑→¬¬⋀𝜓𝜒𝜓 | Modus ponens 5487, 9053 | |
| 9055 | →→𝜓¬¬𝜓→¬¬⋀𝜓𝜒→𝜓¬¬𝜓 | Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬⋀𝜓𝜒] into ax-1 | |
| 9056 | →¬¬⋀𝜓𝜒→𝜓¬¬𝜓 | Modus ponens 448, 9055 | |
| 9057 | →→¬¬⋀𝜓𝜒→𝜓¬¬𝜓→→¬¬⋀𝜓𝜒𝜓→¬¬⋀𝜓𝜒¬¬𝜓 | Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜒↗¬¬𝜓] into ax-2 | |
| 9058 | →→¬¬⋀𝜓𝜒𝜓→¬¬⋀𝜓𝜒¬¬𝜓 | Modus ponens 9056, 9057 | |
| 9059 | →→→¬¬⋀𝜓𝜒𝜓→¬¬⋀𝜓𝜒¬¬𝜓→𝜑→→¬¬⋀𝜓𝜒𝜓→¬¬⋀𝜓𝜒¬¬𝜓 | Subs [𝜑↗→→¬¬⋀𝜓𝜒𝜓→¬¬⋀𝜓𝜒¬¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 9060 | →𝜑→→¬¬⋀𝜓𝜒𝜓→¬¬⋀𝜓𝜒¬¬𝜓 | Modus ponens 9058, 9059 | |
| 9061 | →→𝜑→→¬¬⋀𝜓𝜒𝜓→¬¬⋀𝜓𝜒¬¬𝜓→→𝜑→¬¬⋀𝜓𝜒𝜓→𝜑→¬¬⋀𝜓𝜒¬¬𝜓 | Subs [𝜓↗→¬¬⋀𝜓𝜒𝜓, 𝜒↗→¬¬⋀𝜓𝜒¬¬𝜓] into ax-2 | |
| 9062 | →→𝜑→¬¬⋀𝜓𝜒𝜓→𝜑→¬¬⋀𝜓𝜒¬¬𝜓 | Modus ponens 9060, 9061 | |
| 9063 | →𝜑→¬¬⋀𝜓𝜒¬¬𝜓 | Modus ponens 9054, 9062 | |
| 9064 | →→¬¬⋀𝜓𝜒¬¬𝜓→¬𝜓¬⋀𝜓𝜒 | Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬𝜓] into ax-3 | |
| 9065 | →→→¬¬⋀𝜓𝜒¬¬𝜓→¬𝜓¬⋀𝜓𝜒→𝜑→→¬¬⋀𝜓𝜒¬¬𝜓→¬𝜓¬⋀𝜓𝜒 | Subs [𝜑↗→→¬¬⋀𝜓𝜒¬¬𝜓→¬𝜓¬⋀𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 9066 | →𝜑→→¬¬⋀𝜓𝜒¬¬𝜓→¬𝜓¬⋀𝜓𝜒 | Modus ponens 9064, 9065 | |
| 9067 | →→𝜑→→¬¬⋀𝜓𝜒¬¬𝜓→¬𝜓¬⋀𝜓𝜒→→𝜑→¬¬⋀𝜓𝜒¬¬𝜓→𝜑→¬𝜓¬⋀𝜓𝜒 | Subs [𝜓↗→¬¬⋀𝜓𝜒¬¬𝜓, 𝜒↗→¬𝜓¬⋀𝜓𝜒] into ax-2 | |
| 9068 | →→𝜑→¬¬⋀𝜓𝜒¬¬𝜓→𝜑→¬𝜓¬⋀𝜓𝜒 | Modus ponens 9066, 9067 | |
| 9069 | →𝜑→¬𝜓¬⋀𝜓𝜒 | Modus ponens 9063, 9068 | |
| 9070 | →→𝜑→¬𝜓¬⋀𝜓𝜒→→𝜑¬𝜓→𝜑¬⋀𝜓𝜒 | Subs [𝜓↗¬𝜓, 𝜒↗¬⋀𝜓𝜒] into ax-2 | |
| 9071 | →→𝜑¬𝜓→𝜑¬⋀𝜓𝜒 | Modus ponens 9069, 9070 | |
| 9072 | →→→𝜑¬𝜓→𝜑¬⋀𝜓𝜒→¬𝜓→→𝜑¬𝜓→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→→𝜑¬𝜓→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜓] into ax-1 | |
| 9073 | →¬𝜓→→𝜑¬𝜓→𝜑¬⋀𝜓𝜒 | Modus ponens 9071, 9072 | |
| 9074 | →→¬𝜓→→𝜑¬𝜓→𝜑¬⋀𝜓𝜒→→¬𝜓→𝜑¬𝜓→¬𝜓→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬𝜓, 𝜓↗→𝜑¬𝜓, 𝜒↗→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 9075 | →→¬𝜓→𝜑¬𝜓→¬𝜓→𝜑¬⋀𝜓𝜒 | Modus ponens 9073, 9074 | |
| 9076 | →¬𝜓→𝜑¬⋀𝜓𝜒 | Modus ponens 609, 9075 | |
| 9077 | →→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜓→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜓] into ax-1 | |
| 9078 | →¬𝜓→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 5528, 9077 | |
| 9079 | →¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜓] into ax-1 | |
| 9080 | →→¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1 | |
| 9081 | →¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9079, 9080 | |
| 9082 | →→¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗→¬𝜓¬→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 9083 | →→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9081, 9082 | |
| 9084 | →¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒 | Modus ponens 5531, 9083 | |
| 9085 | →→¬𝜓→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬𝜓, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗¬→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 9086 | →→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9078, 9085 | |
| 9087 | →→→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1 | |
| 9088 | →¬¬¬→𝜑¬⋀𝜓𝜒→→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9086, 9087 | |
| 9089 | →→¬¬¬→𝜑¬⋀𝜓𝜒→→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗→¬𝜓¬→𝜑¬⋀𝜓𝜒, 𝜒↗→¬𝜓¬→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 9090 | →→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9088, 9089 | |
| 9091 | →¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1 | |
| 9092 | →→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬𝜓→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 9093 | →¬𝜓→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓 | Modus ponens 9091, 9092 | |
| 9094 | →→¬𝜓→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓] into ax-2 | |
| 9095 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓 | Modus ponens 9093, 9094 | |
| 9096 | →→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜓, 𝜒↗¬→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 9097 | →→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9084, 9096 | |
| 9098 | →→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜓→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜓] into ax-1 | |
| 9099 | →¬𝜓→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9097, 9098 | |
| 9100 | →→¬𝜓→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓, 𝜒↗→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 9101 | →→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9099, 9100 | |
| 9102 | →¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9091, 9101 | |
| 9103 | →→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→¬𝜓→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜓] into ax-1 | |
| 9104 | →¬𝜓→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒 | Modus ponens 5556, 9103 | |
| 9105 | →→¬𝜓→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜓→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜒↗→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 9106 | →→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜓→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9104, 9105 | |
| 9107 | →¬𝜓→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9102, 9106 | |
| 9108 | →→¬𝜓→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→→¬𝜓→𝜑¬⋀𝜓𝜒→¬𝜓¬¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬𝜓, 𝜓↗→𝜑¬⋀𝜓𝜒, 𝜒↗¬¬→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 9109 | →→¬𝜓→𝜑¬⋀𝜓𝜒→¬𝜓¬¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9107, 9108 | |
| 9110 | →¬𝜓¬¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9076, 9109 | |
| 9111 | →→¬𝜓¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into ax-3 | |
| 9112 | →¬→𝜑¬⋀𝜓𝜒𝜓 | Modus ponens 9110, 9111 | |
| 9113 | →→¬→𝜑¬⋀𝜓𝜒𝜓→⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓 | Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 9114 | →⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓 | Modus ponens 9112, 9113 | |
| 9115 | →→⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓→→⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗𝜓] into ax-2 | |
| 9116 | →→⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓 | Modus ponens 9114, 9115 | |
| 9117 | →⋀𝜑⋀𝜓𝜒𝜓 | Modus ponens 5568, 9116 | simprl |
| 9118 | →⋀𝜑⋀𝜓𝜒𝜑 | Subs [𝜓↗⋀𝜓𝜒] into simpl | |
| 9119 | →→⋀𝜑𝜓𝜓→¬→𝜑¬𝜓→⋀𝜑𝜓𝜓 | Subs [𝜑↗→⋀𝜑𝜓𝜓, 𝜓↗¬→𝜑¬𝜓] into ax-1 | |
| 9120 | →¬→𝜑¬𝜓→⋀𝜑𝜓𝜓 | Modus ponens simpr, 9119 | |
| 9121 | →→¬→𝜑¬𝜓→⋀𝜑𝜓𝜓→→¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓𝜓 | Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜓] into ax-2 | |
| 9122 | →→¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓𝜓 | Modus ponens 9120, 9121 | |
| 9123 | →→¬→𝜑¬𝜓𝜓→𝜓→¬→𝜑¬𝜓𝜓 | Subs [𝜑↗→¬→𝜑¬𝜓𝜓] into ax-1 | |
| 9124 | →𝜓→¬→𝜑¬𝜓𝜓 | Modus ponens simprim, 9123 | |
| 9125 | →→𝜓→¬→𝜑¬𝜓𝜓→→𝜓¬→𝜑¬𝜓→𝜓𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗𝜓] into ax-2 | |
| 9126 | →→𝜓¬→𝜑¬𝜓→𝜓𝜓 | Modus ponens 9124, 9125 | |
| 9127 | →→→𝜓¬→𝜑¬𝜓→𝜓𝜓→𝜑→→𝜓¬→𝜑¬𝜓→𝜓𝜓 | Subs [𝜑↗→→𝜓¬→𝜑¬𝜓→𝜓𝜓, 𝜓↗𝜑] into ax-1 | |
| 9128 | →𝜑→→𝜓¬→𝜑¬𝜓→𝜓𝜓 | Modus ponens 9126, 9127 | |
| 9129 | →→𝜑→→𝜓¬→𝜑¬𝜓→𝜓𝜓→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→𝜓𝜓 | Subs [𝜓↗→𝜓¬→𝜑¬𝜓, 𝜒↗→𝜓𝜓] into ax-2 | |
| 9130 | →→𝜑→𝜓¬→𝜑¬𝜓→𝜑→𝜓𝜓 | Modus ponens 9128, 9129 | |
| 9131 | →→𝜓→𝜑𝜓→⋀𝜑⋀𝜓𝜒→𝜓→𝜑𝜓 | Subs [𝜑↗→𝜓→𝜑𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 9132 | →⋀𝜑⋀𝜓𝜒→𝜓→𝜑𝜓 | Modus ponens 208, 9131 | |
| 9133 | →→⋀𝜑⋀𝜓𝜒→𝜓→𝜑𝜓→→⋀𝜑⋀𝜓𝜒𝜓→⋀𝜑⋀𝜓𝜒→𝜑𝜓 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜑𝜓] into ax-2 | |
| 9134 | →→⋀𝜑⋀𝜓𝜒𝜓→⋀𝜑⋀𝜓𝜒→𝜑𝜓 | Modus ponens 9132, 9133 | |
| 9135 | →⋀𝜑⋀𝜓𝜒→𝜑𝜓 | Modus ponens simprl, 9134 | |
| 9136 | →→→𝜑𝜓→𝜑𝜓→⋀𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→𝜑𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 9137 | →⋀𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜓 | Modus ponens 24, 9136 | |
| 9138 | →→⋀𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜓→→⋀𝜑⋀𝜓𝜒→𝜑𝜓→⋀𝜑⋀𝜓𝜒→𝜑𝜓 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2 | |
| 9139 | →→⋀𝜑⋀𝜓𝜒→𝜑𝜓→⋀𝜑⋀𝜓𝜒→𝜑𝜓 | Modus ponens 9137, 9138 | |
| 9140 | →𝜑→⋀𝜑⋀𝜓𝜒𝜑 | Subs [𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 9141 | →→𝜑→⋀𝜑⋀𝜓𝜒𝜑→𝜑→𝜑→⋀𝜑⋀𝜓𝜒𝜑 | Subs [𝜑↗→𝜑→⋀𝜑⋀𝜓𝜒𝜑, 𝜓↗𝜑] into ax-1 | |
| 9142 | →𝜑→𝜑→⋀𝜑⋀𝜓𝜒𝜑 | Modus ponens 9140, 9141 | |
| 9143 | →→𝜑→𝜑→⋀𝜑⋀𝜓𝜒𝜑→→𝜑𝜑→𝜑→⋀𝜑⋀𝜓𝜒𝜑 | Subs [𝜓↗𝜑, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜑] into ax-2 | |
| 9144 | →→𝜑𝜑→𝜑→⋀𝜑⋀𝜓𝜒𝜑 | Modus ponens 9142, 9143 | |
| 9145 | →→⋀𝜑⋀𝜓𝜒→𝜑𝜓→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒𝜓 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2 | |
| 9146 | →→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒𝜓 | Modus ponens 9135, 9145 | |
| 9147 | →→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒𝜓→𝜑→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒𝜓 | Subs [𝜑↗→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒𝜓, 𝜓↗𝜑] into ax-1 | |
| 9148 | →𝜑→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒𝜓 | Modus ponens 9146, 9147 | |
| 9149 | →→𝜑→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒𝜓→→𝜑→⋀𝜑⋀𝜓𝜒𝜑→𝜑→⋀𝜑⋀𝜓𝜒𝜓 | Subs [𝜓↗→⋀𝜑⋀𝜓𝜒𝜑, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜓] into ax-2 | |
| 9150 | →→𝜑→⋀𝜑⋀𝜓𝜒𝜑→𝜑→⋀𝜑⋀𝜓𝜒𝜓 | Modus ponens 9148, 9149 | |
| 9151 | →𝜑→⋀𝜑⋀𝜓𝜒𝜓 | Modus ponens 9140, 9150 | |
| 9152 | →→𝜑→⋀𝜑⋀𝜓𝜒𝜓→⋀𝜑⋀𝜓𝜒→𝜑→⋀𝜑⋀𝜓𝜒𝜓 | Subs [𝜑↗→𝜑→⋀𝜑⋀𝜓𝜒𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 9153 | →⋀𝜑⋀𝜓𝜒→𝜑→⋀𝜑⋀𝜓𝜒𝜓 | Modus ponens 9151, 9152 | |
| 9154 | →→⋀𝜑⋀𝜓𝜒→𝜑→⋀𝜑⋀𝜓𝜒𝜓→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜓] into ax-2 | |
| 9155 | →→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓 | Modus ponens 9153, 9154 | |
| 9156 | →⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓 | Modus ponens 9118, 9155 | |
| 9157 | →→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓→→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗𝜓] into ax-2 | |
| 9158 | →→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓 | Modus ponens 9156, 9157 | |
| 9159 | →→𝜒→𝜓𝜒→→𝜒𝜓→𝜒𝜒 | Subs [𝜑↗𝜒] into ax-2 | |
| 9160 | →→𝜒𝜓→𝜒𝜒 | Modus ponens 5362, 9159 | |
| 9161 | →→→𝜒𝜓→𝜒𝜒→¬¬𝜓→→𝜒𝜓→𝜒𝜒 | Subs [𝜑↗→→𝜒𝜓→𝜒𝜒, 𝜓↗¬¬𝜓] into ax-1 | |
| 9162 | →¬¬𝜓→→𝜒𝜓→𝜒𝜒 | Modus ponens 9160, 9161 | |
| 9163 | →→¬¬𝜓→→𝜒𝜓→𝜒𝜒→→¬¬𝜓→𝜒𝜓→¬¬𝜓→𝜒𝜒 | Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜒𝜓, 𝜒↗→𝜒𝜒] into ax-2 | |
| 9164 | →→¬¬𝜓→𝜒𝜓→¬¬𝜓→𝜒𝜒 | Modus ponens 9162, 9163 | |
| 9165 | →¬¬𝜓→𝜒𝜒 | Modus ponens 7002, 9164 | |
| 9166 | →→¬¬𝜓→𝜒𝜒→→¬¬𝜓𝜒→¬¬𝜓𝜒 | Subs [𝜑↗¬¬𝜓, 𝜓↗𝜒] into ax-2 | |
| 9167 | →→¬¬𝜓𝜒→¬¬𝜓𝜒 | Modus ponens 9165, 9166 | |
| 9168 | →→→¬¬𝜓𝜒→¬¬𝜓𝜒→𝜒→→¬¬𝜓𝜒→¬¬𝜓𝜒 | Subs [𝜑↗→→¬¬𝜓𝜒→¬¬𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 9169 | →𝜒→→¬¬𝜓𝜒→¬¬𝜓𝜒 | Modus ponens 9167, 9168 | |
| 9170 | →→𝜒→→¬¬𝜓𝜒→¬¬𝜓𝜒→→𝜒→¬¬𝜓𝜒→𝜒→¬¬𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→¬¬𝜓𝜒, 𝜒↗→¬¬𝜓𝜒] into ax-2 | |
| 9171 | →→𝜒→¬¬𝜓𝜒→𝜒→¬¬𝜓𝜒 | Modus ponens 9169, 9170 | |
| 9172 | →𝜒¬¬𝜒 | Subs [𝜑↗𝜒] into notnot | |
| 9173 | →→𝜒¬¬𝜒→¬¬𝜓→𝜒¬¬𝜒 | Subs [𝜑↗→𝜒¬¬𝜒, 𝜓↗¬¬𝜓] into ax-1 | |
| 9174 | →¬¬𝜓→𝜒¬¬𝜒 | Modus ponens 9172, 9173 | |
| 9175 | →→¬¬𝜓→𝜒¬¬𝜒→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒 | Subs [𝜑↗¬¬𝜓, 𝜓↗𝜒, 𝜒↗¬¬𝜒] into ax-2 | |
| 9176 | →→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒 | Modus ponens 9174, 9175 | |
| 9177 | →→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒→𝜒→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒 | Subs [𝜑↗→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒, 𝜓↗𝜒] into ax-1 | |
| 9178 | →𝜒→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒 | Modus ponens 9176, 9177 | |
| 9179 | →→𝜒→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒→→𝜒→¬¬𝜓𝜒→𝜒→¬¬𝜓¬¬𝜒 | Subs [𝜑↗𝜒, 𝜓↗→¬¬𝜓𝜒, 𝜒↗→¬¬𝜓¬¬𝜒] into ax-2 | |
| 9180 | →→𝜒→¬¬𝜓𝜒→𝜒→¬¬𝜓¬¬𝜒 | Modus ponens 9178, 9179 | |
| 9181 | →𝜒→¬¬𝜓¬¬𝜒 | Modus ponens 7010, 9180 | |
| 9182 | →→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜒] into ax-3 | |
| 9183 | →→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓→𝜒→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓 | Subs [𝜑↗→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓, 𝜓↗𝜒] into ax-1 | |
| 9184 | →𝜒→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓 | Modus ponens 9182, 9183 | |
| 9185 | →→𝜒→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓→→𝜒→¬¬𝜓¬¬𝜒→𝜒→¬𝜒¬𝜓 | Subs [𝜑↗𝜒, 𝜓↗→¬¬𝜓¬¬𝜒, 𝜒↗→¬𝜒¬𝜓] into ax-2 | |
| 9186 | →→𝜒→¬¬𝜓¬¬𝜒→𝜒→¬𝜒¬𝜓 | Modus ponens 9184, 9185 | |
| 9187 | →𝜒→¬𝜒¬𝜓 | Modus ponens 9181, 9186 | |
| 9188 | →¬𝜒¬𝜒 | Subs [𝜑↗¬𝜒] into id | |
| 9189 | →¬𝜒→𝜒¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗𝜒] into ax-1 | |
| 9190 | →→¬𝜒→𝜒¬𝜒→¬𝜒→¬𝜒→𝜒¬𝜒 | Subs [𝜑↗→¬𝜒→𝜒¬𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 9191 | →¬𝜒→¬𝜒→𝜒¬𝜒 | Modus ponens 9189, 9190 | |
| 9192 | →→¬𝜒→¬𝜒→𝜒¬𝜒→→¬𝜒¬𝜒→¬𝜒→𝜒¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→𝜒¬𝜒] into ax-2 | |
| 9193 | →→¬𝜒¬𝜒→¬𝜒→𝜒¬𝜒 | Modus ponens 9191, 9192 | |
| 9194 | →→𝜒→¬𝜒¬𝜓→→𝜒¬𝜒→𝜒¬𝜓 | Subs [𝜑↗𝜒, 𝜓↗¬𝜒, 𝜒↗¬𝜓] into ax-2 | |
| 9195 | →→𝜒¬𝜒→𝜒¬𝜓 | Modus ponens 9187, 9194 | |
| 9196 | →→→𝜒¬𝜒→𝜒¬𝜓→¬𝜒→→𝜒¬𝜒→𝜒¬𝜓 | Subs [𝜑↗→→𝜒¬𝜒→𝜒¬𝜓, 𝜓↗¬𝜒] into ax-1 | |
| 9197 | →¬𝜒→→𝜒¬𝜒→𝜒¬𝜓 | Modus ponens 9195, 9196 | |
| 9198 | →→¬𝜒→→𝜒¬𝜒→𝜒¬𝜓→→¬𝜒→𝜒¬𝜒→¬𝜒→𝜒¬𝜓 | Subs [𝜑↗¬𝜒, 𝜓↗→𝜒¬𝜒, 𝜒↗→𝜒¬𝜓] into ax-2 | |
| 9199 | →→¬𝜒→𝜒¬𝜒→¬𝜒→𝜒¬𝜓 | Modus ponens 9197, 9198 | |
| 9200 | →¬𝜒→𝜒¬𝜓 | Modus ponens 9189, 9199 | |
| 9201 | →→¬→𝜒¬𝜓¬→𝜒¬𝜓→¬𝜒→¬→𝜒¬𝜓¬→𝜒¬𝜓 | Subs [𝜑↗→¬→𝜒¬𝜓¬→𝜒¬𝜓, 𝜓↗¬𝜒] into ax-1 | |
| 9202 | →¬𝜒→¬→𝜒¬𝜓¬→𝜒¬𝜓 | Modus ponens 7051, 9201 | |
| 9203 | →¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓 | Subs [𝜑↗¬→𝜒¬𝜓, 𝜓↗¬𝜒] into ax-1 | |
| 9204 | →→¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓 | Subs [𝜑↗→¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓, 𝜓↗¬¬¬→𝜒¬𝜓] into ax-1 | |
| 9205 | →¬¬¬→𝜒¬𝜓→¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓 | Modus ponens 9203, 9204 | |
| 9206 | →→¬¬¬→𝜒¬𝜓→¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓 | Subs [𝜑↗¬¬¬→𝜒¬𝜓, 𝜓↗¬→𝜒¬𝜓, 𝜒↗→¬𝜒¬→𝜒¬𝜓] into ax-2 | |
| 9207 | →→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓 | Modus ponens 9205, 9206 | |
| 9208 | →¬¬¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓 | Modus ponens 7054, 9207 | |
| 9209 | →→¬𝜒→¬→𝜒¬𝜓¬→𝜒¬𝜓→→¬𝜒¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓 | Subs [𝜑↗¬𝜒, 𝜓↗¬→𝜒¬𝜓, 𝜒↗¬→𝜒¬𝜓] into ax-2 | |
| 9210 | →→¬𝜒¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓 | Modus ponens 9202, 9209 | |
| 9211 | →→→¬𝜒¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→→¬𝜒¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓 | Subs [𝜑↗→→¬𝜒¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓, 𝜓↗¬¬¬→𝜒¬𝜓] into ax-1 | |
| 9212 | →¬¬¬→𝜒¬𝜓→→¬𝜒¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓 | Modus ponens 9210, 9211 | |
| 9213 | →→¬¬¬→𝜒¬𝜓→→¬𝜒¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓→→¬¬¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓 | Subs [𝜑↗¬¬¬→𝜒¬𝜓, 𝜓↗→¬𝜒¬→𝜒¬𝜓, 𝜒↗→¬𝜒¬→𝜒¬𝜓] into ax-2 | |
| 9214 | →→¬¬¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓 | Modus ponens 9212, 9213 | |
| 9215 | →¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→𝜒¬𝜓] into ax-1 | |
| 9216 | →→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒→¬𝜒→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒 | Subs [𝜑↗→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 9217 | →¬𝜒→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒 | Modus ponens 9215, 9216 | |
| 9218 | →→¬𝜒→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→𝜒¬𝜓¬𝜒] into ax-2 | |
| 9219 | →→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒 | Modus ponens 9217, 9218 | |
| 9220 | →→¬¬¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓→→¬¬¬→𝜒¬𝜓¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓 | Subs [𝜑↗¬¬¬→𝜒¬𝜓, 𝜓↗¬𝜒, 𝜒↗¬→𝜒¬𝜓] into ax-2 | |
| 9221 | →→¬¬¬→𝜒¬𝜓¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓 | Modus ponens 9208, 9220 | |
| 9222 | →→→¬¬¬→𝜒¬𝜓¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬𝜒→→¬¬¬→𝜒¬𝜓¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓 | Subs [𝜑↗→→¬¬¬→𝜒¬𝜓¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓, 𝜓↗¬𝜒] into ax-1 | |
| 9223 | →¬𝜒→→¬¬¬→𝜒¬𝜓¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓 | Modus ponens 9221, 9222 | |
| 9224 | →→¬𝜒→→¬¬¬→𝜒¬𝜓¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒→¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓 | Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜒¬𝜓¬𝜒, 𝜒↗→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓] into ax-2 | |
| 9225 | →→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒→¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓 | Modus ponens 9223, 9224 | |
| 9226 | →¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓 | Modus ponens 9215, 9225 | |
| 9227 | →→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓→¬𝜒→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓 | Subs [𝜑↗→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓, 𝜓↗¬𝜒] into ax-1 | |
| 9228 | →¬𝜒→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓 | Modus ponens 7079, 9227 | |
| 9229 | →→¬𝜒→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓→→¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬𝜒→→𝜒¬𝜓¬¬→𝜒¬𝜓 | Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓, 𝜒↗→→𝜒¬𝜓¬¬→𝜒¬𝜓] into ax-2 | |
| 9230 | →→¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬𝜒→→𝜒¬𝜓¬¬→𝜒¬𝜓 | Modus ponens 9228, 9229 | |
| 9231 | →¬𝜒→→𝜒¬𝜓¬¬→𝜒¬𝜓 | Modus ponens 9226, 9230 | |
| 9232 | →→¬𝜒→→𝜒¬𝜓¬¬→𝜒¬𝜓→→¬𝜒→𝜒¬𝜓→¬𝜒¬¬→𝜒¬𝜓 | Subs [𝜑↗¬𝜒, 𝜓↗→𝜒¬𝜓, 𝜒↗¬¬→𝜒¬𝜓] into ax-2 | |
| 9233 | →→¬𝜒→𝜒¬𝜓→¬𝜒¬¬→𝜒¬𝜓 | Modus ponens 9231, 9232 | |
| 9234 | →¬𝜒¬¬→𝜒¬𝜓 | Modus ponens 9200, 9233 | |
| 9235 | →→¬𝜒¬¬→𝜒¬𝜓→¬→𝜒¬𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗¬→𝜒¬𝜓] into ax-3 | |
| 9236 | →¬→𝜒¬𝜓𝜒 | Modus ponens 9234, 9235 | |
| 9237 | →→¬→𝜒¬𝜓𝜒→⋀𝜒𝜓→¬→𝜒¬𝜓𝜒 | Subs [𝜑↗→¬→𝜒¬𝜓𝜒, 𝜓↗⋀𝜒𝜓] into ax-1 | |
| 9238 | →⋀𝜒𝜓→¬→𝜒¬𝜓𝜒 | Modus ponens 9236, 9237 | |
| 9239 | →→⋀𝜒𝜓→¬→𝜒¬𝜓𝜒→→⋀𝜒𝜓¬→𝜒¬𝜓→⋀𝜒𝜓𝜒 | Subs [𝜑↗⋀𝜒𝜓, 𝜓↗¬→𝜒¬𝜓] into ax-2 | |
| 9240 | →→⋀𝜒𝜓¬→𝜒¬𝜓→⋀𝜒𝜓𝜒 | Modus ponens 9238, 9239 | |
| 9241 | →⋀𝜒𝜓𝜒 | Modus ponens 7091, 9240 | |
| 9242 | →→⋀𝜒𝜓𝜒→¬→𝜒¬𝜓→⋀𝜒𝜓𝜒 | Subs [𝜑↗→⋀𝜒𝜓𝜒, 𝜓↗¬→𝜒¬𝜓] into ax-1 | |
| 9243 | →¬→𝜒¬𝜓→⋀𝜒𝜓𝜒 | Modus ponens 9241, 9242 | |
| 9244 | →→¬→𝜒¬𝜓→⋀𝜒𝜓𝜒→→¬→𝜒¬𝜓⋀𝜒𝜓→¬→𝜒¬𝜓𝜒 | Subs [𝜑↗¬→𝜒¬𝜓, 𝜓↗⋀𝜒𝜓] into ax-2 | |
| 9245 | →→¬→𝜒¬𝜓⋀𝜒𝜓→¬→𝜒¬𝜓𝜒 | Modus ponens 9243, 9244 | |
| 9246 | →→¬→𝜒¬𝜓𝜒→𝜓→¬→𝜒¬𝜓𝜒 | Subs [𝜑↗→¬→𝜒¬𝜓𝜒] into ax-1 | |
| 9247 | →𝜓→¬→𝜒¬𝜓𝜒 | Modus ponens 9236, 9246 | |
| 9248 | →→𝜓→¬→𝜒¬𝜓𝜒→→𝜓¬→𝜒¬𝜓→𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗¬→𝜒¬𝜓] into ax-2 | |
| 9249 | →→𝜓¬→𝜒¬𝜓→𝜓𝜒 | Modus ponens 9247, 9248 | |
| 9250 | →→→𝜓¬→𝜒¬𝜓→𝜓𝜒→𝜒→→𝜓¬→𝜒¬𝜓→𝜓𝜒 | Subs [𝜑↗→→𝜓¬→𝜒¬𝜓→𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 9251 | →𝜒→→𝜓¬→𝜒¬𝜓→𝜓𝜒 | Modus ponens 9249, 9250 | |
| 9252 | →→𝜒→→𝜓¬→𝜒¬𝜓→𝜓𝜒→→𝜒→𝜓¬→𝜒¬𝜓→𝜒→𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜓¬→𝜒¬𝜓, 𝜒↗→𝜓𝜒] into ax-2 | |
| 9253 | →→𝜒→𝜓¬→𝜒¬𝜓→𝜒→𝜓𝜒 | Modus ponens 9251, 9252 | |
| 9254 | →→→𝜒𝜓→𝜒𝜒→𝜓→→𝜒𝜓→𝜒𝜒 | Subs [𝜑↗→→𝜒𝜓→𝜒𝜒] into ax-1 | |
| 9255 | →𝜓→→𝜒𝜓→𝜒𝜒 | Modus ponens 9160, 9254 | |
| 9256 | →→𝜓→→𝜒𝜓→𝜒𝜒→→𝜓→𝜒𝜓→𝜓→𝜒𝜒 | Subs [𝜑↗𝜓, 𝜓↗→𝜒𝜓, 𝜒↗→𝜒𝜒] into ax-2 | |
| 9257 | →→𝜓→𝜒𝜓→𝜓→𝜒𝜒 | Modus ponens 9255, 9256 | |
| 9258 | →→→𝜓𝜒→𝜓𝜒→¬¬𝜒→→𝜓𝜒→𝜓𝜒 | Subs [𝜑↗→→𝜓𝜒→𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1 | |
| 9259 | →¬¬𝜒→→𝜓𝜒→𝜓𝜒 | Modus ponens 867, 9258 | |
| 9260 | →→¬¬𝜒→→𝜓𝜒→𝜓𝜒→→¬¬𝜒→𝜓𝜒→¬¬𝜒→𝜓𝜒 | Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→𝜓𝜒] into ax-2 | |
| 9261 | →→¬¬𝜒→𝜓𝜒→¬¬𝜒→𝜓𝜒 | Modus ponens 9259, 9260 | |
| 9262 | →→¬¬𝜒→𝜓𝜒→→¬¬𝜒𝜓→¬¬𝜒𝜒 | Subs [𝜑↗¬¬𝜒] into ax-2 | |
| 9263 | →→¬¬𝜒𝜓→¬¬𝜒𝜒 | Modus ponens 5367, 9262 | |
| 9264 | →→→¬¬𝜒𝜓→¬¬𝜒𝜒→𝜓→→¬¬𝜒𝜓→¬¬𝜒𝜒 | Subs [𝜑↗→→¬¬𝜒𝜓→¬¬𝜒𝜒] into ax-1 | |
| 9265 | →𝜓→→¬¬𝜒𝜓→¬¬𝜒𝜒 | Modus ponens 9263, 9264 | |
| 9266 | →→𝜓→→¬¬𝜒𝜓→¬¬𝜒𝜒→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒𝜒 | Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒𝜓, 𝜒↗→¬¬𝜒𝜒] into ax-2 | |
| 9267 | →→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒𝜒 | Modus ponens 9265, 9266 | |
| 9268 | →𝜓→¬¬𝜒𝜒 | Modus ponens 5375, 9267 | |
| 9269 | →→𝜒¬¬𝜒→¬¬𝜒→𝜒¬¬𝜒 | Subs [𝜑↗→𝜒¬¬𝜒, 𝜓↗¬¬𝜒] into ax-1 | |
| 9270 | →¬¬𝜒→𝜒¬¬𝜒 | Modus ponens 9172, 9269 | |
| 9271 | →→¬¬𝜒→𝜒¬¬𝜒→→¬¬𝜒𝜒→¬¬𝜒¬¬𝜒 | Subs [𝜑↗¬¬𝜒, 𝜓↗𝜒, 𝜒↗¬¬𝜒] into ax-2 | |
| 9272 | →→¬¬𝜒𝜒→¬¬𝜒¬¬𝜒 | Modus ponens 9270, 9271 | |
| 9273 | →→→¬¬𝜒𝜒→¬¬𝜒¬¬𝜒→𝜓→→¬¬𝜒𝜒→¬¬𝜒¬¬𝜒 | Subs [𝜑↗→→¬¬𝜒𝜒→¬¬𝜒¬¬𝜒] into ax-1 | |
| 9274 | →𝜓→→¬¬𝜒𝜒→¬¬𝜒¬¬𝜒 | Modus ponens 9272, 9273 | |
| 9275 | →→𝜓→→¬¬𝜒𝜒→¬¬𝜒¬¬𝜒→→𝜓→¬¬𝜒𝜒→𝜓→¬¬𝜒¬¬𝜒 | Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒𝜒, 𝜒↗→¬¬𝜒¬¬𝜒] into ax-2 | |
| 9276 | →→𝜓→¬¬𝜒𝜒→𝜓→¬¬𝜒¬¬𝜒 | Modus ponens 9274, 9275 | |
| 9277 | →𝜓→¬¬𝜒¬¬𝜒 | Modus ponens 9268, 9276 | |
| 9278 | →→¬¬𝜒¬¬𝜒→¬𝜒¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒] into ax-3 | |
| 9279 | →→→¬¬𝜒¬¬𝜒→¬𝜒¬𝜒→𝜓→→¬¬𝜒¬¬𝜒→¬𝜒¬𝜒 | Subs [𝜑↗→→¬¬𝜒¬¬𝜒→¬𝜒¬𝜒] into ax-1 | |
| 9280 | →𝜓→→¬¬𝜒¬¬𝜒→¬𝜒¬𝜒 | Modus ponens 9278, 9279 | |
| 9281 | →→𝜓→→¬¬𝜒¬¬𝜒→¬𝜒¬𝜒→→𝜓→¬¬𝜒¬¬𝜒→𝜓→¬𝜒¬𝜒 | Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒¬¬𝜒, 𝜒↗→¬𝜒¬𝜒] into ax-2 | |
| 9282 | →→𝜓→¬¬𝜒¬¬𝜒→𝜓→¬𝜒¬𝜒 | Modus ponens 9280, 9281 | |
| 9283 | →𝜓→¬𝜒¬𝜒 | Modus ponens 9277, 9282 | |
| 9284 | →¬𝜒→𝜓¬𝜒 | Subs [𝜑↗¬𝜒] into ax-1 | |
| 9285 | →→¬𝜒→𝜓¬𝜒→¬𝜒→¬𝜒→𝜓¬𝜒 | Subs [𝜑↗→¬𝜒→𝜓¬𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 9286 | →¬𝜒→¬𝜒→𝜓¬𝜒 | Modus ponens 9284, 9285 | |
| 9287 | →→¬𝜒→¬𝜒→𝜓¬𝜒→→¬𝜒¬𝜒→¬𝜒→𝜓¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→𝜓¬𝜒] into ax-2 | |
| 9288 | →→¬𝜒¬𝜒→¬𝜒→𝜓¬𝜒 | Modus ponens 9286, 9287 | |
| 9289 | →→𝜓→¬𝜒¬𝜒→→𝜓¬𝜒→𝜓¬𝜒 | Subs [𝜑↗𝜓, 𝜓↗¬𝜒, 𝜒↗¬𝜒] into ax-2 | |
| 9290 | →→𝜓¬𝜒→𝜓¬𝜒 | Modus ponens 9283, 9289 | |
| 9291 | →→→𝜓¬𝜒→𝜓¬𝜒→¬𝜒→→𝜓¬𝜒→𝜓¬𝜒 | Subs [𝜑↗→→𝜓¬𝜒→𝜓¬𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 9292 | →¬𝜒→→𝜓¬𝜒→𝜓¬𝜒 | Modus ponens 9290, 9291 | |
| 9293 | →→¬𝜒→→𝜓¬𝜒→𝜓¬𝜒→→¬𝜒→𝜓¬𝜒→¬𝜒→𝜓¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗→𝜓¬𝜒, 𝜒↗→𝜓¬𝜒] into ax-2 | |
| 9294 | →→¬𝜒→𝜓¬𝜒→¬𝜒→𝜓¬𝜒 | Modus ponens 9292, 9293 | |
| 9295 | →→¬→𝜓¬𝜒¬→𝜓¬𝜒→¬𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒 | Subs [𝜑↗→¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 9296 | →¬𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒 | Modus ponens 5416, 9295 | |
| 9297 | →¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒 | Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 9298 | →→¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒 | Subs [𝜑↗→¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1 | |
| 9299 | →¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒 | Modus ponens 9297, 9298 | |
| 9300 | →→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒 | Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→¬𝜒¬→𝜓¬𝜒] into ax-2 | |
| 9301 | →→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒 | Modus ponens 9299, 9300 | |
| 9302 | →¬¬¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒 | Modus ponens 5419, 9301 | |
| 9303 | →→¬𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒→→¬𝜒¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗¬→𝜓¬𝜒] into ax-2 | |
| 9304 | →→¬𝜒¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒 | Modus ponens 9296, 9303 | |
| 9305 | →→→¬𝜒¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→→¬𝜒¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒 | Subs [𝜑↗→→¬𝜒¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1 | |
| 9306 | →¬¬¬→𝜓¬𝜒→→¬𝜒¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒 | Modus ponens 9304, 9305 | |
| 9307 | →→¬¬¬→𝜓¬𝜒→→¬𝜒¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒 | Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗→¬𝜒¬→𝜓¬𝜒, 𝜒↗→¬𝜒¬→𝜓¬𝜒] into ax-2 | |
| 9308 | →→¬¬¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒 | Modus ponens 9306, 9307 | |
| 9309 | →¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1 | |
| 9310 | →→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒→¬𝜒→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒 | Subs [𝜑↗→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 9311 | →¬𝜒→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒 | Modus ponens 9309, 9310 | |
| 9312 | →→¬𝜒→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→𝜓¬𝜒¬𝜒] into ax-2 | |
| 9313 | →→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒 | Modus ponens 9311, 9312 | |
| 9314 | →→¬¬¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗¬𝜒, 𝜒↗¬→𝜓¬𝜒] into ax-2 | |
| 9315 | →→¬¬¬→𝜓¬𝜒¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Modus ponens 9302, 9314 | |
| 9316 | →→→¬¬¬→𝜓¬𝜒¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬𝜒→→¬¬¬→𝜓¬𝜒¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Subs [𝜑↗→→¬¬¬→𝜓¬𝜒¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 9317 | →¬𝜒→→¬¬¬→𝜓¬𝜒¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Modus ponens 9315, 9316 | |
| 9318 | →→¬𝜒→→¬¬¬→𝜓¬𝜒¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜓¬𝜒¬𝜒, 𝜒↗→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒] into ax-2 | |
| 9319 | →→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Modus ponens 9317, 9318 | |
| 9320 | →¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒 | Modus ponens 9309, 9319 | |
| 9321 | →→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→¬𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒 | Subs [𝜑↗→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 9322 | →¬𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒 | Modus ponens 5444, 9321 | |
| 9323 | →→¬𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→→¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜒↗→→𝜓¬𝜒¬¬→𝜓¬𝜒] into ax-2 | |
| 9324 | →→¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒 | Modus ponens 9322, 9323 | |
| 9325 | →¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒 | Modus ponens 9320, 9324 | |
| 9326 | →→¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→→¬𝜒→𝜓¬𝜒→¬𝜒¬¬→𝜓¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗→𝜓¬𝜒, 𝜒↗¬¬→𝜓¬𝜒] into ax-2 | |
| 9327 | →→¬𝜒→𝜓¬𝜒→¬𝜒¬¬→𝜓¬𝜒 | Modus ponens 9325, 9326 | |
| 9328 | →¬𝜒¬¬→𝜓¬𝜒 | Modus ponens 9284, 9327 | |
| 9329 | →→¬𝜒¬¬→𝜓¬𝜒→¬→𝜓¬𝜒𝜒 | Subs [𝜑↗𝜒, 𝜓↗¬→𝜓¬𝜒] into ax-3 | |
| 9330 | →¬→𝜓¬𝜒𝜒 | Modus ponens 9328, 9329 | |
| 9331 | →→¬→𝜓¬𝜒𝜒→⋀𝜓𝜒→¬→𝜓¬𝜒𝜒 | Subs [𝜑↗→¬→𝜓¬𝜒𝜒, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 9332 | →⋀𝜓𝜒→¬→𝜓¬𝜒𝜒 | Modus ponens 9330, 9331 | |
| 9333 | →→⋀𝜓𝜒→¬→𝜓¬𝜒𝜒→→⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒] into ax-2 | |
| 9334 | →→⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒𝜒 | Modus ponens 9332, 9333 | |
| 9335 | →→𝜒→𝜑𝜒→⋀𝜓𝜒→𝜒→𝜑𝜒 | Subs [𝜑↗→𝜒→𝜑𝜒, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 9336 | →⋀𝜓𝜒→𝜒→𝜑𝜒 | Modus ponens 1834, 9335 | |
| 9337 | →→⋀𝜓𝜒→𝜒→𝜑𝜒→→⋀𝜓𝜒𝜒→⋀𝜓𝜒→𝜑𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜒, 𝜒↗→𝜑𝜒] into ax-2 | |
| 9338 | →→⋀𝜓𝜒𝜒→⋀𝜓𝜒→𝜑𝜒 | Modus ponens 9336, 9337 | |
| 9339 | →⋀𝜓𝜒→𝜑𝜒 | Modus ponens 6077, 9338 | |
| 9340 | →→⋀𝜓𝜒→𝜑𝜒→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜑] into ax-2 | |
| 9341 | →→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒 | Modus ponens 9339, 9340 | |
| 9342 | →→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒→¬¬𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒 | Subs [𝜑↗→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒, 𝜓↗¬¬𝜑] into ax-1 | |
| 9343 | →¬¬𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒 | Modus ponens 9341, 9342 | |
| 9344 | →→¬¬𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒→→¬¬𝜑→⋀𝜓𝜒𝜑→¬¬𝜑→⋀𝜓𝜒𝜒 | Subs [𝜑↗¬¬𝜑, 𝜓↗→⋀𝜓𝜒𝜑, 𝜒↗→⋀𝜓𝜒𝜒] into ax-2 | |
| 9345 | →→¬¬𝜑→⋀𝜓𝜒𝜑→¬¬𝜑→⋀𝜓𝜒𝜒 | Modus ponens 9343, 9344 | |
| 9346 | →¬¬𝜑→⋀𝜓𝜒𝜒 | Modus ponens 8934, 9345 | |
| 9347 | →→¬¬𝜑→⋀𝜓𝜒𝜒→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜒 | Subs [𝜑↗¬¬𝜑, 𝜓↗⋀𝜓𝜒] into ax-2 | |
| 9348 | →→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜒 | Modus ponens 9346, 9347 | |
| 9349 | →→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜒→⋀𝜓𝜒→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜒 | Subs [𝜑↗→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜒, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 9350 | →⋀𝜓𝜒→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜒 | Modus ponens 9348, 9349 | |
| 9351 | →→⋀𝜓𝜒→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜒→→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜑⋀𝜓𝜒, 𝜒↗→¬¬𝜑𝜒] into ax-2 | |
| 9352 | →→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑𝜒 | Modus ponens 9350, 9351 | |
| 9353 | →⋀𝜓𝜒→¬¬𝜑𝜒 | Modus ponens 8942, 9352 | |
| 9354 | →→𝜒¬¬𝜒→¬¬𝜑→𝜒¬¬𝜒 | Subs [𝜑↗→𝜒¬¬𝜒, 𝜓↗¬¬𝜑] into ax-1 | |
| 9355 | →¬¬𝜑→𝜒¬¬𝜒 | Modus ponens 9172, 9354 | |
| 9356 | →→¬¬𝜑→𝜒¬¬𝜒→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒 | Subs [𝜑↗¬¬𝜑, 𝜓↗𝜒, 𝜒↗¬¬𝜒] into ax-2 | |
| 9357 | →→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒 | Modus ponens 9355, 9356 | |
| 9358 | →→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒→⋀𝜓𝜒→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒 | Subs [𝜑↗→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 9359 | →⋀𝜓𝜒→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒 | Modus ponens 9357, 9358 | |
| 9360 | →→⋀𝜓𝜒→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒→→⋀𝜓𝜒→¬¬𝜑𝜒→⋀𝜓𝜒→¬¬𝜑¬¬𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜑𝜒, 𝜒↗→¬¬𝜑¬¬𝜒] into ax-2 | |
| 9361 | →→⋀𝜓𝜒→¬¬𝜑𝜒→⋀𝜓𝜒→¬¬𝜑¬¬𝜒 | Modus ponens 9359, 9360 | |
| 9362 | →⋀𝜓𝜒→¬¬𝜑¬¬𝜒 | Modus ponens 9353, 9361 | |
| 9363 | →→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜒] into ax-3 | |
| 9364 | →→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑→⋀𝜓𝜒→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑 | Subs [𝜑↗→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 9365 | →⋀𝜓𝜒→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑 | Modus ponens 9363, 9364 | |
| 9366 | →→⋀𝜓𝜒→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑→→⋀𝜓𝜒→¬¬𝜑¬¬𝜒→⋀𝜓𝜒→¬𝜒¬𝜑 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜑¬¬𝜒, 𝜒↗→¬𝜒¬𝜑] into ax-2 | |
| 9367 | →→⋀𝜓𝜒→¬¬𝜑¬¬𝜒→⋀𝜓𝜒→¬𝜒¬𝜑 | Modus ponens 9365, 9366 | |
| 9368 | →⋀𝜓𝜒→¬𝜒¬𝜑 | Modus ponens 9362, 9367 | |
| 9369 | →¬𝜒→⋀𝜓𝜒¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 9370 | →→¬𝜒→⋀𝜓𝜒¬𝜒→¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜒 | Subs [𝜑↗→¬𝜒→⋀𝜓𝜒¬𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 9371 | →¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜒 | Modus ponens 9369, 9370 | |
| 9372 | →→¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜒→→¬𝜒¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→⋀𝜓𝜒¬𝜒] into ax-2 | |
| 9373 | →→¬𝜒¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜒 | Modus ponens 9371, 9372 | |
| 9374 | →→⋀𝜓𝜒→¬𝜒¬𝜑→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬𝜒, 𝜒↗¬𝜑] into ax-2 | |
| 9375 | →→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜑 | Modus ponens 9368, 9374 | |
| 9376 | →→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜑→¬𝜒→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜒] into ax-1 | |
| 9377 | →¬𝜒→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜑 | Modus ponens 9375, 9376 | |
| 9378 | →→¬𝜒→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜑→→¬𝜒→⋀𝜓𝜒¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜓𝜒¬𝜒, 𝜒↗→⋀𝜓𝜒¬𝜑] into ax-2 | |
| 9379 | →→¬𝜒→⋀𝜓𝜒¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜑 | Modus ponens 9377, 9378 | |
| 9380 | →¬𝜒→⋀𝜓𝜒¬𝜑 | Modus ponens 9369, 9379 | |
| 9381 | →→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬𝜒→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜒] into ax-1 | |
| 9382 | →¬𝜒→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑 | Modus ponens 8976, 9381 | |
| 9383 | →¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜒] into ax-1 | |
| 9384 | →→¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜑] into ax-1 | |
| 9385 | →¬¬¬→⋀𝜓𝜒¬𝜑→¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑 | Modus ponens 9383, 9384 | |
| 9386 | →→¬¬¬→⋀𝜓𝜒¬𝜑→¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬→⋀𝜓𝜒¬𝜑, 𝜒↗→¬𝜒¬→⋀𝜓𝜒¬𝜑] into ax-2 | |
| 9387 | →→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑 | Modus ponens 9385, 9386 | |
| 9388 | →¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑 | Modus ponens 8979, 9387 | |
| 9389 | →→¬𝜒→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗¬𝜒, 𝜓↗¬→⋀𝜓𝜒¬𝜑, 𝜒↗¬→⋀𝜓𝜒¬𝜑] into ax-2 | |
| 9390 | →→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑 | Modus ponens 9382, 9389 | |
| 9391 | →→→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗→→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜑] into ax-1 | |
| 9392 | →¬¬¬→⋀𝜓𝜒¬𝜑→→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑 | Modus ponens 9390, 9391 | |
| 9393 | →→¬¬¬→⋀𝜓𝜒¬𝜑→→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑→→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗→¬𝜒¬→⋀𝜓𝜒¬𝜑, 𝜒↗→¬𝜒¬→⋀𝜓𝜒¬𝜑] into ax-2 | |
| 9394 | →→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑 | Modus ponens 9392, 9393 | |
| 9395 | →¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜑] into ax-1 | |
| 9396 | →→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒 | Subs [𝜑↗→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 9397 | →¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒 | Modus ponens 9395, 9396 | |
| 9398 | →→¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒] into ax-2 | |
| 9399 | →→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒 | Modus ponens 9397, 9398 | |
| 9400 | →→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜒, 𝜒↗¬→⋀𝜓𝜒¬𝜑] into ax-2 | |
| 9401 | →→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑 | Modus ponens 9388, 9400 | |
| 9402 | →→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜒] into ax-1 | |
| 9403 | →¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑 | Modus ponens 9401, 9402 | |
| 9404 | →→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒, 𝜒↗→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑] into ax-2 | |
| 9405 | →→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑 | Modus ponens 9403, 9404 | |
| 9406 | →¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑 | Modus ponens 9395, 9405 | |
| 9407 | →→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜒] into ax-1 | |
| 9408 | →¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑 | Modus ponens 9004, 9407 | |
| 9409 | →→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑→→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬𝜒→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑, 𝜒↗→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑] into ax-2 | |
| 9410 | →→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬𝜒→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑 | Modus ponens 9408, 9409 | |
| 9411 | →¬𝜒→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑 | Modus ponens 9406, 9410 | |
| 9412 | →→¬𝜒→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑→→¬𝜒→⋀𝜓𝜒¬𝜑→¬𝜒¬¬→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜓𝜒¬𝜑, 𝜒↗¬¬→⋀𝜓𝜒¬𝜑] into ax-2 | |
| 9413 | →→¬𝜒→⋀𝜓𝜒¬𝜑→¬𝜒¬¬→⋀𝜓𝜒¬𝜑 | Modus ponens 9411, 9412 | |
| 9414 | →¬𝜒¬¬→⋀𝜓𝜒¬𝜑 | Modus ponens 9380, 9413 | |
| 9415 | →→¬𝜒¬¬→⋀𝜓𝜒¬𝜑→¬→⋀𝜓𝜒¬𝜑𝜒 | Subs [𝜑↗𝜒, 𝜓↗¬→⋀𝜓𝜒¬𝜑] into ax-3 | |
| 9416 | →¬→⋀𝜓𝜒¬𝜑𝜒 | Modus ponens 9414, 9415 | |
| 9417 | →→¬→⋀𝜓𝜒¬𝜑𝜒→⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜒 | Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜑𝜒, 𝜓↗⋀⋀𝜓𝜒𝜑] into ax-1 | |
| 9418 | →⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜒 | Modus ponens 9416, 9417 | |
| 9419 | →→⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜒→→⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜒 | Subs [𝜑↗⋀⋀𝜓𝜒𝜑, 𝜓↗¬→⋀𝜓𝜒¬𝜑] into ax-2 | |
| 9420 | →→⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜒 | Modus ponens 9418, 9419 | |
| 9421 | →⋀⋀𝜓𝜒𝜑𝜒 | Modus ponens 9016, 9420 | |
| 9422 | →→⋀⋀𝜓𝜒𝜑𝜒→¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜒 | Subs [𝜑↗→⋀⋀𝜓𝜒𝜑𝜒, 𝜓↗¬→⋀𝜓𝜒¬𝜑] into ax-1 | |
| 9423 | →¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜒 | Modus ponens 9421, 9422 | |
| 9424 | →→¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜒→→¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜒 | Subs [𝜑↗¬→⋀𝜓𝜒¬𝜑, 𝜓↗⋀⋀𝜓𝜒𝜑] into ax-2 | |
| 9425 | →→¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜒 | Modus ponens 9423, 9424 | |
| 9426 | →→¬→⋀𝜓𝜒¬𝜑𝜒→𝜑→¬→⋀𝜓𝜒¬𝜑𝜒 | Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜑𝜒, 𝜓↗𝜑] into ax-1 | |
| 9427 | →𝜑→¬→⋀𝜓𝜒¬𝜑𝜒 | Modus ponens 9416, 9426 | |
| 9428 | →→𝜑→¬→⋀𝜓𝜒¬𝜑𝜒→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜒 | Subs [𝜓↗¬→⋀𝜓𝜒¬𝜑] into ax-2 | |
| 9429 | →→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜒 | Modus ponens 9427, 9428 | |
| 9430 | →→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜒→⋀𝜓𝜒→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜒 | Subs [𝜑↗→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜒, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 9431 | →⋀𝜓𝜒→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜒 | Modus ponens 9429, 9430 | |
| 9432 | →→⋀𝜓𝜒→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜒→→⋀𝜓𝜒→𝜑¬→⋀𝜓𝜒¬𝜑→⋀𝜓𝜒→𝜑𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→𝜑¬→⋀𝜓𝜒¬𝜑, 𝜒↗→𝜑𝜒] into ax-2 | |
| 9433 | →→⋀𝜓𝜒→𝜑¬→⋀𝜓𝜒¬𝜑→⋀𝜓𝜒→𝜑𝜒 | Modus ponens 9431, 9432 | |
| 9434 | →→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒→𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒 | Subs [𝜑↗→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1 | |
| 9435 | →𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒 | Modus ponens 9341, 9434 | |
| 9436 | →→𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒→→𝜑→⋀𝜓𝜒𝜑→𝜑→⋀𝜓𝜒𝜒 | Subs [𝜓↗→⋀𝜓𝜒𝜑, 𝜒↗→⋀𝜓𝜒𝜒] into ax-2 | |
| 9437 | →→𝜑→⋀𝜓𝜒𝜑→𝜑→⋀𝜓𝜒𝜒 | Modus ponens 9435, 9436 | |
| 9438 | →→→𝜑⋀𝜓𝜒→𝜑𝜒→¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→→𝜑⋀𝜓𝜒→𝜑𝜒, 𝜓↗¬¬⋀𝜓𝜒] into ax-1 | |
| 9439 | →¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑𝜒 | Modus ponens 6081, 9438 | |
| 9440 | →→¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑𝜒→→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒→¬¬⋀𝜓𝜒→𝜑𝜒 | Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗→𝜑⋀𝜓𝜒, 𝜒↗→𝜑𝜒] into ax-2 | |
| 9441 | →→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒→¬¬⋀𝜓𝜒→𝜑𝜒 | Modus ponens 9439, 9440 | |
| 9442 | →¬¬⋀𝜓𝜒→𝜑𝜒 | Modus ponens 5479, 9441 | |
| 9443 | →→¬¬⋀𝜓𝜒→𝜑𝜒→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜒 | Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗𝜑] into ax-2 | |
| 9444 | →→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜒 | Modus ponens 9442, 9443 | |
| 9445 | →→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜒→𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜒 | Subs [𝜑↗→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1 | |
| 9446 | →𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜒 | Modus ponens 9444, 9445 | |
| 9447 | →→𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜒→→𝜑→¬¬⋀𝜓𝜒𝜑→𝜑→¬¬⋀𝜓𝜒𝜒 | Subs [𝜓↗→¬¬⋀𝜓𝜒𝜑, 𝜒↗→¬¬⋀𝜓𝜒𝜒] into ax-2 | |
| 9448 | →→𝜑→¬¬⋀𝜓𝜒𝜑→𝜑→¬¬⋀𝜓𝜒𝜒 | Modus ponens 9446, 9447 | |
| 9449 | →𝜑→¬¬⋀𝜓𝜒𝜒 | Modus ponens 5487, 9448 | |
| 9450 | →→𝜒¬¬𝜒→¬¬⋀𝜓𝜒→𝜒¬¬𝜒 | Subs [𝜑↗→𝜒¬¬𝜒, 𝜓↗¬¬⋀𝜓𝜒] into ax-1 | |
| 9451 | →¬¬⋀𝜓𝜒→𝜒¬¬𝜒 | Modus ponens 9172, 9450 | |
| 9452 | →→¬¬⋀𝜓𝜒→𝜒¬¬𝜒→→¬¬⋀𝜓𝜒𝜒→¬¬⋀𝜓𝜒¬¬𝜒 | Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗𝜒, 𝜒↗¬¬𝜒] into ax-2 | |
| 9453 | →→¬¬⋀𝜓𝜒𝜒→¬¬⋀𝜓𝜒¬¬𝜒 | Modus ponens 9451, 9452 | |
| 9454 | →→→¬¬⋀𝜓𝜒𝜒→¬¬⋀𝜓𝜒¬¬𝜒→𝜑→→¬¬⋀𝜓𝜒𝜒→¬¬⋀𝜓𝜒¬¬𝜒 | Subs [𝜑↗→→¬¬⋀𝜓𝜒𝜒→¬¬⋀𝜓𝜒¬¬𝜒, 𝜓↗𝜑] into ax-1 | |
| 9455 | →𝜑→→¬¬⋀𝜓𝜒𝜒→¬¬⋀𝜓𝜒¬¬𝜒 | Modus ponens 9453, 9454 | |
| 9456 | →→𝜑→→¬¬⋀𝜓𝜒𝜒→¬¬⋀𝜓𝜒¬¬𝜒→→𝜑→¬¬⋀𝜓𝜒𝜒→𝜑→¬¬⋀𝜓𝜒¬¬𝜒 | Subs [𝜓↗→¬¬⋀𝜓𝜒𝜒, 𝜒↗→¬¬⋀𝜓𝜒¬¬𝜒] into ax-2 | |
| 9457 | →→𝜑→¬¬⋀𝜓𝜒𝜒→𝜑→¬¬⋀𝜓𝜒¬¬𝜒 | Modus ponens 9455, 9456 | |
| 9458 | →𝜑→¬¬⋀𝜓𝜒¬¬𝜒 | Modus ponens 9449, 9457 | |
| 9459 | →→¬¬⋀𝜓𝜒¬¬𝜒→¬𝜒¬⋀𝜓𝜒 | Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬𝜒] into ax-3 | |
| 9460 | →→→¬¬⋀𝜓𝜒¬¬𝜒→¬𝜒¬⋀𝜓𝜒→𝜑→→¬¬⋀𝜓𝜒¬¬𝜒→¬𝜒¬⋀𝜓𝜒 | Subs [𝜑↗→→¬¬⋀𝜓𝜒¬¬𝜒→¬𝜒¬⋀𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 9461 | →𝜑→→¬¬⋀𝜓𝜒¬¬𝜒→¬𝜒¬⋀𝜓𝜒 | Modus ponens 9459, 9460 | |
| 9462 | →→𝜑→→¬¬⋀𝜓𝜒¬¬𝜒→¬𝜒¬⋀𝜓𝜒→→𝜑→¬¬⋀𝜓𝜒¬¬𝜒→𝜑→¬𝜒¬⋀𝜓𝜒 | Subs [𝜓↗→¬¬⋀𝜓𝜒¬¬𝜒, 𝜒↗→¬𝜒¬⋀𝜓𝜒] into ax-2 | |
| 9463 | →→𝜑→¬¬⋀𝜓𝜒¬¬𝜒→𝜑→¬𝜒¬⋀𝜓𝜒 | Modus ponens 9461, 9462 | |
| 9464 | →𝜑→¬𝜒¬⋀𝜓𝜒 | Modus ponens 9458, 9463 | |
| 9465 | →¬𝜒→𝜑¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗𝜑] into ax-1 | |
| 9466 | →→¬𝜒→𝜑¬𝜒→¬𝜒→¬𝜒→𝜑¬𝜒 | Subs [𝜑↗→¬𝜒→𝜑¬𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 9467 | →¬𝜒→¬𝜒→𝜑¬𝜒 | Modus ponens 9465, 9466 | |
| 9468 | →→¬𝜒→¬𝜒→𝜑¬𝜒→→¬𝜒¬𝜒→¬𝜒→𝜑¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→𝜑¬𝜒] into ax-2 | |
| 9469 | →→¬𝜒¬𝜒→¬𝜒→𝜑¬𝜒 | Modus ponens 9467, 9468 | |
| 9470 | →→𝜑→¬𝜒¬⋀𝜓𝜒→→𝜑¬𝜒→𝜑¬⋀𝜓𝜒 | Subs [𝜓↗¬𝜒, 𝜒↗¬⋀𝜓𝜒] into ax-2 | |
| 9471 | →→𝜑¬𝜒→𝜑¬⋀𝜓𝜒 | Modus ponens 9464, 9470 | |
| 9472 | →→→𝜑¬𝜒→𝜑¬⋀𝜓𝜒→¬𝜒→→𝜑¬𝜒→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→→𝜑¬𝜒→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 9473 | →¬𝜒→→𝜑¬𝜒→𝜑¬⋀𝜓𝜒 | Modus ponens 9471, 9472 | |
| 9474 | →→¬𝜒→→𝜑¬𝜒→𝜑¬⋀𝜓𝜒→→¬𝜒→𝜑¬𝜒→¬𝜒→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗→𝜑¬𝜒, 𝜒↗→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 9475 | →→¬𝜒→𝜑¬𝜒→¬𝜒→𝜑¬⋀𝜓𝜒 | Modus ponens 9473, 9474 | |
| 9476 | →¬𝜒→𝜑¬⋀𝜓𝜒 | Modus ponens 9465, 9475 | |
| 9477 | →→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 9478 | →¬𝜒→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 5528, 9477 | |
| 9479 | →¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 9480 | →→¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1 | |
| 9481 | →¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9479, 9480 | |
| 9482 | →→¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗→¬𝜒¬→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 9483 | →→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9481, 9482 | |
| 9484 | →¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 5531, 9483 | |
| 9485 | →→¬𝜒→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗¬→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 9486 | →→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9478, 9485 | |
| 9487 | →→→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1 | |
| 9488 | →¬¬¬→𝜑¬⋀𝜓𝜒→→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9486, 9487 | |
| 9489 | →→¬¬¬→𝜑¬⋀𝜓𝜒→→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗→¬𝜒¬→𝜑¬⋀𝜓𝜒, 𝜒↗→¬𝜒¬→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 9490 | →→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9488, 9489 | |
| 9491 | →¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1 | |
| 9492 | →→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒 | Subs [𝜑↗→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 9493 | →¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒 | Modus ponens 9491, 9492 | |
| 9494 | →→¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒] into ax-2 | |
| 9495 | →→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒 | Modus ponens 9493, 9494 | |
| 9496 | →→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜒, 𝜒↗¬→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 9497 | →→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9484, 9496 | |
| 9498 | →→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 9499 | →¬𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9497, 9498 | |
| 9500 | →→¬𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒, 𝜒↗→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 9501 | →→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9499, 9500 | |
| 9502 | →¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9491, 9501 | |
| 9503 | →→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→¬𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 9504 | →¬𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒 | Modus ponens 5556, 9503 | |
| 9505 | →→¬𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜒↗→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 9506 | →→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9504, 9505 | |
| 9507 | →¬𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9502, 9506 | |
| 9508 | →→¬𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→→¬𝜒→𝜑¬⋀𝜓𝜒→¬𝜒¬¬→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒, 𝜒↗¬¬→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 9509 | →→¬𝜒→𝜑¬⋀𝜓𝜒→¬𝜒¬¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9507, 9508 | |
| 9510 | →¬𝜒¬¬→𝜑¬⋀𝜓𝜒 | Modus ponens 9476, 9509 | |
| 9511 | →→¬𝜒¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒 | Subs [𝜑↗𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into ax-3 | |
| 9512 | →¬→𝜑¬⋀𝜓𝜒𝜒 | Modus ponens 9510, 9511 | |
| 9513 | →→¬→𝜑¬⋀𝜓𝜒𝜒→⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒 | Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 9514 | →⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒 | Modus ponens 9512, 9513 | |
| 9515 | →→⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒→→⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 9516 | →→⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜒 | Modus ponens 9514, 9515 | |
| 9517 | →⋀𝜑⋀𝜓𝜒𝜒 | Modus ponens 5568, 9516 | simprr |
| 9518 | →𝜑→𝜃𝜑 | Subs [𝜓↗𝜃] into ax-1 | |
| 9519 | →→𝜑→𝜃𝜑→⋀𝜑𝜓→𝜑→𝜃𝜑 | Subs [𝜑↗→𝜑→𝜃𝜑, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 9520 | →⋀𝜑𝜓→𝜑→𝜃𝜑 | Modus ponens 9518, 9519 | |
| 9521 | →→⋀𝜑𝜓→𝜑→𝜃𝜑→→⋀𝜑𝜓𝜑→⋀𝜑𝜓→𝜃𝜑 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜑, 𝜒↗→𝜃𝜑] into ax-2 | |
| 9522 | →→⋀𝜑𝜓𝜑→⋀𝜑𝜓→𝜃𝜑 | Modus ponens 9520, 9521 | |
| 9523 | →⋀𝜑𝜓→𝜃𝜑 | Modus ponens simpl, 9522 | |
| 9524 | ↔⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜃] into df-an | |
| 9525 | →¬¬𝜃𝜃 | Subs [𝜑↗𝜃] into notnotr | |
| 9526 | →𝜃→⋀𝜑𝜓𝜃 | Subs [𝜑↗𝜃, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 9527 | →→𝜃→⋀𝜑𝜓𝜃→¬¬𝜃→𝜃→⋀𝜑𝜓𝜃 | Subs [𝜑↗→𝜃→⋀𝜑𝜓𝜃, 𝜓↗¬¬𝜃] into ax-1 | |
| 9528 | →¬¬𝜃→𝜃→⋀𝜑𝜓𝜃 | Modus ponens 9526, 9527 | |
| 9529 | →→¬¬𝜃→𝜃→⋀𝜑𝜓𝜃→→¬¬𝜃𝜃→¬¬𝜃→⋀𝜑𝜓𝜃 | Subs [𝜑↗¬¬𝜃, 𝜓↗𝜃, 𝜒↗→⋀𝜑𝜓𝜃] into ax-2 | |
| 9530 | →→¬¬𝜃𝜃→¬¬𝜃→⋀𝜑𝜓𝜃 | Modus ponens 9528, 9529 | |
| 9531 | →¬¬𝜃→⋀𝜑𝜓𝜃 | Modus ponens 9525, 9530 | |
| 9532 | →→⋀𝜑𝜓→𝜃𝜑→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜃, 𝜒↗𝜑] into ax-2 | |
| 9533 | →→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑 | Modus ponens 9523, 9532 | |
| 9534 | →→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑→¬¬𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑 | Subs [𝜑↗→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑, 𝜓↗¬¬𝜃] into ax-1 | |
| 9535 | →¬¬𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑 | Modus ponens 9533, 9534 | |
| 9536 | →→¬¬𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑→→¬¬𝜃→⋀𝜑𝜓𝜃→¬¬𝜃→⋀𝜑𝜓𝜑 | Subs [𝜑↗¬¬𝜃, 𝜓↗→⋀𝜑𝜓𝜃, 𝜒↗→⋀𝜑𝜓𝜑] into ax-2 | |
| 9537 | →→¬¬𝜃→⋀𝜑𝜓𝜃→¬¬𝜃→⋀𝜑𝜓𝜑 | Modus ponens 9535, 9536 | |
| 9538 | →¬¬𝜃→⋀𝜑𝜓𝜑 | Modus ponens 9531, 9537 | |
| 9539 | →⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬¬𝜃] into ax-1 | |
| 9540 | →→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓→⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓 | Subs [𝜑↗→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 9541 | →⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓 | Modus ponens 9539, 9540 | |
| 9542 | →→⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗→¬¬𝜃⋀𝜑𝜓] into ax-2 | |
| 9543 | →→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓 | Modus ponens 9541, 9542 | |
| 9544 | →→¬¬𝜃→⋀𝜑𝜓𝜑→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜑 | Subs [𝜑↗¬¬𝜃, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜑] into ax-2 | |
| 9545 | →→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜑 | Modus ponens 9538, 9544 | |
| 9546 | →→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜑→⋀𝜑𝜓→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜑 | Subs [𝜑↗→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜑, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 9547 | →⋀𝜑𝜓→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜑 | Modus ponens 9545, 9546 | |
| 9548 | →→⋀𝜑𝜓→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜑→→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃𝜑 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜃⋀𝜑𝜓, 𝜒↗→¬¬𝜃𝜑] into ax-2 | |
| 9549 | →→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃𝜑 | Modus ponens 9547, 9548 | |
| 9550 | →⋀𝜑𝜓→¬¬𝜃𝜑 | Modus ponens 9539, 9549 | |
| 9551 | →→𝜑¬¬𝜑→¬¬𝜃→𝜑¬¬𝜑 | Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜃] into ax-1 | |
| 9552 | →¬¬𝜃→𝜑¬¬𝜑 | Modus ponens notnot, 9551 | |
| 9553 | →→¬¬𝜃→𝜑¬¬𝜑→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑 | Subs [𝜑↗¬¬𝜃, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2 | |
| 9554 | →→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑 | Modus ponens 9552, 9553 | |
| 9555 | →→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑→⋀𝜑𝜓→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑 | Subs [𝜑↗→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 9556 | →⋀𝜑𝜓→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑 | Modus ponens 9554, 9555 | |
| 9557 | →→⋀𝜑𝜓→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑→→⋀𝜑𝜓→¬¬𝜃𝜑→⋀𝜑𝜓→¬¬𝜃¬¬𝜑 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜃𝜑, 𝜒↗→¬¬𝜃¬¬𝜑] into ax-2 | |
| 9558 | →→⋀𝜑𝜓→¬¬𝜃𝜑→⋀𝜑𝜓→¬¬𝜃¬¬𝜑 | Modus ponens 9556, 9557 | |
| 9559 | →⋀𝜑𝜓→¬¬𝜃¬¬𝜑 | Modus ponens 9550, 9558 | |
| 9560 | →→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗¬𝜑] into ax-3 | |
| 9561 | →→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃→⋀𝜑𝜓→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃 | Subs [𝜑↗→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 9562 | →⋀𝜑𝜓→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃 | Modus ponens 9560, 9561 | |
| 9563 | →→⋀𝜑𝜓→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃→→⋀𝜑𝜓→¬¬𝜃¬¬𝜑→⋀𝜑𝜓→¬𝜑¬𝜃 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜃¬¬𝜑, 𝜒↗→¬𝜑¬𝜃] into ax-2 | |
| 9564 | →→⋀𝜑𝜓→¬¬𝜃¬¬𝜑→⋀𝜑𝜓→¬𝜑¬𝜃 | Modus ponens 9562, 9563 | |
| 9565 | →⋀𝜑𝜓→¬𝜑¬𝜃 | Modus ponens 9559, 9564 | |
| 9566 | →→⋀𝜑𝜓→¬𝜑¬𝜃→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬𝜑, 𝜒↗¬𝜃] into ax-2 | |
| 9567 | →→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜃 | Modus ponens 9565, 9566 | |
| 9568 | →→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜃→¬𝜑→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜑] into ax-1 | |
| 9569 | →¬𝜑→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜃 | Modus ponens 9567, 9568 | |
| 9570 | →→¬𝜑→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜃→→¬𝜑→⋀𝜑𝜓¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀𝜑𝜓¬𝜑, 𝜒↗→⋀𝜑𝜓¬𝜃] into ax-2 | |
| 9571 | →→¬𝜑→⋀𝜑𝜓¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜃 | Modus ponens 9569, 9570 | |
| 9572 | →¬𝜑→⋀𝜑𝜓¬𝜃 | Modus ponens 8680, 9571 | |
| 9573 | →¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗¬→⋀𝜑𝜓¬𝜃] into id | |
| 9574 | →→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬𝜑→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜑] into ax-1 | |
| 9575 | →¬𝜑→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9573, 9574 | |
| 9576 | →¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗¬→⋀𝜑𝜓¬𝜃] into notnotr | |
| 9577 | →¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜑] into ax-1 | |
| 9578 | →→¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜃] into ax-1 | |
| 9579 | →¬¬¬→⋀𝜑𝜓¬𝜃→¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9577, 9578 | |
| 9580 | →→¬¬¬→⋀𝜑𝜓¬𝜃→¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬→⋀𝜑𝜓¬𝜃, 𝜒↗→¬𝜑¬→⋀𝜑𝜓¬𝜃] into ax-2 | |
| 9581 | →→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9579, 9580 | |
| 9582 | →¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9576, 9581 | |
| 9583 | →→¬𝜑→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀𝜑𝜓¬𝜃, 𝜒↗¬→⋀𝜑𝜓¬𝜃] into ax-2 | |
| 9584 | →→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9575, 9583 | |
| 9585 | →→→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗→→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜃] into ax-1 | |
| 9586 | →¬¬¬→⋀𝜑𝜓¬𝜃→→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9584, 9585 | |
| 9587 | →→¬¬¬→⋀𝜑𝜓¬𝜃→→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃→→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗→¬𝜑¬→⋀𝜑𝜓¬𝜃, 𝜒↗→¬𝜑¬→⋀𝜑𝜓¬𝜃] into ax-2 | |
| 9588 | →→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9586, 9587 | |
| 9589 | →¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜃] into ax-1 | |
| 9590 | →→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 9591 | →¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑 | Modus ponens 9589, 9590 | |
| 9592 | →→¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑] into ax-2 | |
| 9593 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑 | Modus ponens 9591, 9592 | |
| 9594 | →→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜑, 𝜒↗¬→⋀𝜑𝜓¬𝜃] into ax-2 | |
| 9595 | →→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9582, 9594 | |
| 9596 | →→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜑] into ax-1 | |
| 9597 | →¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9595, 9596 | |
| 9598 | →→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃] into ax-2 | |
| 9599 | →→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9597, 9598 | |
| 9600 | →¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9589, 9599 | |
| 9601 | →→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗→⋀𝜑𝜓¬𝜃] into ax-3 | |
| 9602 | →→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜑] into ax-1 | |
| 9603 | →¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9601, 9602 | |
| 9604 | →→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃→→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬𝜑→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃, 𝜒↗→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃] into ax-2 | |
| 9605 | →→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬𝜑→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9603, 9604 | |
| 9606 | →¬𝜑→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9600, 9605 | |
| 9607 | →→¬𝜑→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃→→¬𝜑→⋀𝜑𝜓¬𝜃→¬𝜑¬¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀𝜑𝜓¬𝜃, 𝜒↗¬¬→⋀𝜑𝜓¬𝜃] into ax-2 | |
| 9608 | →→¬𝜑→⋀𝜑𝜓¬𝜃→¬𝜑¬¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9606, 9607 | |
| 9609 | →¬𝜑¬¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9572, 9608 | |
| 9610 | →→¬𝜑¬¬→⋀𝜑𝜓¬𝜃→¬→⋀𝜑𝜓¬𝜃𝜑 | Subs [𝜓↗¬→⋀𝜑𝜓¬𝜃] into ax-3 | |
| 9611 | →¬→⋀𝜑𝜓¬𝜃𝜑 | Modus ponens 9609, 9610 | |
| 9612 | →↔⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗⋀⋀𝜑𝜓𝜃, 𝜓↗¬→⋀𝜑𝜓¬𝜃] into biimp | |
| 9613 | →⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9524, 9612 | |
| 9614 | →→¬→⋀𝜑𝜓¬𝜃𝜑→⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜑 | Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜃𝜑, 𝜓↗⋀⋀𝜑𝜓𝜃] into ax-1 | |
| 9615 | →⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜑 | Modus ponens 9611, 9614 | |
| 9616 | →→⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜑→→⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜑 | Subs [𝜑↗⋀⋀𝜑𝜓𝜃, 𝜓↗¬→⋀𝜑𝜓¬𝜃, 𝜒↗𝜑] into ax-2 | |
| 9617 | →→⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜑 | Modus ponens 9615, 9616 | |
| 9618 | →⋀⋀𝜑𝜓𝜃𝜑 | Modus ponens 9613, 9617 | |
| 9619 | →⋀⋀𝜑𝜓𝜒⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒] into simpl | |
| 9620 | →↔⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃↔¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃 | Subs [𝜑↗⋀⋀𝜑𝜓𝜃, 𝜓↗¬→⋀𝜑𝜓¬𝜃] into bicom1 | |
| 9621 | ↔¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃 | Modus ponens 9524, 9620 | |
| 9622 | →↔¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃 | Subs [𝜑↗¬→⋀𝜑𝜓¬𝜃, 𝜓↗⋀⋀𝜑𝜓𝜃] into biimp | |
| 9623 | →¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃 | Modus ponens 9621, 9622 | |
| 9624 | →→⋀⋀𝜑𝜓𝜃𝜑→¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜑 | Subs [𝜑↗→⋀⋀𝜑𝜓𝜃𝜑, 𝜓↗¬→⋀𝜑𝜓¬𝜃] into ax-1 | |
| 9625 | →¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜑 | Modus ponens 9618, 9624 | |
| 9626 | →→¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜑→→¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜑 | Subs [𝜑↗¬→⋀𝜑𝜓¬𝜃, 𝜓↗⋀⋀𝜑𝜓𝜃, 𝜒↗𝜑] into ax-2 | |
| 9627 | →→¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜑 | Modus ponens 9625, 9626 | |
| 9628 | →⋀𝜑𝜓→𝜃¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜃] into pm3.2im | |
| 9629 | →→¬→⋀𝜑𝜓¬𝜃𝜑→𝜃→¬→⋀𝜑𝜓¬𝜃𝜑 | Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜃𝜑, 𝜓↗𝜃] into ax-1 | |
| 9630 | →𝜃→¬→⋀𝜑𝜓¬𝜃𝜑 | Modus ponens 9611, 9629 | |
| 9631 | →→𝜃→¬→⋀𝜑𝜓¬𝜃𝜑→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜑 | Subs [𝜑↗𝜃, 𝜓↗¬→⋀𝜑𝜓¬𝜃, 𝜒↗𝜑] into ax-2 | |
| 9632 | →→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜑 | Modus ponens 9630, 9631 | |
| 9633 | →→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜑→⋀𝜑𝜓→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜑 | Subs [𝜑↗→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜑, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 9634 | →⋀𝜑𝜓→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜑 | Modus ponens 9632, 9633 | |
| 9635 | →→⋀𝜑𝜓→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜑→→⋀𝜑𝜓→𝜃¬→⋀𝜑𝜓¬𝜃→⋀𝜑𝜓→𝜃𝜑 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜃¬→⋀𝜑𝜓¬𝜃, 𝜒↗→𝜃𝜑] into ax-2 | |
| 9636 | →→⋀𝜑𝜓→𝜃¬→⋀𝜑𝜓¬𝜃→⋀𝜑𝜓→𝜃𝜑 | Modus ponens 9634, 9635 | |
| 9637 | →𝜃𝜃 | Subs [𝜑↗𝜃] into id | |
| 9638 | →→𝜃→⋀𝜑𝜓𝜃→𝜃→𝜃→⋀𝜑𝜓𝜃 | Subs [𝜑↗→𝜃→⋀𝜑𝜓𝜃, 𝜓↗𝜃] into ax-1 | |
| 9639 | →𝜃→𝜃→⋀𝜑𝜓𝜃 | Modus ponens 9526, 9638 | |
| 9640 | →→𝜃→𝜃→⋀𝜑𝜓𝜃→→𝜃𝜃→𝜃→⋀𝜑𝜓𝜃 | Subs [𝜑↗𝜃, 𝜓↗𝜃, 𝜒↗→⋀𝜑𝜓𝜃] into ax-2 | |
| 9641 | →→𝜃𝜃→𝜃→⋀𝜑𝜓𝜃 | Modus ponens 9639, 9640 | |
| 9642 | →→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑→𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑 | Subs [𝜑↗→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑, 𝜓↗𝜃] into ax-1 | |
| 9643 | →𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑 | Modus ponens 9533, 9642 | |
| 9644 | →→𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑→→𝜃→⋀𝜑𝜓𝜃→𝜃→⋀𝜑𝜓𝜑 | Subs [𝜑↗𝜃, 𝜓↗→⋀𝜑𝜓𝜃, 𝜒↗→⋀𝜑𝜓𝜑] into ax-2 | |
| 9645 | →→𝜃→⋀𝜑𝜓𝜃→𝜃→⋀𝜑𝜓𝜑 | Modus ponens 9643, 9644 | |
| 9646 | →𝜃→⋀𝜑𝜓𝜑 | Modus ponens 9526, 9645 | |
| 9647 | →⋀𝜑𝜓→𝜃⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜃] into ax-1 | |
| 9648 | →→⋀𝜑𝜓→𝜃⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒→⋀𝜑𝜓→𝜃⋀𝜑𝜓 | Subs [𝜑↗→⋀𝜑𝜓→𝜃⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 9649 | →⋀⋀𝜑𝜓𝜒→⋀𝜑𝜓→𝜃⋀𝜑𝜓 | Modus ponens 9647, 9648 | |
| 9650 | →→⋀⋀𝜑𝜓𝜒→⋀𝜑𝜓→𝜃⋀𝜑𝜓→→⋀⋀𝜑𝜓𝜒⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒→𝜃⋀𝜑𝜓 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗→𝜃⋀𝜑𝜓] into ax-2 | |
| 9651 | →→⋀⋀𝜑𝜓𝜒⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒→𝜃⋀𝜑𝜓 | Modus ponens 9649, 9650 | |
| 9652 | →⋀⋀𝜑𝜓𝜒→𝜃⋀𝜑𝜓 | Modus ponens 9619, 9651 | |
| 9653 | →→𝜃→⋀𝜑𝜓𝜑→→𝜃⋀𝜑𝜓→𝜃𝜑 | Subs [𝜑↗𝜃, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜑] into ax-2 | |
| 9654 | →→𝜃⋀𝜑𝜓→𝜃𝜑 | Modus ponens 9646, 9653 | |
| 9655 | →→→𝜃⋀𝜑𝜓→𝜃𝜑→⋀⋀𝜑𝜓𝜒→→𝜃⋀𝜑𝜓→𝜃𝜑 | Subs [𝜑↗→→𝜃⋀𝜑𝜓→𝜃𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 9656 | →⋀⋀𝜑𝜓𝜒→→𝜃⋀𝜑𝜓→𝜃𝜑 | Modus ponens 9654, 9655 | |
| 9657 | →→⋀⋀𝜑𝜓𝜒→→𝜃⋀𝜑𝜓→𝜃𝜑→→⋀⋀𝜑𝜓𝜒→𝜃⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒→𝜃𝜑 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜃⋀𝜑𝜓, 𝜒↗→𝜃𝜑] into ax-2 | |
| 9658 | →→⋀⋀𝜑𝜓𝜒→𝜃⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒→𝜃𝜑 | Modus ponens 9656, 9657 | |
| 9659 | →⋀⋀𝜑𝜓𝜒→𝜃𝜑 | Modus ponens 9652, 9658 | |
| 9660 | →𝜃→⋀⋀𝜑𝜓𝜒𝜃 | Subs [𝜑↗𝜃, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 9661 | →→𝜃→⋀⋀𝜑𝜓𝜒𝜃→𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜃 | Subs [𝜑↗→𝜃→⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜃] into ax-1 | |
| 9662 | →𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜃 | Modus ponens 9660, 9661 | |
| 9663 | →→𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜃→→𝜃𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜃 | Subs [𝜑↗𝜃, 𝜓↗𝜃, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜃] into ax-2 | |
| 9664 | →→𝜃𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜃 | Modus ponens 9662, 9663 | |
| 9665 | →→⋀⋀𝜑𝜓𝜒→𝜃𝜑→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜃, 𝜒↗𝜑] into ax-2 | |
| 9666 | →→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑 | Modus ponens 9659, 9665 | |
| 9667 | →→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑→𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑 | Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑, 𝜓↗𝜃] into ax-1 | |
| 9668 | →𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑 | Modus ponens 9666, 9667 | |
| 9669 | →→𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑→→𝜃→⋀⋀𝜑𝜓𝜒𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜑 | Subs [𝜑↗𝜃, 𝜓↗→⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜑] into ax-2 | |
| 9670 | →→𝜃→⋀⋀𝜑𝜓𝜒𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜑 | Modus ponens 9668, 9669 | |
| 9671 | →𝜃→⋀⋀𝜑𝜓𝜒𝜑 | Modus ponens 9660, 9670 | |
| 9672 | →⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜃] into ax-1 | |
| 9673 | →→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 9674 | →⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒 | Modus ponens 9672, 9673 | |
| 9675 | →→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜃⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 9676 | →→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒 | Modus ponens 9674, 9675 | |
| 9677 | →→𝜃→⋀⋀𝜑𝜓𝜒𝜑→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜑 | Subs [𝜑↗𝜃, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜑] into ax-2 | |
| 9678 | →→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜑 | Modus ponens 9671, 9677 | |
| 9679 | →→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜑→⋀⋀𝜑𝜓𝜒→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜑 | Subs [𝜑↗→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 9680 | →⋀⋀𝜑𝜓𝜒→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜑 | Modus ponens 9678, 9679 | |
| 9681 | →→⋀⋀𝜑𝜓𝜒→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜑→→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃𝜑 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜃⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜃𝜑] into ax-2 | |
| 9682 | →→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃𝜑 | Modus ponens 9680, 9681 | |
| 9683 | ↔⋀⋀⋀𝜑𝜓𝜒𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜃] into df-an | |
| 9684 | →→𝜃→⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜃 | Subs [𝜑↗→𝜃→⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬¬𝜃] into ax-1 | |
| 9685 | →¬¬𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜃 | Modus ponens 9660, 9684 | |
| 9686 | →→¬¬𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜃𝜃→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜃 | Subs [𝜑↗¬¬𝜃, 𝜓↗𝜃, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜃] into ax-2 | |
| 9687 | →→¬¬𝜃𝜃→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜃 | Modus ponens 9685, 9686 | |
| 9688 | →¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜃 | Modus ponens 9525, 9687 | |
| 9689 | →→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑→¬¬𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑 | Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑, 𝜓↗¬¬𝜃] into ax-1 | |
| 9690 | →¬¬𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑 | Modus ponens 9666, 9689 | |
| 9691 | →→¬¬𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑→→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜑 | Subs [𝜑↗¬¬𝜃, 𝜓↗→⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜑] into ax-2 | |
| 9692 | →→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜑 | Modus ponens 9690, 9691 | |
| 9693 | →¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜑 | Modus ponens 9688, 9692 | |
| 9694 | →⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬¬𝜃] into ax-1 | |
| 9695 | →→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 9696 | →⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒 | Modus ponens 9694, 9695 | |
| 9697 | →→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬𝜃⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 9698 | →→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒 | Modus ponens 9696, 9697 | |
| 9699 | →→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜑→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑 | Subs [𝜑↗¬¬𝜃, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜑] into ax-2 | |
| 9700 | →→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑 | Modus ponens 9693, 9699 | |
| 9701 | →→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑→⋀⋀𝜑𝜓𝜒→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑 | Subs [𝜑↗→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 9702 | →⋀⋀𝜑𝜓𝜒→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑 | Modus ponens 9700, 9701 | |
| 9703 | →→⋀⋀𝜑𝜓𝜒→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑→→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜃⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬𝜃𝜑] into ax-2 | |
| 9704 | →→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑 | Modus ponens 9702, 9703 | |
| 9705 | →⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑 | Modus ponens 9694, 9704 | |
| 9706 | →→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑→⋀⋀𝜑𝜓𝜒→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑 | Subs [𝜑↗→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 9707 | →⋀⋀𝜑𝜓𝜒→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑 | Modus ponens 9554, 9706 | |
| 9708 | →→⋀⋀𝜑𝜓𝜒→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑→→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜑 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜃𝜑, 𝜒↗→¬¬𝜃¬¬𝜑] into ax-2 | |
| 9709 | →→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜑 | Modus ponens 9707, 9708 | |
| 9710 | →⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜑 | Modus ponens 9705, 9709 | |
| 9711 | →→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃→⋀⋀𝜑𝜓𝜒→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃 | Subs [𝜑↗→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 9712 | →⋀⋀𝜑𝜓𝜒→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃 | Modus ponens 9560, 9711 | |
| 9713 | →→⋀⋀𝜑𝜓𝜒→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃→→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜑→⋀⋀𝜑𝜓𝜒→¬𝜑¬𝜃 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜃¬¬𝜑, 𝜒↗→¬𝜑¬𝜃] into ax-2 | |
| 9714 | →→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜑→⋀⋀𝜑𝜓𝜒→¬𝜑¬𝜃 | Modus ponens 9712, 9713 | |
| 9715 | →⋀⋀𝜑𝜓𝜒→¬𝜑¬𝜃 | Modus ponens 9710, 9714 | |
| 9716 | →¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 9717 | →→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑→¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑 | Subs [𝜑↗→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 9718 | →¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑 | Modus ponens 9716, 9717 | |
| 9719 | →→¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀𝜑𝜓𝜒¬𝜑] into ax-2 | |
| 9720 | →→¬𝜑¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑 | Modus ponens 9718, 9719 | |
| 9721 | →→⋀⋀𝜑𝜓𝜒→¬𝜑¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬𝜑, 𝜒↗¬𝜃] into ax-2 | |
| 9722 | →→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9715, 9721 | |
| 9723 | →→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜑] into ax-1 | |
| 9724 | →¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9722, 9723 | |
| 9725 | →→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜑, 𝜒↗→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2 | |
| 9726 | →→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9724, 9725 | |
| 9727 | →¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9716, 9726 | |
| 9728 | →¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into id | |
| 9729 | →→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜑] into ax-1 | |
| 9730 | →¬𝜑→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9728, 9729 | |
| 9731 | →¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into notnotr | |
| 9732 | →¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜑] into ax-1 | |
| 9733 | →→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-1 | |
| 9734 | →¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9732, 9733 | |
| 9735 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2 | |
| 9736 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9734, 9735 | |
| 9737 | →¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9731, 9736 | |
| 9738 | →→¬𝜑→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2 | |
| 9739 | →→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9730, 9738 | |
| 9740 | →→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-1 | |
| 9741 | →¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9739, 9740 | |
| 9742 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2 | |
| 9743 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9741, 9742 | |
| 9744 | →¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-1 | |
| 9745 | →→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 9746 | →¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑 | Modus ponens 9744, 9745 | |
| 9747 | →→¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑] into ax-2 | |
| 9748 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑 | Modus ponens 9746, 9747 | |
| 9749 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2 | |
| 9750 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9737, 9749 | |
| 9751 | →→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜑] into ax-1 | |
| 9752 | →¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9750, 9751 | |
| 9753 | →→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑, 𝜒↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2 | |
| 9754 | →→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9752, 9753 | |
| 9755 | →¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9744, 9754 | |
| 9756 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-3 | |
| 9757 | →→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜑] into ax-1 | |
| 9758 | →¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9756, 9757 | |
| 9759 | →→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2 | |
| 9760 | →→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9758, 9759 | |
| 9761 | →¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9755, 9760 | |
| 9762 | →→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2 | |
| 9763 | →→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9761, 9762 | |
| 9764 | →¬𝜑¬¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9727, 9763 | |
| 9765 | →→¬𝜑¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜑 | Subs [𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-3 | |
| 9766 | →¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜑 | Modus ponens 9764, 9765 | |
| 9767 | →↔⋀⋀⋀𝜑𝜓𝜒𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into biimp | |
| 9768 | →⋀⋀⋀𝜑𝜓𝜒𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9683, 9767 | |
| 9769 | →→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜑 | Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 9770 | →⋀⋀⋀𝜑𝜓𝜒𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜑 | Modus ponens 9766, 9769 | |
| 9771 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗𝜑] into ax-2 | |
| 9772 | →→⋀⋀⋀𝜑𝜓𝜒𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Modus ponens 9770, 9771 | |
| 9773 | →⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Modus ponens 9768, 9772 | simplll |
| 9774 | →𝜓→𝜃𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜃] into ax-1 | |
| 9775 | →→𝜓→𝜃𝜓→⋀𝜑𝜓→𝜓→𝜃𝜓 | Subs [𝜑↗→𝜓→𝜃𝜓, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 9776 | →⋀𝜑𝜓→𝜓→𝜃𝜓 | Modus ponens 9774, 9775 | |
| 9777 | →→⋀𝜑𝜓→𝜓→𝜃𝜓→→⋀𝜑𝜓𝜓→⋀𝜑𝜓→𝜃𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜒↗→𝜃𝜓] into ax-2 | |
| 9778 | →→⋀𝜑𝜓𝜓→⋀𝜑𝜓→𝜃𝜓 | Modus ponens 9776, 9777 | |
| 9779 | →⋀𝜑𝜓→𝜃𝜓 | Modus ponens simpr, 9778 | |
| 9780 | →→⋀𝜑𝜓→𝜃𝜓→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜃, 𝜒↗𝜓] into ax-2 | |
| 9781 | →→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓 | Modus ponens 9779, 9780 | |
| 9782 | →→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓→¬¬𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓 | Subs [𝜑↗→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓, 𝜓↗¬¬𝜃] into ax-1 | |
| 9783 | →¬¬𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓 | Modus ponens 9781, 9782 | |
| 9784 | →→¬¬𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓→→¬¬𝜃→⋀𝜑𝜓𝜃→¬¬𝜃→⋀𝜑𝜓𝜓 | Subs [𝜑↗¬¬𝜃, 𝜓↗→⋀𝜑𝜓𝜃, 𝜒↗→⋀𝜑𝜓𝜓] into ax-2 | |
| 9785 | →→¬¬𝜃→⋀𝜑𝜓𝜃→¬¬𝜃→⋀𝜑𝜓𝜓 | Modus ponens 9783, 9784 | |
| 9786 | →¬¬𝜃→⋀𝜑𝜓𝜓 | Modus ponens 9531, 9785 | |
| 9787 | →→¬¬𝜃→⋀𝜑𝜓𝜓→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜓 | Subs [𝜑↗¬¬𝜃, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜓] into ax-2 | |
| 9788 | →→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜓 | Modus ponens 9786, 9787 | |
| 9789 | →→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜓→⋀𝜑𝜓→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜓 | Subs [𝜑↗→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜓, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 9790 | →⋀𝜑𝜓→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜓 | Modus ponens 9788, 9789 | |
| 9791 | →→⋀𝜑𝜓→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜓→→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜃⋀𝜑𝜓, 𝜒↗→¬¬𝜃𝜓] into ax-2 | |
| 9792 | →→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃𝜓 | Modus ponens 9790, 9791 | |
| 9793 | →⋀𝜑𝜓→¬¬𝜃𝜓 | Modus ponens 9539, 9792 | |
| 9794 | →→𝜓¬¬𝜓→¬¬𝜃→𝜓¬¬𝜓 | Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜃] into ax-1 | |
| 9795 | →¬¬𝜃→𝜓¬¬𝜓 | Modus ponens 448, 9794 | |
| 9796 | →→¬¬𝜃→𝜓¬¬𝜓→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓 | Subs [𝜑↗¬¬𝜃, 𝜒↗¬¬𝜓] into ax-2 | |
| 9797 | →→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓 | Modus ponens 9795, 9796 | |
| 9798 | →→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓→⋀𝜑𝜓→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓 | Subs [𝜑↗→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 9799 | →⋀𝜑𝜓→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓 | Modus ponens 9797, 9798 | |
| 9800 | →→⋀𝜑𝜓→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓→→⋀𝜑𝜓→¬¬𝜃𝜓→⋀𝜑𝜓→¬¬𝜃¬¬𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜃𝜓, 𝜒↗→¬¬𝜃¬¬𝜓] into ax-2 | |
| 9801 | →→⋀𝜑𝜓→¬¬𝜃𝜓→⋀𝜑𝜓→¬¬𝜃¬¬𝜓 | Modus ponens 9799, 9800 | |
| 9802 | →⋀𝜑𝜓→¬¬𝜃¬¬𝜓 | Modus ponens 9793, 9801 | |
| 9803 | →→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗¬𝜓] into ax-3 | |
| 9804 | →→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃→⋀𝜑𝜓→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃 | Subs [𝜑↗→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 9805 | →⋀𝜑𝜓→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃 | Modus ponens 9803, 9804 | |
| 9806 | →→⋀𝜑𝜓→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃→→⋀𝜑𝜓→¬¬𝜃¬¬𝜓→⋀𝜑𝜓→¬𝜓¬𝜃 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜃¬¬𝜓, 𝜒↗→¬𝜓¬𝜃] into ax-2 | |
| 9807 | →→⋀𝜑𝜓→¬¬𝜃¬¬𝜓→⋀𝜑𝜓→¬𝜓¬𝜃 | Modus ponens 9805, 9806 | |
| 9808 | →⋀𝜑𝜓→¬𝜓¬𝜃 | Modus ponens 9802, 9807 | |
| 9809 | →→⋀𝜑𝜓→¬𝜓¬𝜃→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬𝜓, 𝜒↗¬𝜃] into ax-2 | |
| 9810 | →→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜃 | Modus ponens 9808, 9809 | |
| 9811 | →→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜃→¬𝜓→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜓] into ax-1 | |
| 9812 | →¬𝜓→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜃 | Modus ponens 9810, 9811 | |
| 9813 | →→¬𝜓→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜃→→¬𝜓→⋀𝜑𝜓¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜑𝜓¬𝜓, 𝜒↗→⋀𝜑𝜓¬𝜃] into ax-2 | |
| 9814 | →→¬𝜓→⋀𝜑𝜓¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜃 | Modus ponens 9812, 9813 | |
| 9815 | →¬𝜓→⋀𝜑𝜓¬𝜃 | Modus ponens 8871, 9814 | |
| 9816 | →→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬𝜓→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜓] into ax-1 | |
| 9817 | →¬𝜓→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9573, 9816 | |
| 9818 | →¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜓] into ax-1 | |
| 9819 | →→¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜃] into ax-1 | |
| 9820 | →¬¬¬→⋀𝜑𝜓¬𝜃→¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9818, 9819 | |
| 9821 | →→¬¬¬→⋀𝜑𝜓¬𝜃→¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬→⋀𝜑𝜓¬𝜃, 𝜒↗→¬𝜓¬→⋀𝜑𝜓¬𝜃] into ax-2 | |
| 9822 | →→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9820, 9821 | |
| 9823 | →¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9576, 9822 | |
| 9824 | →→¬𝜓→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀𝜑𝜓¬𝜃, 𝜒↗¬→⋀𝜑𝜓¬𝜃] into ax-2 | |
| 9825 | →→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9817, 9824 | |
| 9826 | →→→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗→→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜃] into ax-1 | |
| 9827 | →¬¬¬→⋀𝜑𝜓¬𝜃→→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9825, 9826 | |
| 9828 | →→¬¬¬→⋀𝜑𝜓¬𝜃→→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃→→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗→¬𝜓¬→⋀𝜑𝜓¬𝜃, 𝜒↗→¬𝜓¬→⋀𝜑𝜓¬𝜃] into ax-2 | |
| 9829 | →→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9827, 9828 | |
| 9830 | →¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜃] into ax-1 | |
| 9831 | →→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 9832 | →¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓 | Modus ponens 9830, 9831 | |
| 9833 | →→¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓] into ax-2 | |
| 9834 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓 | Modus ponens 9832, 9833 | |
| 9835 | →→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜓, 𝜒↗¬→⋀𝜑𝜓¬𝜃] into ax-2 | |
| 9836 | →→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9823, 9835 | |
| 9837 | →→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜓] into ax-1 | |
| 9838 | →¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9836, 9837 | |
| 9839 | →→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃] into ax-2 | |
| 9840 | →→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9838, 9839 | |
| 9841 | →¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9830, 9840 | |
| 9842 | →→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜓] into ax-1 | |
| 9843 | →¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9601, 9842 | |
| 9844 | →→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃→→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬𝜓→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃, 𝜒↗→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃] into ax-2 | |
| 9845 | →→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬𝜓→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9843, 9844 | |
| 9846 | →¬𝜓→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9841, 9845 | |
| 9847 | →→¬𝜓→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃→→¬𝜓→⋀𝜑𝜓¬𝜃→¬𝜓¬¬→⋀𝜑𝜓¬𝜃 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜑𝜓¬𝜃, 𝜒↗¬¬→⋀𝜑𝜓¬𝜃] into ax-2 | |
| 9848 | →→¬𝜓→⋀𝜑𝜓¬𝜃→¬𝜓¬¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9846, 9847 | |
| 9849 | →¬𝜓¬¬→⋀𝜑𝜓¬𝜃 | Modus ponens 9815, 9848 | |
| 9850 | →→¬𝜓¬¬→⋀𝜑𝜓¬𝜃→¬→⋀𝜑𝜓¬𝜃𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→⋀𝜑𝜓¬𝜃] into ax-3 | |
| 9851 | →¬→⋀𝜑𝜓¬𝜃𝜓 | Modus ponens 9849, 9850 | |
| 9852 | →→¬→⋀𝜑𝜓¬𝜃𝜓→⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜓 | Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜃𝜓, 𝜓↗⋀⋀𝜑𝜓𝜃] into ax-1 | |
| 9853 | →⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜓 | Modus ponens 9851, 9852 | |
| 9854 | →→⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜓→→⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜓 | Subs [𝜑↗⋀⋀𝜑𝜓𝜃, 𝜓↗¬→⋀𝜑𝜓¬𝜃, 𝜒↗𝜓] into ax-2 | |
| 9855 | →→⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜓 | Modus ponens 9853, 9854 | |
| 9856 | →⋀⋀𝜑𝜓𝜃𝜓 | Modus ponens 9613, 9855 | |
| 9857 | →→⋀⋀𝜑𝜓𝜃𝜓→¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜓 | Subs [𝜑↗→⋀⋀𝜑𝜓𝜃𝜓, 𝜓↗¬→⋀𝜑𝜓¬𝜃] into ax-1 | |
| 9858 | →¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜓 | Modus ponens 9856, 9857 | |
| 9859 | →→¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜓→→¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜓 | Subs [𝜑↗¬→⋀𝜑𝜓¬𝜃, 𝜓↗⋀⋀𝜑𝜓𝜃, 𝜒↗𝜓] into ax-2 | |
| 9860 | →→¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜓 | Modus ponens 9858, 9859 | |
| 9861 | →→¬→⋀𝜑𝜓¬𝜃𝜓→𝜃→¬→⋀𝜑𝜓¬𝜃𝜓 | Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜃𝜓, 𝜓↗𝜃] into ax-1 | |
| 9862 | →𝜃→¬→⋀𝜑𝜓¬𝜃𝜓 | Modus ponens 9851, 9861 | |
| 9863 | →→𝜃→¬→⋀𝜑𝜓¬𝜃𝜓→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜓 | Subs [𝜑↗𝜃, 𝜓↗¬→⋀𝜑𝜓¬𝜃, 𝜒↗𝜓] into ax-2 | |
| 9864 | →→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜓 | Modus ponens 9862, 9863 | |
| 9865 | →→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜓→⋀𝜑𝜓→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜓 | Subs [𝜑↗→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜓, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 9866 | →⋀𝜑𝜓→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜓 | Modus ponens 9864, 9865 | |
| 9867 | →→⋀𝜑𝜓→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜓→→⋀𝜑𝜓→𝜃¬→⋀𝜑𝜓¬𝜃→⋀𝜑𝜓→𝜃𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜃¬→⋀𝜑𝜓¬𝜃, 𝜒↗→𝜃𝜓] into ax-2 | |
| 9868 | →→⋀𝜑𝜓→𝜃¬→⋀𝜑𝜓¬𝜃→⋀𝜑𝜓→𝜃𝜓 | Modus ponens 9866, 9867 | |
| 9869 | →→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓→𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓 | Subs [𝜑↗→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓, 𝜓↗𝜃] into ax-1 | |
| 9870 | →𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓 | Modus ponens 9781, 9869 | |
| 9871 | →→𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓→→𝜃→⋀𝜑𝜓𝜃→𝜃→⋀𝜑𝜓𝜓 | Subs [𝜑↗𝜃, 𝜓↗→⋀𝜑𝜓𝜃, 𝜒↗→⋀𝜑𝜓𝜓] into ax-2 | |
| 9872 | →→𝜃→⋀𝜑𝜓𝜃→𝜃→⋀𝜑𝜓𝜓 | Modus ponens 9870, 9871 | |
| 9873 | →𝜃→⋀𝜑𝜓𝜓 | Modus ponens 9526, 9872 | |
| 9874 | →→𝜃→⋀𝜑𝜓𝜓→→𝜃⋀𝜑𝜓→𝜃𝜓 | Subs [𝜑↗𝜃, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜓] into ax-2 | |
| 9875 | →→𝜃⋀𝜑𝜓→𝜃𝜓 | Modus ponens 9873, 9874 | |
| 9876 | →→→𝜃⋀𝜑𝜓→𝜃𝜓→⋀⋀𝜑𝜓𝜒→→𝜃⋀𝜑𝜓→𝜃𝜓 | Subs [𝜑↗→→𝜃⋀𝜑𝜓→𝜃𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 9877 | →⋀⋀𝜑𝜓𝜒→→𝜃⋀𝜑𝜓→𝜃𝜓 | Modus ponens 9875, 9876 | |
| 9878 | →→⋀⋀𝜑𝜓𝜒→→𝜃⋀𝜑𝜓→𝜃𝜓→→⋀⋀𝜑𝜓𝜒→𝜃⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒→𝜃𝜓 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜃⋀𝜑𝜓, 𝜒↗→𝜃𝜓] into ax-2 | |
| 9879 | →→⋀⋀𝜑𝜓𝜒→𝜃⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒→𝜃𝜓 | Modus ponens 9877, 9878 | |
| 9880 | →⋀⋀𝜑𝜓𝜒→𝜃𝜓 | Modus ponens 9652, 9879 | |
| 9881 | →→⋀⋀𝜑𝜓𝜒→𝜃𝜓→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜃, 𝜒↗𝜓] into ax-2 | |
| 9882 | →→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓 | Modus ponens 9880, 9881 | |
| 9883 | →→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓→𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓 | Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓, 𝜓↗𝜃] into ax-1 | |
| 9884 | →𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓 | Modus ponens 9882, 9883 | |
| 9885 | →→𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓→→𝜃→⋀⋀𝜑𝜓𝜒𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜓 | Subs [𝜑↗𝜃, 𝜓↗→⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜓] into ax-2 | |
| 9886 | →→𝜃→⋀⋀𝜑𝜓𝜒𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜓 | Modus ponens 9884, 9885 | |
| 9887 | →𝜃→⋀⋀𝜑𝜓𝜒𝜓 | Modus ponens 9660, 9886 | |
| 9888 | →→𝜃→⋀⋀𝜑𝜓𝜒𝜓→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜓 | Subs [𝜑↗𝜃, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜓] into ax-2 | |
| 9889 | →→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜓 | Modus ponens 9887, 9888 | |
| 9890 | →→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜓→⋀⋀𝜑𝜓𝜒→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜓 | Subs [𝜑↗→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 9891 | →⋀⋀𝜑𝜓𝜒→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜓 | Modus ponens 9889, 9890 | |
| 9892 | →→⋀⋀𝜑𝜓𝜒→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜓→→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃𝜓 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜃⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜃𝜓] into ax-2 | |
| 9893 | →→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃𝜓 | Modus ponens 9891, 9892 | |
| 9894 | →→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓→¬¬𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓 | Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓, 𝜓↗¬¬𝜃] into ax-1 | |
| 9895 | →¬¬𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓 | Modus ponens 9882, 9894 | |
| 9896 | →→¬¬𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓→→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜓 | Subs [𝜑↗¬¬𝜃, 𝜓↗→⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜓] into ax-2 | |
| 9897 | →→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜓 | Modus ponens 9895, 9896 | |
| 9898 | →¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜓 | Modus ponens 9688, 9897 | |
| 9899 | →→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜓→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓 | Subs [𝜑↗¬¬𝜃, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜓] into ax-2 | |
| 9900 | →→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓 | Modus ponens 9898, 9899 | |
| 9901 | →→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓→⋀⋀𝜑𝜓𝜒→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓 | Subs [𝜑↗→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 9902 | →⋀⋀𝜑𝜓𝜒→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓 | Modus ponens 9900, 9901 | |
| 9903 | →→⋀⋀𝜑𝜓𝜒→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓→→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜃⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬𝜃𝜓] into ax-2 | |
| 9904 | →→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓 | Modus ponens 9902, 9903 | |
| 9905 | →⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓 | Modus ponens 9694, 9904 | |
| 9906 | →→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓→⋀⋀𝜑𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓 | Subs [𝜑↗→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 9907 | →⋀⋀𝜑𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓 | Modus ponens 9797, 9906 | |
| 9908 | →→⋀⋀𝜑𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓→→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜓 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜃𝜓, 𝜒↗→¬¬𝜃¬¬𝜓] into ax-2 | |
| 9909 | →→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜓 | Modus ponens 9907, 9908 | |
| 9910 | →⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜓 | Modus ponens 9905, 9909 | |
| 9911 | →→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃→⋀⋀𝜑𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃 | Subs [𝜑↗→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 9912 | →⋀⋀𝜑𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃 | Modus ponens 9803, 9911 | |
| 9913 | →→⋀⋀𝜑𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃→→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜓→⋀⋀𝜑𝜓𝜒→¬𝜓¬𝜃 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜃¬¬𝜓, 𝜒↗→¬𝜓¬𝜃] into ax-2 | |
| 9914 | →→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜓→⋀⋀𝜑𝜓𝜒→¬𝜓¬𝜃 | Modus ponens 9912, 9913 | |
| 9915 | →⋀⋀𝜑𝜓𝜒→¬𝜓¬𝜃 | Modus ponens 9910, 9914 | |
| 9916 | →¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 9917 | →→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓→¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓 | Subs [𝜑↗→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 9918 | →¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓 | Modus ponens 9916, 9917 | |
| 9919 | →→¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀𝜑𝜓𝜒¬𝜓] into ax-2 | |
| 9920 | →→¬𝜓¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓 | Modus ponens 9918, 9919 | |
| 9921 | →→⋀⋀𝜑𝜓𝜒→¬𝜓¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬𝜓, 𝜒↗¬𝜃] into ax-2 | |
| 9922 | →→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9915, 9921 | |
| 9923 | →→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1 | |
| 9924 | →¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9922, 9923 | |
| 9925 | →→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜓, 𝜒↗→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2 | |
| 9926 | →→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9924, 9925 | |
| 9927 | →¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9916, 9926 | |
| 9928 | →→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1 | |
| 9929 | →¬𝜓→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9728, 9928 | |
| 9930 | →¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1 | |
| 9931 | →→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-1 | |
| 9932 | →¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9930, 9931 | |
| 9933 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2 | |
| 9934 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9932, 9933 | |
| 9935 | →¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9731, 9934 | |
| 9936 | →→¬𝜓→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2 | |
| 9937 | →→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9929, 9936 | |
| 9938 | →→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-1 | |
| 9939 | →¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9937, 9938 | |
| 9940 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2 | |
| 9941 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9939, 9940 | |
| 9942 | →¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-1 | |
| 9943 | →→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 9944 | →¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓 | Modus ponens 9942, 9943 | |
| 9945 | →→¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓] into ax-2 | |
| 9946 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓 | Modus ponens 9944, 9945 | |
| 9947 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2 | |
| 9948 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9935, 9947 | |
| 9949 | →→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1 | |
| 9950 | →¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9948, 9949 | |
| 9951 | →→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓, 𝜒↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2 | |
| 9952 | →→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9950, 9951 | |
| 9953 | →¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9942, 9952 | |
| 9954 | →→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1 | |
| 9955 | →¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9756, 9954 | |
| 9956 | →→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2 | |
| 9957 | →→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9955, 9956 | |
| 9958 | →¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9953, 9957 | |
| 9959 | →→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2 | |
| 9960 | →→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9958, 9959 | |
| 9961 | →¬𝜓¬¬→⋀⋀𝜑𝜓𝜒¬𝜃 | Modus ponens 9927, 9960 | |
| 9962 | →→¬𝜓¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-3 | |
| 9963 | →¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜓 | Modus ponens 9961, 9962 | |
| 9964 | →→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜓 | Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 9965 | →⋀⋀⋀𝜑𝜓𝜒𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜓 | Modus ponens 9963, 9964 | |
| 9966 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗𝜓] into ax-2 | |
| 9967 | →→⋀⋀⋀𝜑𝜓𝜒𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Modus ponens 9965, 9966 | |
| 9968 | →⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Modus ponens 9768, 9967 | simpllr |
| 9969 | →→𝜓→𝜃𝜓→⋀𝜓𝜒→𝜓→𝜃𝜓 | Subs [𝜑↗→𝜓→𝜃𝜓, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 9970 | →⋀𝜓𝜒→𝜓→𝜃𝜓 | Modus ponens 9774, 9969 | |
| 9971 | →→⋀𝜓𝜒→𝜓→𝜃𝜓→→⋀𝜓𝜒𝜓→⋀𝜓𝜒→𝜃𝜓 | Subs [𝜑↗⋀𝜓𝜒, 𝜒↗→𝜃𝜓] into ax-2 | |
| 9972 | →→⋀𝜓𝜒𝜓→⋀𝜓𝜒→𝜃𝜓 | Modus ponens 9970, 9971 | |
| 9973 | →⋀𝜓𝜒→𝜃𝜓 | Modus ponens 6072, 9972 | |
| 9974 | ↔⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜃] into df-an | |
| 9975 | →𝜃→⋀𝜓𝜒𝜃 | Subs [𝜑↗𝜃, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 9976 | →→𝜃→⋀𝜓𝜒𝜃→¬¬𝜃→𝜃→⋀𝜓𝜒𝜃 | Subs [𝜑↗→𝜃→⋀𝜓𝜒𝜃, 𝜓↗¬¬𝜃] into ax-1 | |
| 9977 | →¬¬𝜃→𝜃→⋀𝜓𝜒𝜃 | Modus ponens 9975, 9976 | |
| 9978 | →→¬¬𝜃→𝜃→⋀𝜓𝜒𝜃→→¬¬𝜃𝜃→¬¬𝜃→⋀𝜓𝜒𝜃 | Subs [𝜑↗¬¬𝜃, 𝜓↗𝜃, 𝜒↗→⋀𝜓𝜒𝜃] into ax-2 | |
| 9979 | →→¬¬𝜃𝜃→¬¬𝜃→⋀𝜓𝜒𝜃 | Modus ponens 9977, 9978 | |
| 9980 | →¬¬𝜃→⋀𝜓𝜒𝜃 | Modus ponens 9525, 9979 | |
| 9981 | →→⋀𝜓𝜒→𝜃𝜓→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜃, 𝜒↗𝜓] into ax-2 | |
| 9982 | →→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓 | Modus ponens 9973, 9981 | |
| 9983 | →→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓→¬¬𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓 | Subs [𝜑↗→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓, 𝜓↗¬¬𝜃] into ax-1 | |
| 9984 | →¬¬𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓 | Modus ponens 9982, 9983 | |
| 9985 | →→¬¬𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓→→¬¬𝜃→⋀𝜓𝜒𝜃→¬¬𝜃→⋀𝜓𝜒𝜓 | Subs [𝜑↗¬¬𝜃, 𝜓↗→⋀𝜓𝜒𝜃, 𝜒↗→⋀𝜓𝜒𝜓] into ax-2 | |
| 9986 | →→¬¬𝜃→⋀𝜓𝜒𝜃→¬¬𝜃→⋀𝜓𝜒𝜓 | Modus ponens 9984, 9985 | |
| 9987 | →¬¬𝜃→⋀𝜓𝜒𝜓 | Modus ponens 9980, 9986 | |
| 9988 | →⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬¬𝜃] into ax-1 | |
| 9989 | →→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒→⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒 | Subs [𝜑↗→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 9990 | →⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒 | Modus ponens 9988, 9989 | |
| 9991 | →→⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→¬¬𝜃⋀𝜓𝜒] into ax-2 | |
| 9992 | →→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒 | Modus ponens 9990, 9991 | |
| 9993 | →→¬¬𝜃→⋀𝜓𝜒𝜓→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜓 | Subs [𝜑↗¬¬𝜃, 𝜓↗⋀𝜓𝜒, 𝜒↗𝜓] into ax-2 | |
| 9994 | →→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜓 | Modus ponens 9987, 9993 | |
| 9995 | →→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜓→⋀𝜓𝜒→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜓 | Subs [𝜑↗→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜓, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 9996 | →⋀𝜓𝜒→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜓 | Modus ponens 9994, 9995 | |
| 9997 | →→⋀𝜓𝜒→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜓→→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃𝜓 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜃⋀𝜓𝜒, 𝜒↗→¬¬𝜃𝜓] into ax-2 | |
| 9998 | →→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃𝜓 | Modus ponens 9996, 9997 | |
| 9999 | →⋀𝜓𝜒→¬¬𝜃𝜓 | Modus ponens 9988, 9998 | |
| 10000 | →→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓→⋀𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓 | Subs [𝜑↗→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 10001 | →⋀𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓 | Modus ponens 9797, 10000 | |
| 10002 | →→⋀𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓→→⋀𝜓𝜒→¬¬𝜃𝜓→⋀𝜓𝜒→¬¬𝜃¬¬𝜓 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜃𝜓, 𝜒↗→¬¬𝜃¬¬𝜓] into ax-2 | |
| 10003 | →→⋀𝜓𝜒→¬¬𝜃𝜓→⋀𝜓𝜒→¬¬𝜃¬¬𝜓 | Modus ponens 10001, 10002 | |
| 10004 | →⋀𝜓𝜒→¬¬𝜃¬¬𝜓 | Modus ponens 9999, 10003 | |
| 10005 | →→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃→⋀𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃 | Subs [𝜑↗→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 10006 | →⋀𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃 | Modus ponens 9803, 10005 | |
| 10007 | →→⋀𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃→→⋀𝜓𝜒→¬¬𝜃¬¬𝜓→⋀𝜓𝜒→¬𝜓¬𝜃 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜃¬¬𝜓, 𝜒↗→¬𝜓¬𝜃] into ax-2 | |
| 10008 | →→⋀𝜓𝜒→¬¬𝜃¬¬𝜓→⋀𝜓𝜒→¬𝜓¬𝜃 | Modus ponens 10006, 10007 | |
| 10009 | →⋀𝜓𝜒→¬𝜓¬𝜃 | Modus ponens 10004, 10008 | |
| 10010 | →→⋀𝜓𝜒→¬𝜓¬𝜃→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬𝜓, 𝜒↗¬𝜃] into ax-2 | |
| 10011 | →→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜃 | Modus ponens 10009, 10010 | |
| 10012 | →→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜃→¬𝜓→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1 | |
| 10013 | →¬𝜓→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜃 | Modus ponens 10011, 10012 | |
| 10014 | →→¬𝜓→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜃→→¬𝜓→⋀𝜓𝜒¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜓𝜒¬𝜓, 𝜒↗→⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10015 | →→¬𝜓→⋀𝜓𝜒¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜃 | Modus ponens 10013, 10014 | |
| 10016 | →¬𝜓→⋀𝜓𝜒¬𝜃 | Modus ponens 8964, 10015 | |
| 10017 | →¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬→⋀𝜓𝜒¬𝜃] into id | |
| 10018 | →→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬𝜓→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1 | |
| 10019 | →¬𝜓→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10017, 10018 | |
| 10020 | →¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬→⋀𝜓𝜒¬𝜃] into notnotr | |
| 10021 | →¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1 | |
| 10022 | →→¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜃] into ax-1 | |
| 10023 | →¬¬¬→⋀𝜓𝜒¬𝜃→¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10021, 10022 | |
| 10024 | →→¬¬¬→⋀𝜓𝜒¬𝜃→¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬→⋀𝜓𝜒¬𝜃, 𝜒↗→¬𝜓¬→⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10025 | →→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10023, 10024 | |
| 10026 | →¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10020, 10025 | |
| 10027 | →→¬𝜓→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀𝜓𝜒¬𝜃, 𝜒↗¬→⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10028 | →→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10019, 10027 | |
| 10029 | →→→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗→→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜃] into ax-1 | |
| 10030 | →¬¬¬→⋀𝜓𝜒¬𝜃→→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10028, 10029 | |
| 10031 | →→¬¬¬→⋀𝜓𝜒¬𝜃→→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗→¬𝜓¬→⋀𝜓𝜒¬𝜃, 𝜒↗→¬𝜓¬→⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10032 | →→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10030, 10031 | |
| 10033 | →¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜃] into ax-1 | |
| 10034 | →→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 10035 | →¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓 | Modus ponens 10033, 10034 | |
| 10036 | →→¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓] into ax-2 | |
| 10037 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓 | Modus ponens 10035, 10036 | |
| 10038 | →→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓, 𝜒↗¬→⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10039 | →→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10026, 10038 | |
| 10040 | →→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1 | |
| 10041 | →¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10039, 10040 | |
| 10042 | →→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓, 𝜒↗→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10043 | →→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10041, 10042 | |
| 10044 | →¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10033, 10043 | |
| 10045 | →→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗→⋀𝜓𝜒¬𝜃] into ax-3 | |
| 10046 | →→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1 | |
| 10047 | →¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10045, 10046 | |
| 10048 | →→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃→→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬𝜓→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃, 𝜒↗→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10049 | →→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬𝜓→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10047, 10048 | |
| 10050 | →¬𝜓→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10044, 10049 | |
| 10051 | →→¬𝜓→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃→→¬𝜓→⋀𝜓𝜒¬𝜃→¬𝜓¬¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜓𝜒¬𝜃, 𝜒↗¬¬→⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10052 | →→¬𝜓→⋀𝜓𝜒¬𝜃→¬𝜓¬¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10050, 10051 | |
| 10053 | →¬𝜓¬¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10016, 10052 | |
| 10054 | →→¬𝜓¬¬→⋀𝜓𝜒¬𝜃→¬→⋀𝜓𝜒¬𝜃𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→⋀𝜓𝜒¬𝜃] into ax-3 | |
| 10055 | →¬→⋀𝜓𝜒¬𝜃𝜓 | Modus ponens 10053, 10054 | |
| 10056 | →↔⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗¬→⋀𝜓𝜒¬𝜃] into biimp | |
| 10057 | →⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃 | Modus ponens 9974, 10056 | |
| 10058 | →→¬→⋀𝜓𝜒¬𝜃𝜓→⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜓 | Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜃𝜓, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1 | |
| 10059 | →⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜓 | Modus ponens 10055, 10058 | |
| 10060 | →→⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜓→→⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜓 | Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗¬→⋀𝜓𝜒¬𝜃, 𝜒↗𝜓] into ax-2 | |
| 10061 | →→⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜓 | Modus ponens 10059, 10060 | |
| 10062 | →⋀⋀𝜓𝜒𝜃𝜓 | Modus ponens 10057, 10061 | |
| 10063 | →⋀𝜑⋀𝜓𝜒⋀𝜓𝜒 | Subs [𝜓↗⋀𝜓𝜒] into simpr | |
| 10064 | →↔⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃↔¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗¬→⋀𝜓𝜒¬𝜃] into bicom1 | |
| 10065 | ↔¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃 | Modus ponens 9974, 10064 | |
| 10066 | →↔¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗¬→⋀𝜓𝜒¬𝜃, 𝜓↗⋀⋀𝜓𝜒𝜃] into biimp | |
| 10067 | →¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃 | Modus ponens 10065, 10066 | |
| 10068 | →→⋀⋀𝜓𝜒𝜃𝜓→¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜓 | Subs [𝜑↗→⋀⋀𝜓𝜒𝜃𝜓, 𝜓↗¬→⋀𝜓𝜒¬𝜃] into ax-1 | |
| 10069 | →¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜓 | Modus ponens 10062, 10068 | |
| 10070 | →→¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜓→→¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜓 | Subs [𝜑↗¬→⋀𝜓𝜒¬𝜃, 𝜓↗⋀⋀𝜓𝜒𝜃, 𝜒↗𝜓] into ax-2 | |
| 10071 | →→¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜓 | Modus ponens 10069, 10070 | |
| 10072 | →⋀𝜓𝜒→𝜃¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜃] into pm3.2im | |
| 10073 | →→¬→⋀𝜓𝜒¬𝜃𝜓→𝜃→¬→⋀𝜓𝜒¬𝜃𝜓 | Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜃𝜓, 𝜓↗𝜃] into ax-1 | |
| 10074 | →𝜃→¬→⋀𝜓𝜒¬𝜃𝜓 | Modus ponens 10055, 10073 | |
| 10075 | →→𝜃→¬→⋀𝜓𝜒¬𝜃𝜓→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜓 | Subs [𝜑↗𝜃, 𝜓↗¬→⋀𝜓𝜒¬𝜃, 𝜒↗𝜓] into ax-2 | |
| 10076 | →→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜓 | Modus ponens 10074, 10075 | |
| 10077 | →→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜓→⋀𝜓𝜒→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜓 | Subs [𝜑↗→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜓, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 10078 | →⋀𝜓𝜒→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜓 | Modus ponens 10076, 10077 | |
| 10079 | →→⋀𝜓𝜒→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜓→→⋀𝜓𝜒→𝜃¬→⋀𝜓𝜒¬𝜃→⋀𝜓𝜒→𝜃𝜓 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→𝜃¬→⋀𝜓𝜒¬𝜃, 𝜒↗→𝜃𝜓] into ax-2 | |
| 10080 | →→⋀𝜓𝜒→𝜃¬→⋀𝜓𝜒¬𝜃→⋀𝜓𝜒→𝜃𝜓 | Modus ponens 10078, 10079 | |
| 10081 | →→𝜃→⋀𝜓𝜒𝜃→𝜃→𝜃→⋀𝜓𝜒𝜃 | Subs [𝜑↗→𝜃→⋀𝜓𝜒𝜃, 𝜓↗𝜃] into ax-1 | |
| 10082 | →𝜃→𝜃→⋀𝜓𝜒𝜃 | Modus ponens 9975, 10081 | |
| 10083 | →→𝜃→𝜃→⋀𝜓𝜒𝜃→→𝜃𝜃→𝜃→⋀𝜓𝜒𝜃 | Subs [𝜑↗𝜃, 𝜓↗𝜃, 𝜒↗→⋀𝜓𝜒𝜃] into ax-2 | |
| 10084 | →→𝜃𝜃→𝜃→⋀𝜓𝜒𝜃 | Modus ponens 10082, 10083 | |
| 10085 | →→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓→𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓 | Subs [𝜑↗→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓, 𝜓↗𝜃] into ax-1 | |
| 10086 | →𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓 | Modus ponens 9982, 10085 | |
| 10087 | →→𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓→→𝜃→⋀𝜓𝜒𝜃→𝜃→⋀𝜓𝜒𝜓 | Subs [𝜑↗𝜃, 𝜓↗→⋀𝜓𝜒𝜃, 𝜒↗→⋀𝜓𝜒𝜓] into ax-2 | |
| 10088 | →→𝜃→⋀𝜓𝜒𝜃→𝜃→⋀𝜓𝜒𝜓 | Modus ponens 10086, 10087 | |
| 10089 | →𝜃→⋀𝜓𝜒𝜓 | Modus ponens 9975, 10088 | |
| 10090 | →⋀𝜓𝜒→𝜃⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜃] into ax-1 | |
| 10091 | →→⋀𝜓𝜒→𝜃⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→⋀𝜓𝜒→𝜃⋀𝜓𝜒 | Subs [𝜑↗→⋀𝜓𝜒→𝜃⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 10092 | →⋀𝜑⋀𝜓𝜒→⋀𝜓𝜒→𝜃⋀𝜓𝜒 | Modus ponens 10090, 10091 | |
| 10093 | →→⋀𝜑⋀𝜓𝜒→⋀𝜓𝜒→𝜃⋀𝜓𝜒→→⋀𝜑⋀𝜓𝜒⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜃⋀𝜓𝜒] into ax-2 | |
| 10094 | →→⋀𝜑⋀𝜓𝜒⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜓𝜒 | Modus ponens 10092, 10093 | |
| 10095 | →⋀𝜑⋀𝜓𝜒→𝜃⋀𝜓𝜒 | Modus ponens 10063, 10094 | |
| 10096 | →→𝜃→⋀𝜓𝜒𝜓→→𝜃⋀𝜓𝜒→𝜃𝜓 | Subs [𝜑↗𝜃, 𝜓↗⋀𝜓𝜒, 𝜒↗𝜓] into ax-2 | |
| 10097 | →→𝜃⋀𝜓𝜒→𝜃𝜓 | Modus ponens 10089, 10096 | |
| 10098 | →→→𝜃⋀𝜓𝜒→𝜃𝜓→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜓𝜒→𝜃𝜓 | Subs [𝜑↗→→𝜃⋀𝜓𝜒→𝜃𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 10099 | →⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜓𝜒→𝜃𝜓 | Modus ponens 10097, 10098 | |
| 10100 | →→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜓𝜒→𝜃𝜓→→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃𝜓 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→𝜃⋀𝜓𝜒, 𝜒↗→𝜃𝜓] into ax-2 | |
| 10101 | →→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃𝜓 | Modus ponens 10099, 10100 | |
| 10102 | →⋀𝜑⋀𝜓𝜒→𝜃𝜓 | Modus ponens 10095, 10101 | |
| 10103 | →𝜃→⋀𝜑⋀𝜓𝜒𝜃 | Subs [𝜑↗𝜃, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 10104 | →→𝜃→⋀𝜑⋀𝜓𝜒𝜃→𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜃 | Subs [𝜑↗→𝜃→⋀𝜑⋀𝜓𝜒𝜃, 𝜓↗𝜃] into ax-1 | |
| 10105 | →𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜃 | Modus ponens 10103, 10104 | |
| 10106 | →→𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜃→→𝜃𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜃 | Subs [𝜑↗𝜃, 𝜓↗𝜃, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜃] into ax-2 | |
| 10107 | →→𝜃𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜃 | Modus ponens 10105, 10106 | |
| 10108 | →→⋀𝜑⋀𝜓𝜒→𝜃𝜓→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗𝜃, 𝜒↗𝜓] into ax-2 | |
| 10109 | →→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓 | Modus ponens 10102, 10108 | |
| 10110 | →→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓→𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓 | Subs [𝜑↗→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓, 𝜓↗𝜃] into ax-1 | |
| 10111 | →𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓 | Modus ponens 10109, 10110 | |
| 10112 | →→𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓→→𝜃→⋀𝜑⋀𝜓𝜒𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜓 | Subs [𝜑↗𝜃, 𝜓↗→⋀𝜑⋀𝜓𝜒𝜃, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜓] into ax-2 | |
| 10113 | →→𝜃→⋀𝜑⋀𝜓𝜒𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜓 | Modus ponens 10111, 10112 | |
| 10114 | →𝜃→⋀𝜑⋀𝜓𝜒𝜓 | Modus ponens 10103, 10113 | |
| 10115 | →⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗𝜃] into ax-1 | |
| 10116 | →→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 10117 | →⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒 | Modus ponens 10115, 10116 | |
| 10118 | →→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒→→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜃⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 10119 | →→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒 | Modus ponens 10117, 10118 | |
| 10120 | →→𝜃→⋀𝜑⋀𝜓𝜒𝜓→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜓 | Subs [𝜑↗𝜃, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗𝜓] into ax-2 | |
| 10121 | →→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜓 | Modus ponens 10114, 10120 | |
| 10122 | →→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜓→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜓 | Subs [𝜑↗→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 10123 | →⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜓 | Modus ponens 10121, 10122 | |
| 10124 | →→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜓→→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃𝜓 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→𝜃⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜃𝜓] into ax-2 | |
| 10125 | →→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃𝜓 | Modus ponens 10123, 10124 | |
| 10126 | ↔⋀⋀𝜑⋀𝜓𝜒𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗𝜃] into df-an | |
| 10127 | →→𝜃→⋀𝜑⋀𝜓𝜒𝜃→¬¬𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜃 | Subs [𝜑↗→𝜃→⋀𝜑⋀𝜓𝜒𝜃, 𝜓↗¬¬𝜃] into ax-1 | |
| 10128 | →¬¬𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜃 | Modus ponens 10103, 10127 | |
| 10129 | →→¬¬𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜃→→¬¬𝜃𝜃→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜃 | Subs [𝜑↗¬¬𝜃, 𝜓↗𝜃, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜃] into ax-2 | |
| 10130 | →→¬¬𝜃𝜃→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜃 | Modus ponens 10128, 10129 | |
| 10131 | →¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜃 | Modus ponens 9525, 10130 | |
| 10132 | →→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓→¬¬𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓 | Subs [𝜑↗→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓, 𝜓↗¬¬𝜃] into ax-1 | |
| 10133 | →¬¬𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓 | Modus ponens 10109, 10132 | |
| 10134 | →→¬¬𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓→→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜃→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜓 | Subs [𝜑↗¬¬𝜃, 𝜓↗→⋀𝜑⋀𝜓𝜒𝜃, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜓] into ax-2 | |
| 10135 | →→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜃→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜓 | Modus ponens 10133, 10134 | |
| 10136 | →¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜓 | Modus ponens 10131, 10135 | |
| 10137 | →⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬¬𝜃] into ax-1 | |
| 10138 | →→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 10139 | →⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒 | Modus ponens 10137, 10138 | |
| 10140 | →→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒→→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬𝜃⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 10141 | →→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒 | Modus ponens 10139, 10140 | |
| 10142 | →→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜓→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓 | Subs [𝜑↗¬¬𝜃, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗𝜓] into ax-2 | |
| 10143 | →→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓 | Modus ponens 10136, 10142 | |
| 10144 | →→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓→⋀𝜑⋀𝜓𝜒→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓 | Subs [𝜑↗→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 10145 | →⋀𝜑⋀𝜓𝜒→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓 | Modus ponens 10143, 10144 | |
| 10146 | →→⋀𝜑⋀𝜓𝜒→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓→→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬𝜃⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬𝜃𝜓] into ax-2 | |
| 10147 | →→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓 | Modus ponens 10145, 10146 | |
| 10148 | →⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓 | Modus ponens 10137, 10147 | |
| 10149 | →→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓→⋀𝜑⋀𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓 | Subs [𝜑↗→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 10150 | →⋀𝜑⋀𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓 | Modus ponens 9797, 10149 | |
| 10151 | →→⋀𝜑⋀𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓→→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜓 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬𝜃𝜓, 𝜒↗→¬¬𝜃¬¬𝜓] into ax-2 | |
| 10152 | →→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜓 | Modus ponens 10150, 10151 | |
| 10153 | →⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜓 | Modus ponens 10148, 10152 | |
| 10154 | →→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃→⋀𝜑⋀𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃 | Subs [𝜑↗→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 10155 | →⋀𝜑⋀𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃 | Modus ponens 9803, 10154 | |
| 10156 | →→⋀𝜑⋀𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃→→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜓→⋀𝜑⋀𝜓𝜒→¬𝜓¬𝜃 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬𝜃¬¬𝜓, 𝜒↗→¬𝜓¬𝜃] into ax-2 | |
| 10157 | →→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜓→⋀𝜑⋀𝜓𝜒→¬𝜓¬𝜃 | Modus ponens 10155, 10156 | |
| 10158 | →⋀𝜑⋀𝜓𝜒→¬𝜓¬𝜃 | Modus ponens 10153, 10157 | |
| 10159 | →¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 10160 | →→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓→¬𝜓→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓 | Subs [𝜑↗→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 10161 | →¬𝜓→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓 | Modus ponens 10159, 10160 | |
| 10162 | →→¬𝜓→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀𝜑⋀𝜓𝜒¬𝜓] into ax-2 | |
| 10163 | →→¬𝜓¬𝜓→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓 | Modus ponens 10161, 10162 | |
| 10164 | →→⋀𝜑⋀𝜓𝜒→¬𝜓¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬𝜓, 𝜒↗¬𝜃] into ax-2 | |
| 10165 | →→⋀𝜑⋀𝜓𝜒¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10158, 10164 | |
| 10166 | →→→⋀𝜑⋀𝜓𝜒¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓→→⋀𝜑⋀𝜓𝜒¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗→→⋀𝜑⋀𝜓𝜒¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1 | |
| 10167 | →¬𝜓→→⋀𝜑⋀𝜓𝜒¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10165, 10166 | |
| 10168 | →→¬𝜓→→⋀𝜑⋀𝜓𝜒¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜑⋀𝜓𝜒¬𝜓, 𝜒↗→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10169 | →→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10167, 10168 | |
| 10170 | →¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10159, 10169 | |
| 10171 | →¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into id | |
| 10172 | →→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1 | |
| 10173 | →¬𝜓→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10171, 10172 | |
| 10174 | →¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into notnotr | |
| 10175 | →¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1 | |
| 10176 | →→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-1 | |
| 10177 | →¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10175, 10176 | |
| 10178 | →→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10179 | →→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10177, 10178 | |
| 10180 | →¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10174, 10179 | |
| 10181 | →→¬𝜓→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10182 | →→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10173, 10181 | |
| 10183 | →→→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗→→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-1 | |
| 10184 | →¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10182, 10183 | |
| 10185 | →→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10186 | →→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10184, 10185 | |
| 10187 | →¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-1 | |
| 10188 | →→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 10189 | →¬𝜓→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓 | Modus ponens 10187, 10188 | |
| 10190 | →→¬𝜓→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓] into ax-2 | |
| 10191 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓 | Modus ponens 10189, 10190 | |
| 10192 | →→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓, 𝜒↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10193 | →→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10180, 10192 | |
| 10194 | →→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1 | |
| 10195 | →¬𝜓→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10193, 10194 | |
| 10196 | →→¬𝜓→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓, 𝜒↗→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10197 | →→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10195, 10196 | |
| 10198 | →¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10187, 10197 | |
| 10199 | →→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-3 | |
| 10200 | →→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1 | |
| 10201 | →¬𝜓→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10199, 10200 | |
| 10202 | →→¬𝜓→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10203 | →→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10201, 10202 | |
| 10204 | →¬𝜓→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10198, 10203 | |
| 10205 | →→¬𝜓→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10206 | →→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10204, 10205 | |
| 10207 | →¬𝜓¬¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10170, 10206 | |
| 10208 | →→¬𝜓¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-3 | |
| 10209 | →¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜓 | Modus ponens 10207, 10208 | |
| 10210 | →↔⋀⋀𝜑⋀𝜓𝜒𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→⋀⋀𝜑⋀𝜓𝜒𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗⋀⋀𝜑⋀𝜓𝜒𝜃, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into biimp | |
| 10211 | →⋀⋀𝜑⋀𝜓𝜒𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10126, 10210 | |
| 10212 | →→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜓→⋀⋀𝜑⋀𝜓𝜒𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜓 | Subs [𝜑↗→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜓, 𝜓↗⋀⋀𝜑⋀𝜓𝜒𝜃] into ax-1 | |
| 10213 | →⋀⋀𝜑⋀𝜓𝜒𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜓 | Modus ponens 10209, 10212 | |
| 10214 | →→⋀⋀𝜑⋀𝜓𝜒𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜓→→⋀⋀𝜑⋀𝜓𝜒𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→⋀⋀𝜑⋀𝜓𝜒𝜃𝜓 | Subs [𝜑↗⋀⋀𝜑⋀𝜓𝜒𝜃, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗𝜓] into ax-2 | |
| 10215 | →→⋀⋀𝜑⋀𝜓𝜒𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→⋀⋀𝜑⋀𝜓𝜒𝜃𝜓 | Modus ponens 10213, 10214 | |
| 10216 | →⋀⋀𝜑⋀𝜓𝜒𝜃𝜓 | Modus ponens 10211, 10215 | simplrl |
| 10217 | →𝜒→𝜃𝜒 | Subs [𝜑↗𝜒, 𝜓↗𝜃] into ax-1 | |
| 10218 | →→𝜒→𝜃𝜒→⋀𝜓𝜒→𝜒→𝜃𝜒 | Subs [𝜑↗→𝜒→𝜃𝜒, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 10219 | →⋀𝜓𝜒→𝜒→𝜃𝜒 | Modus ponens 10217, 10218 | |
| 10220 | →→⋀𝜓𝜒→𝜒→𝜃𝜒→→⋀𝜓𝜒𝜒→⋀𝜓𝜒→𝜃𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜒, 𝜒↗→𝜃𝜒] into ax-2 | |
| 10221 | →→⋀𝜓𝜒𝜒→⋀𝜓𝜒→𝜃𝜒 | Modus ponens 10219, 10220 | |
| 10222 | →⋀𝜓𝜒→𝜃𝜒 | Modus ponens 6077, 10221 | |
| 10223 | →→⋀𝜓𝜒→𝜃𝜒→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜃] into ax-2 | |
| 10224 | →→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒 | Modus ponens 10222, 10223 | |
| 10225 | →→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒→¬¬𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒 | Subs [𝜑↗→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒, 𝜓↗¬¬𝜃] into ax-1 | |
| 10226 | →¬¬𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒 | Modus ponens 10224, 10225 | |
| 10227 | →→¬¬𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒→→¬¬𝜃→⋀𝜓𝜒𝜃→¬¬𝜃→⋀𝜓𝜒𝜒 | Subs [𝜑↗¬¬𝜃, 𝜓↗→⋀𝜓𝜒𝜃, 𝜒↗→⋀𝜓𝜒𝜒] into ax-2 | |
| 10228 | →→¬¬𝜃→⋀𝜓𝜒𝜃→¬¬𝜃→⋀𝜓𝜒𝜒 | Modus ponens 10226, 10227 | |
| 10229 | →¬¬𝜃→⋀𝜓𝜒𝜒 | Modus ponens 9980, 10228 | |
| 10230 | →→¬¬𝜃→⋀𝜓𝜒𝜒→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜒 | Subs [𝜑↗¬¬𝜃, 𝜓↗⋀𝜓𝜒] into ax-2 | |
| 10231 | →→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜒 | Modus ponens 10229, 10230 | |
| 10232 | →→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜒→⋀𝜓𝜒→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜒 | Subs [𝜑↗→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜒, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 10233 | →⋀𝜓𝜒→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜒 | Modus ponens 10231, 10232 | |
| 10234 | →→⋀𝜓𝜒→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜒→→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜃⋀𝜓𝜒, 𝜒↗→¬¬𝜃𝜒] into ax-2 | |
| 10235 | →→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃𝜒 | Modus ponens 10233, 10234 | |
| 10236 | →⋀𝜓𝜒→¬¬𝜃𝜒 | Modus ponens 9988, 10235 | |
| 10237 | →→𝜒¬¬𝜒→¬¬𝜃→𝜒¬¬𝜒 | Subs [𝜑↗→𝜒¬¬𝜒, 𝜓↗¬¬𝜃] into ax-1 | |
| 10238 | →¬¬𝜃→𝜒¬¬𝜒 | Modus ponens 9172, 10237 | |
| 10239 | →→¬¬𝜃→𝜒¬¬𝜒→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒 | Subs [𝜑↗¬¬𝜃, 𝜓↗𝜒, 𝜒↗¬¬𝜒] into ax-2 | |
| 10240 | →→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒 | Modus ponens 10238, 10239 | |
| 10241 | →→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒→⋀𝜓𝜒→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒 | Subs [𝜑↗→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 10242 | →⋀𝜓𝜒→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒 | Modus ponens 10240, 10241 | |
| 10243 | →→⋀𝜓𝜒→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒→→⋀𝜓𝜒→¬¬𝜃𝜒→⋀𝜓𝜒→¬¬𝜃¬¬𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜃𝜒, 𝜒↗→¬¬𝜃¬¬𝜒] into ax-2 | |
| 10244 | →→⋀𝜓𝜒→¬¬𝜃𝜒→⋀𝜓𝜒→¬¬𝜃¬¬𝜒 | Modus ponens 10242, 10243 | |
| 10245 | →⋀𝜓𝜒→¬¬𝜃¬¬𝜒 | Modus ponens 10236, 10244 | |
| 10246 | →→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗¬𝜒] into ax-3 | |
| 10247 | →→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃→⋀𝜓𝜒→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃 | Subs [𝜑↗→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 10248 | →⋀𝜓𝜒→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃 | Modus ponens 10246, 10247 | |
| 10249 | →→⋀𝜓𝜒→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃→→⋀𝜓𝜒→¬¬𝜃¬¬𝜒→⋀𝜓𝜒→¬𝜒¬𝜃 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜃¬¬𝜒, 𝜒↗→¬𝜒¬𝜃] into ax-2 | |
| 10250 | →→⋀𝜓𝜒→¬¬𝜃¬¬𝜒→⋀𝜓𝜒→¬𝜒¬𝜃 | Modus ponens 10248, 10249 | |
| 10251 | →⋀𝜓𝜒→¬𝜒¬𝜃 | Modus ponens 10245, 10250 | |
| 10252 | →→⋀𝜓𝜒→¬𝜒¬𝜃→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬𝜒, 𝜒↗¬𝜃] into ax-2 | |
| 10253 | →→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜃 | Modus ponens 10251, 10252 | |
| 10254 | →→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜃→¬𝜒→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1 | |
| 10255 | →¬𝜒→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜃 | Modus ponens 10253, 10254 | |
| 10256 | →→¬𝜒→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜃→→¬𝜒→⋀𝜓𝜒¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜓𝜒¬𝜒, 𝜒↗→⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10257 | →→¬𝜒→⋀𝜓𝜒¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜃 | Modus ponens 10255, 10256 | |
| 10258 | →¬𝜒→⋀𝜓𝜒¬𝜃 | Modus ponens 9369, 10257 | |
| 10259 | →→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬𝜒→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1 | |
| 10260 | →¬𝜒→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10017, 10259 | |
| 10261 | →¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1 | |
| 10262 | →→¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜃] into ax-1 | |
| 10263 | →¬¬¬→⋀𝜓𝜒¬𝜃→¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10261, 10262 | |
| 10264 | →→¬¬¬→⋀𝜓𝜒¬𝜃→¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬→⋀𝜓𝜒¬𝜃, 𝜒↗→¬𝜒¬→⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10265 | →→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10263, 10264 | |
| 10266 | →¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10020, 10265 | |
| 10267 | →→¬𝜒→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜒, 𝜓↗¬→⋀𝜓𝜒¬𝜃, 𝜒↗¬→⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10268 | →→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10260, 10267 | |
| 10269 | →→→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗→→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜃] into ax-1 | |
| 10270 | →¬¬¬→⋀𝜓𝜒¬𝜃→→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10268, 10269 | |
| 10271 | →→¬¬¬→⋀𝜓𝜒¬𝜃→→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗→¬𝜒¬→⋀𝜓𝜒¬𝜃, 𝜒↗→¬𝜒¬→⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10272 | →→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10270, 10271 | |
| 10273 | →¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜃] into ax-1 | |
| 10274 | →→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒 | Subs [𝜑↗→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 10275 | →¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒 | Modus ponens 10273, 10274 | |
| 10276 | →→¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒] into ax-2 | |
| 10277 | →→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒 | Modus ponens 10275, 10276 | |
| 10278 | →→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒, 𝜒↗¬→⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10279 | →→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10266, 10278 | |
| 10280 | →→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1 | |
| 10281 | →¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10279, 10280 | |
| 10282 | →→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒, 𝜒↗→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10283 | →→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10281, 10282 | |
| 10284 | →¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10273, 10283 | |
| 10285 | →→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1 | |
| 10286 | →¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10045, 10285 | |
| 10287 | →→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃→→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬𝜒→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃, 𝜒↗→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10288 | →→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬𝜒→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10286, 10287 | |
| 10289 | →¬𝜒→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10284, 10288 | |
| 10290 | →→¬𝜒→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃→→¬𝜒→⋀𝜓𝜒¬𝜃→¬𝜒¬¬→⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜓𝜒¬𝜃, 𝜒↗¬¬→⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10291 | →→¬𝜒→⋀𝜓𝜒¬𝜃→¬𝜒¬¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10289, 10290 | |
| 10292 | →¬𝜒¬¬→⋀𝜓𝜒¬𝜃 | Modus ponens 10258, 10291 | |
| 10293 | →→¬𝜒¬¬→⋀𝜓𝜒¬𝜃→¬→⋀𝜓𝜒¬𝜃𝜒 | Subs [𝜑↗𝜒, 𝜓↗¬→⋀𝜓𝜒¬𝜃] into ax-3 | |
| 10294 | →¬→⋀𝜓𝜒¬𝜃𝜒 | Modus ponens 10292, 10293 | |
| 10295 | →→¬→⋀𝜓𝜒¬𝜃𝜒→⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜒 | Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜃𝜒, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1 | |
| 10296 | →⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜒 | Modus ponens 10294, 10295 | |
| 10297 | →→⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜒→→⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜒 | Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗¬→⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10298 | →→⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜒 | Modus ponens 10296, 10297 | |
| 10299 | →⋀⋀𝜓𝜒𝜃𝜒 | Modus ponens 10057, 10298 | |
| 10300 | →→⋀⋀𝜓𝜒𝜃𝜒→¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜒 | Subs [𝜑↗→⋀⋀𝜓𝜒𝜃𝜒, 𝜓↗¬→⋀𝜓𝜒¬𝜃] into ax-1 | |
| 10301 | →¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜒 | Modus ponens 10299, 10300 | |
| 10302 | →→¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜒→→¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜒 | Subs [𝜑↗¬→⋀𝜓𝜒¬𝜃, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-2 | |
| 10303 | →→¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜒 | Modus ponens 10301, 10302 | |
| 10304 | →→¬→⋀𝜓𝜒¬𝜃𝜒→𝜃→¬→⋀𝜓𝜒¬𝜃𝜒 | Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜃𝜒, 𝜓↗𝜃] into ax-1 | |
| 10305 | →𝜃→¬→⋀𝜓𝜒¬𝜃𝜒 | Modus ponens 10294, 10304 | |
| 10306 | →→𝜃→¬→⋀𝜓𝜒¬𝜃𝜒→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜒 | Subs [𝜑↗𝜃, 𝜓↗¬→⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10307 | →→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜒 | Modus ponens 10305, 10306 | |
| 10308 | →→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜒→⋀𝜓𝜒→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜒 | Subs [𝜑↗→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜒, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 10309 | →⋀𝜓𝜒→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜒 | Modus ponens 10307, 10308 | |
| 10310 | →→⋀𝜓𝜒→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜒→→⋀𝜓𝜒→𝜃¬→⋀𝜓𝜒¬𝜃→⋀𝜓𝜒→𝜃𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→𝜃¬→⋀𝜓𝜒¬𝜃, 𝜒↗→𝜃𝜒] into ax-2 | |
| 10311 | →→⋀𝜓𝜒→𝜃¬→⋀𝜓𝜒¬𝜃→⋀𝜓𝜒→𝜃𝜒 | Modus ponens 10309, 10310 | |
| 10312 | →→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒→𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒 | Subs [𝜑↗→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒, 𝜓↗𝜃] into ax-1 | |
| 10313 | →𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒 | Modus ponens 10224, 10312 | |
| 10314 | →→𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒→→𝜃→⋀𝜓𝜒𝜃→𝜃→⋀𝜓𝜒𝜒 | Subs [𝜑↗𝜃, 𝜓↗→⋀𝜓𝜒𝜃, 𝜒↗→⋀𝜓𝜒𝜒] into ax-2 | |
| 10315 | →→𝜃→⋀𝜓𝜒𝜃→𝜃→⋀𝜓𝜒𝜒 | Modus ponens 10313, 10314 | |
| 10316 | →𝜃→⋀𝜓𝜒𝜒 | Modus ponens 9975, 10315 | |
| 10317 | →→𝜃→⋀𝜓𝜒𝜒→→𝜃⋀𝜓𝜒→𝜃𝜒 | Subs [𝜑↗𝜃, 𝜓↗⋀𝜓𝜒] into ax-2 | |
| 10318 | →→𝜃⋀𝜓𝜒→𝜃𝜒 | Modus ponens 10316, 10317 | |
| 10319 | →→→𝜃⋀𝜓𝜒→𝜃𝜒→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜓𝜒→𝜃𝜒 | Subs [𝜑↗→→𝜃⋀𝜓𝜒→𝜃𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 10320 | →⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜓𝜒→𝜃𝜒 | Modus ponens 10318, 10319 | |
| 10321 | →→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜓𝜒→𝜃𝜒→→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→𝜃⋀𝜓𝜒, 𝜒↗→𝜃𝜒] into ax-2 | |
| 10322 | →→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃𝜒 | Modus ponens 10320, 10321 | |
| 10323 | →⋀𝜑⋀𝜓𝜒→𝜃𝜒 | Modus ponens 10095, 10322 | |
| 10324 | →→⋀𝜑⋀𝜓𝜒→𝜃𝜒→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗𝜃] into ax-2 | |
| 10325 | →→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒 | Modus ponens 10323, 10324 | |
| 10326 | →→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒→𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒 | Subs [𝜑↗→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒, 𝜓↗𝜃] into ax-1 | |
| 10327 | →𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒 | Modus ponens 10325, 10326 | |
| 10328 | →→𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒→→𝜃→⋀𝜑⋀𝜓𝜒𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜒 | Subs [𝜑↗𝜃, 𝜓↗→⋀𝜑⋀𝜓𝜒𝜃, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜒] into ax-2 | |
| 10329 | →→𝜃→⋀𝜑⋀𝜓𝜒𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜒 | Modus ponens 10327, 10328 | |
| 10330 | →𝜃→⋀𝜑⋀𝜓𝜒𝜒 | Modus ponens 10103, 10329 | |
| 10331 | →→𝜃→⋀𝜑⋀𝜓𝜒𝜒→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜒 | Subs [𝜑↗𝜃, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 10332 | →→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜒 | Modus ponens 10330, 10331 | |
| 10333 | →→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜒→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜒 | Subs [𝜑↗→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 10334 | →⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜒 | Modus ponens 10332, 10333 | |
| 10335 | →→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜒→→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→𝜃⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜃𝜒] into ax-2 | |
| 10336 | →→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃𝜒 | Modus ponens 10334, 10335 | |
| 10337 | →→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒→¬¬𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒 | Subs [𝜑↗→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒, 𝜓↗¬¬𝜃] into ax-1 | |
| 10338 | →¬¬𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒 | Modus ponens 10325, 10337 | |
| 10339 | →→¬¬𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒→→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜃→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜒 | Subs [𝜑↗¬¬𝜃, 𝜓↗→⋀𝜑⋀𝜓𝜒𝜃, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜒] into ax-2 | |
| 10340 | →→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜃→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜒 | Modus ponens 10338, 10339 | |
| 10341 | →¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜒 | Modus ponens 10131, 10340 | |
| 10342 | →→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜒→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒 | Subs [𝜑↗¬¬𝜃, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 10343 | →→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒 | Modus ponens 10341, 10342 | |
| 10344 | →→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒→⋀𝜑⋀𝜓𝜒→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒 | Subs [𝜑↗→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 10345 | →⋀𝜑⋀𝜓𝜒→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒 | Modus ponens 10343, 10344 | |
| 10346 | →→⋀𝜑⋀𝜓𝜒→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒→→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬𝜃⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬𝜃𝜒] into ax-2 | |
| 10347 | →→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒 | Modus ponens 10345, 10346 | |
| 10348 | →⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒 | Modus ponens 10137, 10347 | |
| 10349 | →→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒→⋀𝜑⋀𝜓𝜒→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒 | Subs [𝜑↗→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 10350 | →⋀𝜑⋀𝜓𝜒→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒 | Modus ponens 10240, 10349 | |
| 10351 | →→⋀𝜑⋀𝜓𝜒→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒→→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬𝜃𝜒, 𝜒↗→¬¬𝜃¬¬𝜒] into ax-2 | |
| 10352 | →→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜒 | Modus ponens 10350, 10351 | |
| 10353 | →⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜒 | Modus ponens 10348, 10352 | |
| 10354 | →→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃→⋀𝜑⋀𝜓𝜒→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃 | Subs [𝜑↗→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 10355 | →⋀𝜑⋀𝜓𝜒→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃 | Modus ponens 10246, 10354 | |
| 10356 | →→⋀𝜑⋀𝜓𝜒→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜒→⋀𝜑⋀𝜓𝜒→¬𝜒¬𝜃 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬𝜃¬¬𝜒, 𝜒↗→¬𝜒¬𝜃] into ax-2 | |
| 10357 | →→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜒→⋀𝜑⋀𝜓𝜒→¬𝜒¬𝜃 | Modus ponens 10355, 10356 | |
| 10358 | →⋀𝜑⋀𝜓𝜒→¬𝜒¬𝜃 | Modus ponens 10353, 10357 | |
| 10359 | →¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1 | |
| 10360 | →→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒→¬𝜒→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒 | Subs [𝜑↗→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 10361 | →¬𝜒→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒 | Modus ponens 10359, 10360 | |
| 10362 | →→¬𝜒→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒→→¬𝜒¬𝜒→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→⋀𝜑⋀𝜓𝜒¬𝜒] into ax-2 | |
| 10363 | →→¬𝜒¬𝜒→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒 | Modus ponens 10361, 10362 | |
| 10364 | →→⋀𝜑⋀𝜓𝜒→¬𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬𝜒, 𝜒↗¬𝜃] into ax-2 | |
| 10365 | →→⋀𝜑⋀𝜓𝜒¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10358, 10364 | |
| 10366 | →→→⋀𝜑⋀𝜓𝜒¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒→→⋀𝜑⋀𝜓𝜒¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗→→⋀𝜑⋀𝜓𝜒¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1 | |
| 10367 | →¬𝜒→→⋀𝜑⋀𝜓𝜒¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10365, 10366 | |
| 10368 | →→¬𝜒→→⋀𝜑⋀𝜓𝜒¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜑⋀𝜓𝜒¬𝜒, 𝜒↗→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10369 | →→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10367, 10368 | |
| 10370 | →¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10359, 10369 | |
| 10371 | →→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1 | |
| 10372 | →¬𝜒→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10171, 10371 | |
| 10373 | →¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1 | |
| 10374 | →→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-1 | |
| 10375 | →¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10373, 10374 | |
| 10376 | →→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10377 | →→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10375, 10376 | |
| 10378 | →¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10174, 10377 | |
| 10379 | →→¬𝜒→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜒, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10380 | →→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10372, 10379 | |
| 10381 | →→→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗→→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-1 | |
| 10382 | →¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10380, 10381 | |
| 10383 | →→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10384 | →→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10382, 10383 | |
| 10385 | →¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-1 | |
| 10386 | →→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬𝜒→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒 | Subs [𝜑↗→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 10387 | →¬𝜒→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒 | Modus ponens 10385, 10386 | |
| 10388 | →→¬𝜒→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒] into ax-2 | |
| 10389 | →→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒 | Modus ponens 10387, 10388 | |
| 10390 | →→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒, 𝜒↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10391 | →→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10378, 10390 | |
| 10392 | →→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1 | |
| 10393 | →¬𝜒→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10391, 10392 | |
| 10394 | →→¬𝜒→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒, 𝜒↗→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10395 | →→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10393, 10394 | |
| 10396 | →¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10385, 10395 | |
| 10397 | →→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1 | |
| 10398 | →¬𝜒→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10199, 10397 | |
| 10399 | →→¬𝜒→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10400 | →→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10398, 10399 | |
| 10401 | →¬𝜒→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10396, 10400 | |
| 10402 | →→¬𝜒→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10403 | →→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10401, 10402 | |
| 10404 | →¬𝜒¬¬→⋀𝜑⋀𝜓𝜒¬𝜃 | Modus ponens 10370, 10403 | |
| 10405 | →→¬𝜒¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜒 | Subs [𝜑↗𝜒, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-3 | |
| 10406 | →¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜒 | Modus ponens 10404, 10405 | |
| 10407 | →→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜒→⋀⋀𝜑⋀𝜓𝜒𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜒 | Subs [𝜑↗→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜒, 𝜓↗⋀⋀𝜑⋀𝜓𝜒𝜃] into ax-1 | |
| 10408 | →⋀⋀𝜑⋀𝜓𝜒𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜒 | Modus ponens 10406, 10407 | |
| 10409 | →→⋀⋀𝜑⋀𝜓𝜒𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜒→→⋀⋀𝜑⋀𝜓𝜒𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→⋀⋀𝜑⋀𝜓𝜒𝜃𝜒 | Subs [𝜑↗⋀⋀𝜑⋀𝜓𝜒𝜃, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2 | |
| 10410 | →→⋀⋀𝜑⋀𝜓𝜒𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→⋀⋀𝜑⋀𝜓𝜒𝜃𝜒 | Modus ponens 10408, 10409 | |
| 10411 | →⋀⋀𝜑⋀𝜓𝜒𝜃𝜒 | Modus ponens 10211, 10410 | simplrr |
| 10412 | →⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜃] into simpl | |
| 10413 | →→⋀𝜓𝜒→𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗→⋀𝜓𝜒→𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1 | |
| 10414 | →⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Modus ponens 5001, 10413 | |
| 10415 | →→⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒→𝜑⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2 | |
| 10416 | →→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒 | Modus ponens 10414, 10415 | |
| 10417 | →⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒 | Modus ponens 10412, 10416 | |
| 10418 | ↔⋀⋀⋀𝜓𝜒𝜃𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑] into df-an | |
| 10419 | →𝜑→⋀⋀𝜓𝜒𝜃𝜑 | Subs [𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1 | |
| 10420 | →→𝜑→⋀⋀𝜓𝜒𝜃𝜑→¬¬𝜑→𝜑→⋀⋀𝜓𝜒𝜃𝜑 | Subs [𝜑↗→𝜑→⋀⋀𝜓𝜒𝜃𝜑, 𝜓↗¬¬𝜑] into ax-1 | |
| 10421 | →¬¬𝜑→𝜑→⋀⋀𝜓𝜒𝜃𝜑 | Modus ponens 10419, 10420 | |
| 10422 | →→¬¬𝜑→𝜑→⋀⋀𝜓𝜒𝜃𝜑→→¬¬𝜑𝜑→¬¬𝜑→⋀⋀𝜓𝜒𝜃𝜑 | Subs [𝜑↗¬¬𝜑, 𝜓↗𝜑, 𝜒↗→⋀⋀𝜓𝜒𝜃𝜑] into ax-2 | |
| 10423 | →→¬¬𝜑𝜑→¬¬𝜑→⋀⋀𝜓𝜒𝜃𝜑 | Modus ponens 10421, 10422 | |
| 10424 | →¬¬𝜑→⋀⋀𝜓𝜒𝜃𝜑 | Modus ponens notnotr, 10423 | |
| 10425 | →→⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑, 𝜒↗⋀𝜓𝜒] into ax-2 | |
| 10426 | →→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Modus ponens 10417, 10425 | |
| 10427 | →→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→¬¬𝜑→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Subs [𝜑↗→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒, 𝜓↗¬¬𝜑] into ax-1 | |
| 10428 | →¬¬𝜑→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Modus ponens 10426, 10427 | |
| 10429 | →→¬¬𝜑→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→→¬¬𝜑→⋀⋀𝜓𝜒𝜃𝜑→¬¬𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Subs [𝜑↗¬¬𝜑, 𝜓↗→⋀⋀𝜓𝜒𝜃𝜑, 𝜒↗→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒] into ax-2 | |
| 10430 | →→¬¬𝜑→⋀⋀𝜓𝜒𝜃𝜑→¬¬𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Modus ponens 10428, 10429 | |
| 10431 | →¬¬𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Modus ponens 10424, 10430 | |
| 10432 | →⋀⋀𝜓𝜒𝜃⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗⋀⋀𝜓𝜒𝜃] into id | |
| 10433 | →⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗¬¬𝜑] into ax-1 | |
| 10434 | →→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1 | |
| 10435 | →⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃 | Modus ponens 10433, 10434 | |
| 10436 | →→⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃→→⋀⋀𝜓𝜒𝜃⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗⋀⋀𝜓𝜒𝜃, 𝜒↗→¬¬𝜑⋀⋀𝜓𝜒𝜃] into ax-2 | |
| 10437 | →→⋀⋀𝜓𝜒𝜃⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃 | Modus ponens 10435, 10436 | |
| 10438 | →→¬¬𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→→¬¬𝜑⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒 | Subs [𝜑↗¬¬𝜑, 𝜓↗⋀⋀𝜓𝜒𝜃, 𝜒↗⋀𝜓𝜒] into ax-2 | |
| 10439 | →→¬¬𝜑⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒 | Modus ponens 10431, 10438 | |
| 10440 | →→→¬¬𝜑⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→→¬¬𝜑⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒 | Subs [𝜑↗→→¬¬𝜑⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1 | |
| 10441 | →⋀⋀𝜓𝜒𝜃→→¬¬𝜑⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒 | Modus ponens 10439, 10440 | |
| 10442 | →→⋀⋀𝜓𝜒𝜃→→¬¬𝜑⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗→¬¬𝜑⋀⋀𝜓𝜒𝜃, 𝜒↗→¬¬𝜑⋀𝜓𝜒] into ax-2 | |
| 10443 | →→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒 | Modus ponens 10441, 10442 | |
| 10444 | →⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒 | Modus ponens 10433, 10443 | |
| 10445 | →⋀𝜓𝜒¬¬⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒] into notnot | |
| 10446 | →→⋀𝜓𝜒¬¬⋀𝜓𝜒→¬¬𝜑→⋀𝜓𝜒¬¬⋀𝜓𝜒 | Subs [𝜑↗→⋀𝜓𝜒¬¬⋀𝜓𝜒, 𝜓↗¬¬𝜑] into ax-1 | |
| 10447 | →¬¬𝜑→⋀𝜓𝜒¬¬⋀𝜓𝜒 | Modus ponens 10445, 10446 | |
| 10448 | →→¬¬𝜑→⋀𝜓𝜒¬¬⋀𝜓𝜒→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑¬¬⋀𝜓𝜒 | Subs [𝜑↗¬¬𝜑, 𝜓↗⋀𝜓𝜒, 𝜒↗¬¬⋀𝜓𝜒] into ax-2 | |
| 10449 | →→¬¬𝜑⋀𝜓𝜒→¬¬𝜑¬¬⋀𝜓𝜒 | Modus ponens 10447, 10448 | |
| 10450 | →→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑¬¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑¬¬⋀𝜓𝜒 | Subs [𝜑↗→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑¬¬⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1 | |
| 10451 | →⋀⋀𝜓𝜒𝜃→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑¬¬⋀𝜓𝜒 | Modus ponens 10449, 10450 | |
| 10452 | →→⋀⋀𝜓𝜒𝜃→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑¬¬⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→¬¬𝜑¬¬⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗→¬¬𝜑⋀𝜓𝜒, 𝜒↗→¬¬𝜑¬¬⋀𝜓𝜒] into ax-2 | |
| 10453 | →→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→¬¬𝜑¬¬⋀𝜓𝜒 | Modus ponens 10451, 10452 | |
| 10454 | →⋀⋀𝜓𝜒𝜃→¬¬𝜑¬¬⋀𝜓𝜒 | Modus ponens 10444, 10453 | |
| 10455 | →→¬¬𝜑¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬⋀𝜓𝜒] into ax-3 | |
| 10456 | →→→¬¬𝜑¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜃→→¬¬𝜑¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬𝜑 | Subs [𝜑↗→→¬¬𝜑¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬𝜑, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1 | |
| 10457 | →⋀⋀𝜓𝜒𝜃→→¬¬𝜑¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬𝜑 | Modus ponens 10455, 10456 | |
| 10458 | →→⋀⋀𝜓𝜒𝜃→→¬¬𝜑¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬𝜑→→⋀⋀𝜓𝜒𝜃→¬¬𝜑¬¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬𝜑 | Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗→¬¬𝜑¬¬⋀𝜓𝜒, 𝜒↗→¬⋀𝜓𝜒¬𝜑] into ax-2 | |
| 10459 | →→⋀⋀𝜓𝜒𝜃→¬¬𝜑¬¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬𝜑 | Modus ponens 10457, 10458 | |
| 10460 | →⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬𝜑 | Modus ponens 10454, 10459 | |
| 10461 | →¬⋀𝜓𝜒¬⋀𝜓𝜒 | Subs [𝜑↗¬⋀𝜓𝜒] into id | |
| 10462 | →¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒 | Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1 | |
| 10463 | →→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒 | Subs [𝜑↗→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒, 𝜓↗¬⋀𝜓𝜒] into ax-1 | |
| 10464 | →¬⋀𝜓𝜒→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒 | Modus ponens 10462, 10463 | |
| 10465 | →→¬⋀𝜓𝜒→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→→¬⋀𝜓𝜒¬⋀𝜓𝜒→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒 | Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬⋀𝜓𝜒, 𝜒↗→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒] into ax-2 | |
| 10466 | →→¬⋀𝜓𝜒¬⋀𝜓𝜒→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒 | Modus ponens 10464, 10465 | |
| 10467 | →→⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬𝜑→→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗¬⋀𝜓𝜒, 𝜒↗¬𝜑] into ax-2 | |
| 10468 | →→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑 | Modus ponens 10460, 10467 | |
| 10469 | →→→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗→→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬⋀𝜓𝜒] into ax-1 | |
| 10470 | →¬⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑 | Modus ponens 10468, 10469 | |
| 10471 | →→¬⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑→→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒, 𝜒↗→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-2 | |
| 10472 | →→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑 | Modus ponens 10470, 10471 | |
| 10473 | →¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑 | Modus ponens 10462, 10472 | |
| 10474 | →¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗¬→⋀⋀𝜓𝜒𝜃¬𝜑] into id | |
| 10475 | →→¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒→¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗→¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬⋀𝜓𝜒] into ax-1 | |
| 10476 | →¬⋀𝜓𝜒→¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Modus ponens 10474, 10475 | |
| 10477 | →¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗¬→⋀⋀𝜓𝜒𝜃¬𝜑] into notnotr | |
| 10478 | →¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬⋀𝜓𝜒] into ax-1 | |
| 10479 | →→¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗→¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-1 | |
| 10480 | →¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Modus ponens 10478, 10479 | |
| 10481 | →→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜒↗→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-2 | |
| 10482 | →→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Modus ponens 10480, 10481 | |
| 10483 | →¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Modus ponens 10477, 10482 | |
| 10484 | →→¬⋀𝜓𝜒→¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜒↗¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-2 | |
| 10485 | →→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Modus ponens 10476, 10484 | |
| 10486 | →→→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗→→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-1 | |
| 10487 | →¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Modus ponens 10485, 10486 | |
| 10488 | →→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜒↗→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-2 | |
| 10489 | →→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Modus ponens 10487, 10488 | |
| 10490 | →¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-1 | |
| 10491 | →→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒, 𝜓↗¬⋀𝜓𝜒] into ax-1 | |
| 10492 | →¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒 | Modus ponens 10490, 10491 | |
| 10493 | →→¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→→¬⋀𝜓𝜒¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬⋀𝜓𝜒, 𝜒↗→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒] into ax-2 | |
| 10494 | →→¬⋀𝜓𝜒¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒 | Modus ponens 10492, 10493 | |
| 10495 | →→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬⋀𝜓𝜒, 𝜒↗¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-2 | |
| 10496 | →→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Modus ponens 10483, 10495 | |
| 10497 | →→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬⋀𝜓𝜒] into ax-1 | |
| 10498 | →¬⋀𝜓𝜒→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Modus ponens 10496, 10497 | |
| 10499 | →→¬⋀𝜓𝜒→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒, 𝜒↗→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-2 | |
| 10500 | →→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Modus ponens 10498, 10499 | |
| 10501 | →¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Modus ponens 10490, 10500 | |
| 10502 | →→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗¬¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-3 | |
| 10503 | →→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬⋀𝜓𝜒] into ax-1 | |
| 10504 | →¬⋀𝜓𝜒→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Modus ponens 10502, 10503 | |
| 10505 | →→¬⋀𝜓𝜒→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜒↗→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-2 | |
| 10506 | →→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Modus ponens 10504, 10505 | |
| 10507 | →¬⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Modus ponens 10501, 10506 | |
| 10508 | →→¬⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜒↗¬¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-2 | |
| 10509 | →→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Modus ponens 10507, 10508 | |
| 10510 | →¬⋀𝜓𝜒¬¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Modus ponens 10473, 10509 | |
| 10511 | →→¬⋀𝜓𝜒¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-3 | |
| 10512 | →¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒 | Modus ponens 10510, 10511 | |
| 10513 | →↔⋀⋀⋀𝜓𝜒𝜃𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜓𝜒𝜃𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗⋀⋀⋀𝜓𝜒𝜃𝜑, 𝜓↗¬→⋀⋀𝜓𝜒𝜃¬𝜑] into biimp | |
| 10514 | →⋀⋀⋀𝜓𝜒𝜃𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Modus ponens 10418, 10513 | |
| 10515 | →→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒→⋀⋀⋀𝜓𝜒𝜃𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒 | Subs [𝜑↗→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒, 𝜓↗⋀⋀⋀𝜓𝜒𝜃𝜑] into ax-1 | |
| 10516 | →⋀⋀⋀𝜓𝜒𝜃𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒 | Modus ponens 10512, 10515 | |
| 10517 | →→⋀⋀⋀𝜓𝜒𝜃𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒→→⋀⋀⋀𝜓𝜒𝜃𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜓𝜒𝜃𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀⋀𝜓𝜒𝜃𝜑, 𝜓↗¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜒↗⋀𝜓𝜒] into ax-2 | |
| 10518 | →→⋀⋀⋀𝜓𝜒𝜃𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜓𝜒𝜃𝜑⋀𝜓𝜒 | Modus ponens 10516, 10517 | |
| 10519 | →⋀⋀⋀𝜓𝜒𝜃𝜑⋀𝜓𝜒 | Modus ponens 10514, 10518 | |
| 10520 | →↔⋀⋀⋀𝜓𝜒𝜃𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑↔¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀⋀⋀𝜓𝜒𝜃𝜑 | Subs [𝜑↗⋀⋀⋀𝜓𝜒𝜃𝜑, 𝜓↗¬→⋀⋀𝜓𝜒𝜃¬𝜑] into bicom1 | |
| 10521 | ↔¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀⋀⋀𝜓𝜒𝜃𝜑 | Modus ponens 10418, 10520 | |
| 10522 | →↔¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀⋀⋀𝜓𝜒𝜃𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀⋀⋀𝜓𝜒𝜃𝜑 | Subs [𝜑↗¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗⋀⋀⋀𝜓𝜒𝜃𝜑] into biimp | |
| 10523 | →¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀⋀⋀𝜓𝜒𝜃𝜑 | Modus ponens 10521, 10522 | |
| 10524 | →→⋀⋀⋀𝜓𝜒𝜃𝜑⋀𝜓𝜒→¬→⋀⋀𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜓𝜒𝜃𝜑⋀𝜓𝜒 | Subs [𝜑↗→⋀⋀⋀𝜓𝜒𝜃𝜑⋀𝜓𝜒, 𝜓↗¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-1 | |
| 10525 | →¬→⋀⋀𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜓𝜒𝜃𝜑⋀𝜓𝜒 | Modus ponens 10519, 10524 | |
| 10526 | →→¬→⋀⋀𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜓𝜒𝜃𝜑⋀𝜓𝜒→→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀⋀⋀𝜓𝜒𝜃𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒 | Subs [𝜑↗¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗⋀⋀⋀𝜓𝜒𝜃𝜑, 𝜒↗⋀𝜓𝜒] into ax-2 | |
| 10527 | →→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀⋀⋀𝜓𝜒𝜃𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒 | Modus ponens 10525, 10526 | |
| 10528 | →⋀⋀𝜓𝜒𝜃→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑] into pm3.2im | |
| 10529 | →→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒→𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒 | Subs [𝜑↗→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 10530 | →𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒 | Modus ponens 10512, 10529 | |
| 10531 | →→𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒→→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→𝜑⋀𝜓𝜒 | Subs [𝜓↗¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜒↗⋀𝜓𝜒] into ax-2 | |
| 10532 | →→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→𝜑⋀𝜓𝜒 | Modus ponens 10530, 10531 | |
| 10533 | →→→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→𝜑⋀𝜓𝜒 | Subs [𝜑↗→→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1 | |
| 10534 | →⋀⋀𝜓𝜒𝜃→→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→𝜑⋀𝜓𝜒 | Modus ponens 10532, 10533 | |
| 10535 | →→⋀⋀𝜓𝜒𝜃→→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→𝜑⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2 | |
| 10536 | →→⋀⋀𝜓𝜒𝜃→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒 | Modus ponens 10534, 10535 | |
| 10537 | →→𝜑→⋀⋀𝜓𝜒𝜃𝜑→𝜑→𝜑→⋀⋀𝜓𝜒𝜃𝜑 | Subs [𝜑↗→𝜑→⋀⋀𝜓𝜒𝜃𝜑, 𝜓↗𝜑] into ax-1 | |
| 10538 | →𝜑→𝜑→⋀⋀𝜓𝜒𝜃𝜑 | Modus ponens 10419, 10537 | |
| 10539 | →→𝜑→𝜑→⋀⋀𝜓𝜒𝜃𝜑→→𝜑𝜑→𝜑→⋀⋀𝜓𝜒𝜃𝜑 | Subs [𝜓↗𝜑, 𝜒↗→⋀⋀𝜓𝜒𝜃𝜑] into ax-2 | |
| 10540 | →→𝜑𝜑→𝜑→⋀⋀𝜓𝜒𝜃𝜑 | Modus ponens 10538, 10539 | |
| 10541 | →→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→𝜑→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Subs [𝜑↗→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 10542 | →𝜑→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Modus ponens 10426, 10541 | |
| 10543 | →→𝜑→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→→𝜑→⋀⋀𝜓𝜒𝜃𝜑→𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Subs [𝜓↗→⋀⋀𝜓𝜒𝜃𝜑, 𝜒↗→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒] into ax-2 | |
| 10544 | →→𝜑→⋀⋀𝜓𝜒𝜃𝜑→𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Modus ponens 10542, 10543 | |
| 10545 | →𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Modus ponens 10419, 10544 | |
| 10546 | ↔⋀𝜑⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Subs [𝜓↗⋀⋀𝜓𝜒𝜃] into df-an | |
| 10547 | →¬¬⋀⋀𝜓𝜒𝜃⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗⋀⋀𝜓𝜒𝜃] into notnotr | |
| 10548 | →⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑] into ax-1 | |
| 10549 | →→⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃→¬¬⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗→⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗¬¬⋀⋀𝜓𝜒𝜃] into ax-1 | |
| 10550 | →¬¬⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃 | Modus ponens 10548, 10549 | |
| 10551 | →→¬¬⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃→→¬¬⋀⋀𝜓𝜒𝜃⋀⋀𝜓𝜒𝜃→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗¬¬⋀⋀𝜓𝜒𝜃, 𝜓↗⋀⋀𝜓𝜒𝜃, 𝜒↗→𝜑⋀⋀𝜓𝜒𝜃] into ax-2 | |
| 10552 | →→¬¬⋀⋀𝜓𝜒𝜃⋀⋀𝜓𝜒𝜃→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃 | Modus ponens 10550, 10551 | |
| 10553 | →¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃 | Modus ponens 10547, 10552 | |
| 10554 | →→𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→→𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒 | Subs [𝜓↗⋀⋀𝜓𝜒𝜃, 𝜒↗⋀𝜓𝜒] into ax-2 | |
| 10555 | →→𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒 | Modus ponens 10545, 10554 | |
| 10556 | →→→𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃→→𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒 | Subs [𝜑↗→→𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒, 𝜓↗¬¬⋀⋀𝜓𝜒𝜃] into ax-1 | |
| 10557 | →¬¬⋀⋀𝜓𝜒𝜃→→𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒 | Modus ponens 10555, 10556 | |
| 10558 | →→¬¬⋀⋀𝜓𝜒𝜃→→𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒→→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒 | Subs [𝜑↗¬¬⋀⋀𝜓𝜒𝜃, 𝜓↗→𝜑⋀⋀𝜓𝜒𝜃, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2 | |
| 10559 | →→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒 | Modus ponens 10557, 10558 | |
| 10560 | →¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒 | Modus ponens 10553, 10559 | |
| 10561 | →𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑 | Subs [𝜓↗¬¬⋀⋀𝜓𝜒𝜃] into ax-1 | |
| 10562 | →→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑→𝜑→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑 | Subs [𝜑↗→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑, 𝜓↗𝜑] into ax-1 | |
| 10563 | →𝜑→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑 | Modus ponens 10561, 10562 | |
| 10564 | →→𝜑→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑→→𝜑𝜑→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑 | Subs [𝜓↗𝜑, 𝜒↗→¬¬⋀⋀𝜓𝜒𝜃𝜑] into ax-2 | |
| 10565 | →→𝜑𝜑→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑 | Modus ponens 10563, 10564 | |
| 10566 | →→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒→→¬¬⋀⋀𝜓𝜒𝜃𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Subs [𝜑↗¬¬⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑, 𝜒↗⋀𝜓𝜒] into ax-2 | |
| 10567 | →→¬¬⋀⋀𝜓𝜒𝜃𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Modus ponens 10560, 10566 | |
| 10568 | →→→¬¬⋀⋀𝜓𝜒𝜃𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→𝜑→→¬¬⋀⋀𝜓𝜒𝜃𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Subs [𝜑↗→→¬¬⋀⋀𝜓𝜒𝜃𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 10569 | →𝜑→→¬¬⋀⋀𝜓𝜒𝜃𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Modus ponens 10567, 10568 | |
| 10570 | →→𝜑→→¬¬⋀⋀𝜓𝜒𝜃𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑→𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Subs [𝜓↗→¬¬⋀⋀𝜓𝜒𝜃𝜑, 𝜒↗→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒] into ax-2 | |
| 10571 | →→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑→𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Modus ponens 10569, 10570 | |
| 10572 | →𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Modus ponens 10561, 10571 | |
| 10573 | →→⋀𝜓𝜒¬¬⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒¬¬⋀𝜓𝜒 | Subs [𝜑↗→⋀𝜓𝜒¬¬⋀𝜓𝜒, 𝜓↗¬¬⋀⋀𝜓𝜒𝜃] into ax-1 | |
| 10574 | →¬¬⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒¬¬⋀𝜓𝜒 | Modus ponens 10445, 10573 | |
| 10575 | →→¬¬⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒¬¬⋀𝜓𝜒→→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒 | Subs [𝜑↗¬¬⋀⋀𝜓𝜒𝜃, 𝜓↗⋀𝜓𝜒, 𝜒↗¬¬⋀𝜓𝜒] into ax-2 | |
| 10576 | →→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒 | Modus ponens 10574, 10575 | |
| 10577 | →→→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→𝜑→→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒 | Subs [𝜑↗→→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 10578 | →𝜑→→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒 | Modus ponens 10576, 10577 | |
| 10579 | →→𝜑→→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→→𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→𝜑→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒 | Subs [𝜓↗→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒, 𝜒↗→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒] into ax-2 | |
| 10580 | →→𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→𝜑→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒 | Modus ponens 10578, 10579 | |
| 10581 | →𝜑→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒 | Modus ponens 10572, 10580 | |
| 10582 | →→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬⋀𝜓𝜒] into ax-3 | |
| 10583 | →→→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃→𝜑→→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗→→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑] into ax-1 | |
| 10584 | →𝜑→→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃 | Modus ponens 10582, 10583 | |
| 10585 | →→𝜑→→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃→→𝜑→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→𝜑→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃 | Subs [𝜓↗→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒, 𝜒↗→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃] into ax-2 | |
| 10586 | →→𝜑→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→𝜑→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃 | Modus ponens 10584, 10585 | |
| 10587 | →𝜑→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃 | Modus ponens 10581, 10586 | |
| 10588 | →¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 10589 | →→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒, 𝜓↗¬⋀𝜓𝜒] into ax-1 | |
| 10590 | →¬⋀𝜓𝜒→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒 | Modus ponens 10588, 10589 | |
| 10591 | →→¬⋀𝜓𝜒→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒→→¬⋀𝜓𝜒¬⋀𝜓𝜒→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬⋀𝜓𝜒, 𝜒↗→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 10592 | →→¬⋀𝜓𝜒¬⋀𝜓𝜒→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒 | Modus ponens 10590, 10591 | |
| 10593 | →→𝜑→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃→→𝜑¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃 | Subs [𝜓↗¬⋀𝜓𝜒, 𝜒↗¬⋀⋀𝜓𝜒𝜃] into ax-2 | |
| 10594 | →→𝜑¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃 | Modus ponens 10587, 10593 | |
| 10595 | →→→𝜑¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗→→𝜑¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬⋀𝜓𝜒] into ax-1 | |
| 10596 | →¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃 | Modus ponens 10594, 10595 | |
| 10597 | →→¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃→→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒→¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒, 𝜒↗→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-2 | |
| 10598 | →→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒→¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃 | Modus ponens 10596, 10597 | |
| 10599 | →¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃 | Modus ponens 10588, 10598 | |
| 10600 | →¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗¬→𝜑¬⋀⋀𝜓𝜒𝜃] into id | |
| 10601 | →→¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒→¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗→¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬⋀𝜓𝜒] into ax-1 | |
| 10602 | →¬⋀𝜓𝜒→¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Modus ponens 10600, 10601 | |
| 10603 | →¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗¬→𝜑¬⋀⋀𝜓𝜒𝜃] into notnotr | |
| 10604 | →¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬⋀𝜓𝜒] into ax-1 | |
| 10605 | →→¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗→¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-1 | |
| 10606 | →¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Modus ponens 10604, 10605 | |
| 10607 | →→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜒↗→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-2 | |
| 10608 | →→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Modus ponens 10606, 10607 | |
| 10609 | →¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Modus ponens 10603, 10608 | |
| 10610 | →→¬⋀𝜓𝜒→¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜒↗¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-2 | |
| 10611 | →→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Modus ponens 10602, 10610 | |
| 10612 | →→→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗→→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-1 | |
| 10613 | →¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Modus ponens 10611, 10612 | |
| 10614 | →→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜒↗→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-2 | |
| 10615 | →→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Modus ponens 10613, 10614 | |
| 10616 | →¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒 | Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-1 | |
| 10617 | →→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒 | Subs [𝜑↗→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒, 𝜓↗¬⋀𝜓𝜒] into ax-1 | |
| 10618 | →¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒 | Modus ponens 10616, 10617 | |
| 10619 | →→¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→→¬⋀𝜓𝜒¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒 | Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒] into ax-2 | |
| 10620 | →→¬⋀𝜓𝜒¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒 | Modus ponens 10618, 10619 | |
| 10621 | →→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬⋀𝜓𝜒, 𝜒↗¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-2 | |
| 10622 | →→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Modus ponens 10609, 10621 | |
| 10623 | →→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬⋀𝜓𝜒] into ax-1 | |
| 10624 | →¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Modus ponens 10622, 10623 | |
| 10625 | →→¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-2 | |
| 10626 | →→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Modus ponens 10624, 10625 | |
| 10627 | →¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Modus ponens 10616, 10626 | |
| 10628 | →→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗¬¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-3 | |
| 10629 | →→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬⋀𝜓𝜒] into ax-1 | |
| 10630 | →¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Modus ponens 10628, 10629 | |
| 10631 | →→¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜒↗→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-2 | |
| 10632 | →→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Modus ponens 10630, 10631 | |
| 10633 | →¬⋀𝜓𝜒→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Modus ponens 10627, 10632 | |
| 10634 | →→¬⋀𝜓𝜒→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜒↗¬¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-2 | |
| 10635 | →→¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Modus ponens 10633, 10634 | |
| 10636 | →¬⋀𝜓𝜒¬¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Modus ponens 10599, 10635 | |
| 10637 | →→¬⋀𝜓𝜒¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬→𝜑¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-3 | |
| 10638 | →¬→𝜑¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Modus ponens 10636, 10637 | |
| 10639 | →↔⋀𝜑⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗¬→𝜑¬⋀⋀𝜓𝜒𝜃] into biimp | |
| 10640 | →⋀𝜑⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃 | Modus ponens 10546, 10639 | |
| 10641 | →→¬→𝜑¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→¬→𝜑¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Subs [𝜑↗→¬→𝜑¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒, 𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃] into ax-1 | |
| 10642 | →⋀𝜑⋀⋀𝜓𝜒𝜃→¬→𝜑¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Modus ponens 10638, 10641 | |
| 10643 | →→⋀𝜑⋀⋀𝜓𝜒𝜃→¬→𝜑¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→→⋀𝜑⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜒↗⋀𝜓𝜒] into ax-2 | |
| 10644 | →→⋀𝜑⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Modus ponens 10642, 10643 | |
| 10645 | →⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜓𝜒 | Modus ponens 10640, 10644 | |
| 10646 | →⋀𝜑⋀⋀𝜓𝜒𝜃𝜑 | Subs [𝜓↗⋀⋀𝜓𝜒𝜃] into simpl | |
| 10647 | →→⋀𝜑⋀𝜓𝜒𝜓→¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓 | Subs [𝜑↗→⋀𝜑⋀𝜓𝜒𝜓, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into ax-1 | |
| 10648 | →¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓 | Modus ponens simprl, 10647 | |
| 10649 | →→¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓→→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓 | Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗𝜓] into ax-2 | |
| 10650 | →→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓 | Modus ponens 10648, 10649 | |
| 10651 | →→¬→𝜑¬⋀𝜓𝜒𝜓→⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓 | Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒𝜓, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 10652 | →⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓 | Modus ponens 9112, 10651 | |
| 10653 | →→⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜓 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗𝜓] into ax-2 | |
| 10654 | →→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜓 | Modus ponens 10652, 10653 | |
| 10655 | →→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜓→𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜓 | Subs [𝜑↗→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜓, 𝜓↗𝜑] into ax-1 | |
| 10656 | →𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜓 | Modus ponens 10654, 10655 | |
| 10657 | →→𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜓→→𝜑→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→𝜑→⋀𝜓𝜒𝜓 | Subs [𝜓↗→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜒↗→⋀𝜓𝜒𝜓] into ax-2 | |
| 10658 | →→𝜑→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→𝜑→⋀𝜓𝜒𝜓 | Modus ponens 10656, 10657 | |
| 10659 | →→⋀𝜓𝜒→𝜑⋀𝜓𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗→⋀𝜓𝜒→𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃] into ax-1 | |
| 10660 | →⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒→𝜑⋀𝜓𝜒 | Modus ponens 5001, 10659 | |
| 10661 | →→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒→𝜑⋀𝜓𝜒→→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2 | |
| 10662 | →→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒 | Modus ponens 10660, 10661 | |
| 10663 | →⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒 | Modus ponens 10645, 10662 | |
| 10664 | →→→𝜑⋀𝜓𝜒→𝜑𝜓→⋀𝜑⋀⋀𝜓𝜒𝜃→→𝜑⋀𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜑⋀𝜓𝜒→𝜑𝜓, 𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃] into ax-1 | |
| 10665 | →⋀𝜑⋀⋀𝜓𝜒𝜃→→𝜑⋀𝜓𝜒→𝜑𝜓 | Modus ponens 6076, 10664 | |
| 10666 | →→⋀𝜑⋀⋀𝜓𝜒𝜃→→𝜑⋀𝜓𝜒→𝜑𝜓→→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑𝜓 | Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗→𝜑⋀𝜓𝜒, 𝜒↗→𝜑𝜓] into ax-2 | |
| 10667 | →→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑𝜓 | Modus ponens 10665, 10666 | |
| 10668 | →⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑𝜓 | Modus ponens 10663, 10667 | |
| 10669 | →𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑 | Subs [𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃] into ax-1 | |
| 10670 | →→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑 | Subs [𝜑↗→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑, 𝜓↗𝜑] into ax-1 | |
| 10671 | →𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑 | Modus ponens 10669, 10670 | |
| 10672 | →→𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→→𝜑𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑 | Subs [𝜓↗𝜑, 𝜒↗→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑] into ax-2 | |
| 10673 | →→𝜑𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑 | Modus ponens 10671, 10672 | |
| 10674 | →→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑𝜓→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓 | Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2 | |
| 10675 | →→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓 | Modus ponens 10668, 10674 | |
| 10676 | →→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓→𝜑→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓 | Subs [𝜑↗→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓, 𝜓↗𝜑] into ax-1 | |
| 10677 | →𝜑→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓 | Modus ponens 10675, 10676 | |
| 10678 | →→𝜑→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓→→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓 | Subs [𝜓↗→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑, 𝜒↗→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓] into ax-2 | |
| 10679 | →→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓 | Modus ponens 10677, 10678 | |
| 10680 | →𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓 | Modus ponens 10669, 10679 | |
| 10681 | →→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓 | Subs [𝜑↗→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓, 𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃] into ax-1 | |
| 10682 | →⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓 | Modus ponens 10680, 10681 | |
| 10683 | →→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓 | Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑, 𝜒↗→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓] into ax-2 | |
| 10684 | →→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓 | Modus ponens 10682, 10683 | |
| 10685 | →⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓 | Modus ponens 10646, 10684 | |
| 10686 | →⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜑⋀⋀𝜓𝜒𝜃 | Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃] into id | |
| 10687 | →→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓→→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓 | Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜒↗𝜓] into ax-2 | |
| 10688 | →→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓 | Modus ponens 10685, 10687 | |
| 10689 | →⋀𝜑⋀⋀𝜓𝜒𝜃𝜓 | Modus ponens 10686, 10688 | simprll |
| 10690 | →→⋀𝜑⋀𝜓𝜒𝜒→¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜒 | Subs [𝜑↗→⋀𝜑⋀𝜓𝜒𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into ax-1 | |
| 10691 | →¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜒 | Modus ponens simprr, 10690 | |
| 10692 | →→¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜒→→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒 | Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-2 | |
| 10693 | →→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒 | Modus ponens 10691, 10692 | |
| 10694 | →→¬→𝜑¬⋀𝜓𝜒𝜒→⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒 | Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒𝜒, 𝜓↗⋀𝜓𝜒] into ax-1 | |
| 10695 | →⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒 | Modus ponens 9512, 10694 | |
| 10696 | →→⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 10697 | →→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜒 | Modus ponens 10695, 10696 | |
| 10698 | →→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜒→𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜒 | Subs [𝜑↗→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1 | |
| 10699 | →𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜒 | Modus ponens 10697, 10698 | |
| 10700 | →→𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜒→→𝜑→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→𝜑→⋀𝜓𝜒𝜒 | Subs [𝜓↗→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜒↗→⋀𝜓𝜒𝜒] into ax-2 | |
| 10701 | →→𝜑→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→𝜑→⋀𝜓𝜒𝜒 | Modus ponens 10699, 10700 | |
| 10702 | →→→𝜑⋀𝜓𝜒→𝜑𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→→𝜑⋀𝜓𝜒→𝜑𝜒 | Subs [𝜑↗→→𝜑⋀𝜓𝜒→𝜑𝜒, 𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃] into ax-1 | |
| 10703 | →⋀𝜑⋀⋀𝜓𝜒𝜃→→𝜑⋀𝜓𝜒→𝜑𝜒 | Modus ponens 6081, 10702 | |
| 10704 | →→⋀𝜑⋀⋀𝜓𝜒𝜃→→𝜑⋀𝜓𝜒→𝜑𝜒→→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑𝜒 | Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗→𝜑⋀𝜓𝜒, 𝜒↗→𝜑𝜒] into ax-2 | |
| 10705 | →→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑𝜒 | Modus ponens 10703, 10704 | |
| 10706 | →⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑𝜒 | Modus ponens 10663, 10705 | |
| 10707 | →→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑𝜒→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒 | Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑] into ax-2 | |
| 10708 | →→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒 | Modus ponens 10706, 10707 | |
| 10709 | →→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒→𝜑→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒 | Subs [𝜑↗→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒, 𝜓↗𝜑] into ax-1 | |
| 10710 | →𝜑→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒 | Modus ponens 10708, 10709 | |
| 10711 | →→𝜑→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒→→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒 | Subs [𝜓↗→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑, 𝜒↗→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒] into ax-2 | |
| 10712 | →→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒 | Modus ponens 10710, 10711 | |
| 10713 | →𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒 | Modus ponens 10669, 10712 | |
| 10714 | →→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒 | Subs [𝜑↗→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒, 𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃] into ax-1 | |
| 10715 | →⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒 | Modus ponens 10713, 10714 | |
| 10716 | →→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒 | Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑, 𝜒↗→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒] into ax-2 | |
| 10717 | →→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒 | Modus ponens 10715, 10716 | |
| 10718 | →⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒 | Modus ponens 10646, 10717 | |
| 10719 | →→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒→→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒 | Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃] into ax-2 | |
| 10720 | →→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒 | Modus ponens 10718, 10719 | |
| 10721 | →⋀𝜑⋀⋀𝜓𝜒𝜃𝜒 | Modus ponens 10686, 10720 | simprlr |
| 10722 | →⋀𝜒𝜃𝜒 | Subs [𝜑↗𝜒, 𝜓↗𝜃] into simpl | |
| 10723 | →→𝜒→𝜓𝜒→⋀𝜒𝜃→𝜒→𝜓𝜒 | Subs [𝜑↗→𝜒→𝜓𝜒, 𝜓↗⋀𝜒𝜃] into ax-1 | |
| 10724 | →⋀𝜒𝜃→𝜒→𝜓𝜒 | Modus ponens 5362, 10723 | |
| 10725 | →→⋀𝜒𝜃→𝜒→𝜓𝜒→→⋀𝜒𝜃𝜒→⋀𝜒𝜃→𝜓𝜒 | Subs [𝜑↗⋀𝜒𝜃, 𝜓↗𝜒, 𝜒↗→𝜓𝜒] into ax-2 | |
| 10726 | →→⋀𝜒𝜃𝜒→⋀𝜒𝜃→𝜓𝜒 | Modus ponens 10724, 10725 | |
| 10727 | →⋀𝜒𝜃→𝜓𝜒 | Modus ponens 10722, 10726 | |
| 10728 | ↔⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗⋀𝜒𝜃] into df-an | |
| 10729 | →𝜓→⋀𝜒𝜃𝜓 | Subs [𝜑↗𝜓, 𝜓↗⋀𝜒𝜃] into ax-1 | |
| 10730 | →→𝜓→⋀𝜒𝜃𝜓→¬¬𝜓→𝜓→⋀𝜒𝜃𝜓 | Subs [𝜑↗→𝜓→⋀𝜒𝜃𝜓, 𝜓↗¬¬𝜓] into ax-1 | |
| 10731 | →¬¬𝜓→𝜓→⋀𝜒𝜃𝜓 | Modus ponens 10729, 10730 | |
| 10732 | →→¬¬𝜓→𝜓→⋀𝜒𝜃𝜓→→¬¬𝜓𝜓→¬¬𝜓→⋀𝜒𝜃𝜓 | Subs [𝜑↗¬¬𝜓, 𝜒↗→⋀𝜒𝜃𝜓] into ax-2 | |
| 10733 | →→¬¬𝜓𝜓→¬¬𝜓→⋀𝜒𝜃𝜓 | Modus ponens 10731, 10732 | |
| 10734 | →¬¬𝜓→⋀𝜒𝜃𝜓 | Modus ponens 570, 10733 | |
| 10735 | →→⋀𝜒𝜃→𝜓𝜒→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒 | Subs [𝜑↗⋀𝜒𝜃] into ax-2 | |
| 10736 | →→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒 | Modus ponens 10727, 10735 | |
| 10737 | →→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒→¬¬𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒 | Subs [𝜑↗→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒, 𝜓↗¬¬𝜓] into ax-1 | |
| 10738 | →¬¬𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒 | Modus ponens 10736, 10737 | |
| 10739 | →→¬¬𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒→→¬¬𝜓→⋀𝜒𝜃𝜓→¬¬𝜓→⋀𝜒𝜃𝜒 | Subs [𝜑↗¬¬𝜓, 𝜓↗→⋀𝜒𝜃𝜓, 𝜒↗→⋀𝜒𝜃𝜒] into ax-2 | |
| 10740 | →→¬¬𝜓→⋀𝜒𝜃𝜓→¬¬𝜓→⋀𝜒𝜃𝜒 | Modus ponens 10738, 10739 | |
| 10741 | →¬¬𝜓→⋀𝜒𝜃𝜒 | Modus ponens 10734, 10740 | |
| 10742 | →⋀𝜒𝜃⋀𝜒𝜃 | Subs [𝜑↗⋀𝜒𝜃] into id | |
| 10743 | →⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀𝜒𝜃, 𝜓↗¬¬𝜓] into ax-1 | |
| 10744 | →→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃→⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃 | Subs [𝜑↗→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃, 𝜓↗⋀𝜒𝜃] into ax-1 | |
| 10745 | →⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃 | Modus ponens 10743, 10744 | |
| 10746 | →→⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃→→⋀𝜒𝜃⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀𝜒𝜃, 𝜓↗⋀𝜒𝜃, 𝜒↗→¬¬𝜓⋀𝜒𝜃] into ax-2 | |
| 10747 | →→⋀𝜒𝜃⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃 | Modus ponens 10745, 10746 | |
| 10748 | →→¬¬𝜓→⋀𝜒𝜃𝜒→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜒 | Subs [𝜑↗¬¬𝜓, 𝜓↗⋀𝜒𝜃] into ax-2 | |
| 10749 | →→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜒 | Modus ponens 10741, 10748 | |
| 10750 | →→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜒→⋀𝜒𝜃→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜒 | Subs [𝜑↗→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜒, 𝜓↗⋀𝜒𝜃] into ax-1 | |
| 10751 | →⋀𝜒𝜃→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜒 | Modus ponens 10749, 10750 | |
| 10752 | →→⋀𝜒𝜃→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜒→→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓𝜒 | Subs [𝜑↗⋀𝜒𝜃, 𝜓↗→¬¬𝜓⋀𝜒𝜃, 𝜒↗→¬¬𝜓𝜒] into ax-2 | |
| 10753 | →→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓𝜒 | Modus ponens 10751, 10752 | |
| 10754 | →⋀𝜒𝜃→¬¬𝜓𝜒 | Modus ponens 10743, 10753 | |
| 10755 | →→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒→⋀𝜒𝜃→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒 | Subs [𝜑↗→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒, 𝜓↗⋀𝜒𝜃] into ax-1 | |
| 10756 | →⋀𝜒𝜃→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒 | Modus ponens 9176, 10755 | |
| 10757 | →→⋀𝜒𝜃→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒→→⋀𝜒𝜃→¬¬𝜓𝜒→⋀𝜒𝜃→¬¬𝜓¬¬𝜒 | Subs [𝜑↗⋀𝜒𝜃, 𝜓↗→¬¬𝜓𝜒, 𝜒↗→¬¬𝜓¬¬𝜒] into ax-2 | |
| 10758 | →→⋀𝜒𝜃→¬¬𝜓𝜒→⋀𝜒𝜃→¬¬𝜓¬¬𝜒 | Modus ponens 10756, 10757 | |
| 10759 | →⋀𝜒𝜃→¬¬𝜓¬¬𝜒 | Modus ponens 10754, 10758 | |
| 10760 | →→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓→⋀𝜒𝜃→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓 | Subs [𝜑↗→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓, 𝜓↗⋀𝜒𝜃] into ax-1 | |
| 10761 | →⋀𝜒𝜃→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓 | Modus ponens 9182, 10760 | |
| 10762 | →→⋀𝜒𝜃→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓→→⋀𝜒𝜃→¬¬𝜓¬¬𝜒→⋀𝜒𝜃→¬𝜒¬𝜓 | Subs [𝜑↗⋀𝜒𝜃, 𝜓↗→¬¬𝜓¬¬𝜒, 𝜒↗→¬𝜒¬𝜓] into ax-2 | |
| 10763 | →→⋀𝜒𝜃→¬¬𝜓¬¬𝜒→⋀𝜒𝜃→¬𝜒¬𝜓 | Modus ponens 10761, 10762 | |
| 10764 | →⋀𝜒𝜃→¬𝜒¬𝜓 | Modus ponens 10759, 10763 | |
| 10765 | →¬𝜒→⋀𝜒𝜃¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗⋀𝜒𝜃] into ax-1 | |
| 10766 | →→¬𝜒→⋀𝜒𝜃¬𝜒→¬𝜒→¬𝜒→⋀𝜒𝜃¬𝜒 | Subs [𝜑↗→¬𝜒→⋀𝜒𝜃¬𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 10767 | →¬𝜒→¬𝜒→⋀𝜒𝜃¬𝜒 | Modus ponens 10765, 10766 | |
| 10768 | →→¬𝜒→¬𝜒→⋀𝜒𝜃¬𝜒→→¬𝜒¬𝜒→¬𝜒→⋀𝜒𝜃¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→⋀𝜒𝜃¬𝜒] into ax-2 | |
| 10769 | →→¬𝜒¬𝜒→¬𝜒→⋀𝜒𝜃¬𝜒 | Modus ponens 10767, 10768 | |
| 10770 | →→⋀𝜒𝜃→¬𝜒¬𝜓→→⋀𝜒𝜃¬𝜒→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗⋀𝜒𝜃, 𝜓↗¬𝜒, 𝜒↗¬𝜓] into ax-2 | |
| 10771 | →→⋀𝜒𝜃¬𝜒→⋀𝜒𝜃¬𝜓 | Modus ponens 10764, 10770 | |
| 10772 | →→→⋀𝜒𝜃¬𝜒→⋀𝜒𝜃¬𝜓→¬𝜒→→⋀𝜒𝜃¬𝜒→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗→→⋀𝜒𝜃¬𝜒→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜒] into ax-1 | |
| 10773 | →¬𝜒→→⋀𝜒𝜃¬𝜒→⋀𝜒𝜃¬𝜓 | Modus ponens 10771, 10772 | |
| 10774 | →→¬𝜒→→⋀𝜒𝜃¬𝜒→⋀𝜒𝜃¬𝜓→→¬𝜒→⋀𝜒𝜃¬𝜒→¬𝜒→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜒𝜃¬𝜒, 𝜒↗→⋀𝜒𝜃¬𝜓] into ax-2 | |
| 10775 | →→¬𝜒→⋀𝜒𝜃¬𝜒→¬𝜒→⋀𝜒𝜃¬𝜓 | Modus ponens 10773, 10774 | |
| 10776 | →¬𝜒→⋀𝜒𝜃¬𝜓 | Modus ponens 10765, 10775 | |
| 10777 | →¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗¬→⋀𝜒𝜃¬𝜓] into id | |
| 10778 | →→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬𝜒→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜒] into ax-1 | |
| 10779 | →¬𝜒→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓 | Modus ponens 10777, 10778 | |
| 10780 | →¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗¬→⋀𝜒𝜃¬𝜓] into notnotr | |
| 10781 | →¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜒] into ax-1 | |
| 10782 | →→¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗→¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬¬¬→⋀𝜒𝜃¬𝜓] into ax-1 | |
| 10783 | →¬¬¬→⋀𝜒𝜃¬𝜓→¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓 | Modus ponens 10781, 10782 | |
| 10784 | →→¬¬¬→⋀𝜒𝜃¬𝜓→¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗¬¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬→⋀𝜒𝜃¬𝜓, 𝜒↗→¬𝜒¬→⋀𝜒𝜃¬𝜓] into ax-2 | |
| 10785 | →→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓 | Modus ponens 10783, 10784 | |
| 10786 | →¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓 | Modus ponens 10780, 10785 | |
| 10787 | →→¬𝜒→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗¬𝜒, 𝜓↗¬→⋀𝜒𝜃¬𝜓, 𝜒↗¬→⋀𝜒𝜃¬𝜓] into ax-2 | |
| 10788 | →→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓 | Modus ponens 10779, 10787 | |
| 10789 | →→→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗→→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬¬¬→⋀𝜒𝜃¬𝜓] into ax-1 | |
| 10790 | →¬¬¬→⋀𝜒𝜃¬𝜓→→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓 | Modus ponens 10788, 10789 | |
| 10791 | →→¬¬¬→⋀𝜒𝜃¬𝜓→→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓→→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗¬¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗→¬𝜒¬→⋀𝜒𝜃¬𝜓, 𝜒↗→¬𝜒¬→⋀𝜒𝜃¬𝜓] into ax-2 | |
| 10792 | →→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓 | Modus ponens 10790, 10791 | |
| 10793 | →¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→⋀𝜒𝜃¬𝜓] into ax-1 | |
| 10794 | →→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬𝜒→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒 | Subs [𝜑↗→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 10795 | →¬𝜒→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒 | Modus ponens 10793, 10794 | |
| 10796 | →→¬𝜒→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒] into ax-2 | |
| 10797 | →→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒 | Modus ponens 10795, 10796 | |
| 10798 | →→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗¬¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜒, 𝜒↗¬→⋀𝜒𝜃¬𝜓] into ax-2 | |
| 10799 | →→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓 | Modus ponens 10786, 10798 | |
| 10800 | →→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬𝜒→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜒] into ax-1 | |
| 10801 | →¬𝜒→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓 | Modus ponens 10799, 10800 | |
| 10802 | →→¬𝜒→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒, 𝜒↗→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓] into ax-2 | |
| 10803 | →→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓 | Modus ponens 10801, 10802 | |
| 10804 | →¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓 | Modus ponens 10793, 10803 | |
| 10805 | →→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗→⋀𝜒𝜃¬𝜓] into ax-3 | |
| 10806 | →→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓→¬𝜒→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜒] into ax-1 | |
| 10807 | →¬𝜒→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓 | Modus ponens 10805, 10806 | |
| 10808 | →→¬𝜒→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓→→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬𝜒→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓, 𝜒↗→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓] into ax-2 | |
| 10809 | →→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬𝜒→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓 | Modus ponens 10807, 10808 | |
| 10810 | →¬𝜒→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓 | Modus ponens 10804, 10809 | |
| 10811 | →→¬𝜒→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓→→¬𝜒→⋀𝜒𝜃¬𝜓→¬𝜒¬¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜒𝜃¬𝜓, 𝜒↗¬¬→⋀𝜒𝜃¬𝜓] into ax-2 | |
| 10812 | →→¬𝜒→⋀𝜒𝜃¬𝜓→¬𝜒¬¬→⋀𝜒𝜃¬𝜓 | Modus ponens 10810, 10811 | |
| 10813 | →¬𝜒¬¬→⋀𝜒𝜃¬𝜓 | Modus ponens 10776, 10812 | |
| 10814 | →→¬𝜒¬¬→⋀𝜒𝜃¬𝜓→¬→⋀𝜒𝜃¬𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗¬→⋀𝜒𝜃¬𝜓] into ax-3 | |
| 10815 | →¬→⋀𝜒𝜃¬𝜓𝜒 | Modus ponens 10813, 10814 | |
| 10816 | →↔⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗⋀⋀𝜒𝜃𝜓, 𝜓↗¬→⋀𝜒𝜃¬𝜓] into biimp | |
| 10817 | →⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓 | Modus ponens 10728, 10816 | |
| 10818 | →→¬→⋀𝜒𝜃¬𝜓𝜒→⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜒 | Subs [𝜑↗→¬→⋀𝜒𝜃¬𝜓𝜒, 𝜓↗⋀⋀𝜒𝜃𝜓] into ax-1 | |
| 10819 | →⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜒 | Modus ponens 10815, 10818 | |
| 10820 | →→⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜒→→⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜒 | Subs [𝜑↗⋀⋀𝜒𝜃𝜓, 𝜓↗¬→⋀𝜒𝜃¬𝜓] into ax-2 | |
| 10821 | →→⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜒 | Modus ponens 10819, 10820 | |
| 10822 | →⋀⋀𝜒𝜃𝜓𝜒 | Modus ponens 10817, 10821 | |
| 10823 | →↔⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓↔¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓 | Subs [𝜑↗⋀⋀𝜒𝜃𝜓, 𝜓↗¬→⋀𝜒𝜃¬𝜓] into bicom1 | |
| 10824 | ↔¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓 | Modus ponens 10728, 10823 | |
| 10825 | →↔¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓 | Subs [𝜑↗¬→⋀𝜒𝜃¬𝜓, 𝜓↗⋀⋀𝜒𝜃𝜓] into biimp | |
| 10826 | →¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓 | Modus ponens 10824, 10825 | |
| 10827 | →→⋀⋀𝜒𝜃𝜓𝜒→¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜒 | Subs [𝜑↗→⋀⋀𝜒𝜃𝜓𝜒, 𝜓↗¬→⋀𝜒𝜃¬𝜓] into ax-1 | |
| 10828 | →¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜒 | Modus ponens 10822, 10827 | |
| 10829 | →→¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜒→→¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜒 | Subs [𝜑↗¬→⋀𝜒𝜃¬𝜓, 𝜓↗⋀⋀𝜒𝜃𝜓] into ax-2 | |
| 10830 | →→¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜒 | Modus ponens 10828, 10829 | |
| 10831 | →⋀𝜒𝜃→𝜓¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗⋀𝜒𝜃] into pm3.2im | |
| 10832 | →→¬→⋀𝜒𝜃¬𝜓𝜒→𝜓→¬→⋀𝜒𝜃¬𝜓𝜒 | Subs [𝜑↗→¬→⋀𝜒𝜃¬𝜓𝜒] into ax-1 | |
| 10833 | →𝜓→¬→⋀𝜒𝜃¬𝜓𝜒 | Modus ponens 10815, 10832 | |
| 10834 | →→𝜓→¬→⋀𝜒𝜃¬𝜓𝜒→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗¬→⋀𝜒𝜃¬𝜓] into ax-2 | |
| 10835 | →→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜒 | Modus ponens 10833, 10834 | |
| 10836 | →→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜒→⋀𝜒𝜃→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜒 | Subs [𝜑↗→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜒, 𝜓↗⋀𝜒𝜃] into ax-1 | |
| 10837 | →⋀𝜒𝜃→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜒 | Modus ponens 10835, 10836 | |
| 10838 | →→⋀𝜒𝜃→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜒→→⋀𝜒𝜃→𝜓¬→⋀𝜒𝜃¬𝜓→⋀𝜒𝜃→𝜓𝜒 | Subs [𝜑↗⋀𝜒𝜃, 𝜓↗→𝜓¬→⋀𝜒𝜃¬𝜓, 𝜒↗→𝜓𝜒] into ax-2 | |
| 10839 | →→⋀𝜒𝜃→𝜓¬→⋀𝜒𝜃¬𝜓→⋀𝜒𝜃→𝜓𝜒 | Modus ponens 10837, 10838 | |
| 10840 | →→𝜓→⋀𝜒𝜃𝜓→𝜓→𝜓→⋀𝜒𝜃𝜓 | Subs [𝜑↗→𝜓→⋀𝜒𝜃𝜓] into ax-1 | |
| 10841 | →𝜓→𝜓→⋀𝜒𝜃𝜓 | Modus ponens 10729, 10840 | |
| 10842 | →→𝜓→𝜓→⋀𝜒𝜃𝜓→→𝜓𝜓→𝜓→⋀𝜒𝜃𝜓 | Subs [𝜑↗𝜓, 𝜒↗→⋀𝜒𝜃𝜓] into ax-2 | |
| 10843 | →→𝜓𝜓→𝜓→⋀𝜒𝜃𝜓 | Modus ponens 10841, 10842 | |
| 10844 | →→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒→𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒 | Subs [𝜑↗→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒] into ax-1 | |
| 10845 | →𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒 | Modus ponens 10736, 10844 | |
| 10846 | →→𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒→→𝜓→⋀𝜒𝜃𝜓→𝜓→⋀𝜒𝜃𝜒 | Subs [𝜑↗𝜓, 𝜓↗→⋀𝜒𝜃𝜓, 𝜒↗→⋀𝜒𝜃𝜒] into ax-2 | |
| 10847 | →→𝜓→⋀𝜒𝜃𝜓→𝜓→⋀𝜒𝜃𝜒 | Modus ponens 10845, 10846 | |
| 10848 | →𝜓→⋀𝜒𝜃𝜒 | Modus ponens 10729, 10847 | |
| 10849 | ↔⋀𝜓⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗𝜓, 𝜓↗⋀𝜒𝜃] into df-an | |
| 10850 | →¬¬⋀𝜒𝜃⋀𝜒𝜃 | Subs [𝜑↗⋀𝜒𝜃] into notnotr | |
| 10851 | →⋀𝜒𝜃→𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀𝜒𝜃] into ax-1 | |
| 10852 | →→⋀𝜒𝜃→𝜓⋀𝜒𝜃→¬¬⋀𝜒𝜃→⋀𝜒𝜃→𝜓⋀𝜒𝜃 | Subs [𝜑↗→⋀𝜒𝜃→𝜓⋀𝜒𝜃, 𝜓↗¬¬⋀𝜒𝜃] into ax-1 | |
| 10853 | →¬¬⋀𝜒𝜃→⋀𝜒𝜃→𝜓⋀𝜒𝜃 | Modus ponens 10851, 10852 | |
| 10854 | →→¬¬⋀𝜒𝜃→⋀𝜒𝜃→𝜓⋀𝜒𝜃→→¬¬⋀𝜒𝜃⋀𝜒𝜃→¬¬⋀𝜒𝜃→𝜓⋀𝜒𝜃 | Subs [𝜑↗¬¬⋀𝜒𝜃, 𝜓↗⋀𝜒𝜃, 𝜒↗→𝜓⋀𝜒𝜃] into ax-2 | |
| 10855 | →→¬¬⋀𝜒𝜃⋀𝜒𝜃→¬¬⋀𝜒𝜃→𝜓⋀𝜒𝜃 | Modus ponens 10853, 10854 | |
| 10856 | →¬¬⋀𝜒𝜃→𝜓⋀𝜒𝜃 | Modus ponens 10850, 10855 | |
| 10857 | →→𝜓→⋀𝜒𝜃𝜒→→𝜓⋀𝜒𝜃→𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗⋀𝜒𝜃] into ax-2 | |
| 10858 | →→𝜓⋀𝜒𝜃→𝜓𝜒 | Modus ponens 10848, 10857 | |
| 10859 | →→→𝜓⋀𝜒𝜃→𝜓𝜒→¬¬⋀𝜒𝜃→→𝜓⋀𝜒𝜃→𝜓𝜒 | Subs [𝜑↗→→𝜓⋀𝜒𝜃→𝜓𝜒, 𝜓↗¬¬⋀𝜒𝜃] into ax-1 | |
| 10860 | →¬¬⋀𝜒𝜃→→𝜓⋀𝜒𝜃→𝜓𝜒 | Modus ponens 10858, 10859 | |
| 10861 | →→¬¬⋀𝜒𝜃→→𝜓⋀𝜒𝜃→𝜓𝜒→→¬¬⋀𝜒𝜃→𝜓⋀𝜒𝜃→¬¬⋀𝜒𝜃→𝜓𝜒 | Subs [𝜑↗¬¬⋀𝜒𝜃, 𝜓↗→𝜓⋀𝜒𝜃, 𝜒↗→𝜓𝜒] into ax-2 | |
| 10862 | →→¬¬⋀𝜒𝜃→𝜓⋀𝜒𝜃→¬¬⋀𝜒𝜃→𝜓𝜒 | Modus ponens 10860, 10861 | |
| 10863 | →¬¬⋀𝜒𝜃→𝜓𝜒 | Modus ponens 10856, 10862 | |
| 10864 | →𝜓→¬¬⋀𝜒𝜃𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬¬⋀𝜒𝜃] into ax-1 | |
| 10865 | →→𝜓→¬¬⋀𝜒𝜃𝜓→𝜓→𝜓→¬¬⋀𝜒𝜃𝜓 | Subs [𝜑↗→𝜓→¬¬⋀𝜒𝜃𝜓] into ax-1 | |
| 10866 | →𝜓→𝜓→¬¬⋀𝜒𝜃𝜓 | Modus ponens 10864, 10865 | |
| 10867 | →→𝜓→𝜓→¬¬⋀𝜒𝜃𝜓→→𝜓𝜓→𝜓→¬¬⋀𝜒𝜃𝜓 | Subs [𝜑↗𝜓, 𝜒↗→¬¬⋀𝜒𝜃𝜓] into ax-2 | |
| 10868 | →→𝜓𝜓→𝜓→¬¬⋀𝜒𝜃𝜓 | Modus ponens 10866, 10867 | |
| 10869 | →→¬¬⋀𝜒𝜃→𝜓𝜒→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜒 | Subs [𝜑↗¬¬⋀𝜒𝜃] into ax-2 | |
| 10870 | →→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜒 | Modus ponens 10863, 10869 | |
| 10871 | →→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜒→𝜓→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜒 | Subs [𝜑↗→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜒] into ax-1 | |
| 10872 | →𝜓→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜒 | Modus ponens 10870, 10871 | |
| 10873 | →→𝜓→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜒→→𝜓→¬¬⋀𝜒𝜃𝜓→𝜓→¬¬⋀𝜒𝜃𝜒 | Subs [𝜑↗𝜓, 𝜓↗→¬¬⋀𝜒𝜃𝜓, 𝜒↗→¬¬⋀𝜒𝜃𝜒] into ax-2 | |
| 10874 | →→𝜓→¬¬⋀𝜒𝜃𝜓→𝜓→¬¬⋀𝜒𝜃𝜒 | Modus ponens 10872, 10873 | |
| 10875 | →𝜓→¬¬⋀𝜒𝜃𝜒 | Modus ponens 10864, 10874 | |
| 10876 | →→𝜒¬¬𝜒→¬¬⋀𝜒𝜃→𝜒¬¬𝜒 | Subs [𝜑↗→𝜒¬¬𝜒, 𝜓↗¬¬⋀𝜒𝜃] into ax-1 | |
| 10877 | →¬¬⋀𝜒𝜃→𝜒¬¬𝜒 | Modus ponens 9172, 10876 | |
| 10878 | →→¬¬⋀𝜒𝜃→𝜒¬¬𝜒→→¬¬⋀𝜒𝜃𝜒→¬¬⋀𝜒𝜃¬¬𝜒 | Subs [𝜑↗¬¬⋀𝜒𝜃, 𝜓↗𝜒, 𝜒↗¬¬𝜒] into ax-2 | |
| 10879 | →→¬¬⋀𝜒𝜃𝜒→¬¬⋀𝜒𝜃¬¬𝜒 | Modus ponens 10877, 10878 | |
| 10880 | →→→¬¬⋀𝜒𝜃𝜒→¬¬⋀𝜒𝜃¬¬𝜒→𝜓→→¬¬⋀𝜒𝜃𝜒→¬¬⋀𝜒𝜃¬¬𝜒 | Subs [𝜑↗→→¬¬⋀𝜒𝜃𝜒→¬¬⋀𝜒𝜃¬¬𝜒] into ax-1 | |
| 10881 | →𝜓→→¬¬⋀𝜒𝜃𝜒→¬¬⋀𝜒𝜃¬¬𝜒 | Modus ponens 10879, 10880 | |
| 10882 | →→𝜓→→¬¬⋀𝜒𝜃𝜒→¬¬⋀𝜒𝜃¬¬𝜒→→𝜓→¬¬⋀𝜒𝜃𝜒→𝜓→¬¬⋀𝜒𝜃¬¬𝜒 | Subs [𝜑↗𝜓, 𝜓↗→¬¬⋀𝜒𝜃𝜒, 𝜒↗→¬¬⋀𝜒𝜃¬¬𝜒] into ax-2 | |
| 10883 | →→𝜓→¬¬⋀𝜒𝜃𝜒→𝜓→¬¬⋀𝜒𝜃¬¬𝜒 | Modus ponens 10881, 10882 | |
| 10884 | →𝜓→¬¬⋀𝜒𝜃¬¬𝜒 | Modus ponens 10875, 10883 | |
| 10885 | →→¬¬⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜒𝜃 | Subs [𝜑↗¬⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-3 | |
| 10886 | →→→¬¬⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜒𝜃→𝜓→→¬¬⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜒𝜃 | Subs [𝜑↗→→¬¬⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜒𝜃] into ax-1 | |
| 10887 | →𝜓→→¬¬⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜒𝜃 | Modus ponens 10885, 10886 | |
| 10888 | →→𝜓→→¬¬⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜒𝜃→→𝜓→¬¬⋀𝜒𝜃¬¬𝜒→𝜓→¬𝜒¬⋀𝜒𝜃 | Subs [𝜑↗𝜓, 𝜓↗→¬¬⋀𝜒𝜃¬¬𝜒, 𝜒↗→¬𝜒¬⋀𝜒𝜃] into ax-2 | |
| 10889 | →→𝜓→¬¬⋀𝜒𝜃¬¬𝜒→𝜓→¬𝜒¬⋀𝜒𝜃 | Modus ponens 10887, 10888 | |
| 10890 | →𝜓→¬𝜒¬⋀𝜒𝜃 | Modus ponens 10884, 10889 | |
| 10891 | →→𝜓→¬𝜒¬⋀𝜒𝜃→→𝜓¬𝜒→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗𝜓, 𝜓↗¬𝜒, 𝜒↗¬⋀𝜒𝜃] into ax-2 | |
| 10892 | →→𝜓¬𝜒→𝜓¬⋀𝜒𝜃 | Modus ponens 10890, 10891 | |
| 10893 | →→→𝜓¬𝜒→𝜓¬⋀𝜒𝜃→¬𝜒→→𝜓¬𝜒→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗→→𝜓¬𝜒→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1 | |
| 10894 | →¬𝜒→→𝜓¬𝜒→𝜓¬⋀𝜒𝜃 | Modus ponens 10892, 10893 | |
| 10895 | →→¬𝜒→→𝜓¬𝜒→𝜓¬⋀𝜒𝜃→→¬𝜒→𝜓¬𝜒→¬𝜒→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗¬𝜒, 𝜓↗→𝜓¬𝜒, 𝜒↗→𝜓¬⋀𝜒𝜃] into ax-2 | |
| 10896 | →→¬𝜒→𝜓¬𝜒→¬𝜒→𝜓¬⋀𝜒𝜃 | Modus ponens 10894, 10895 | |
| 10897 | →¬𝜒→𝜓¬⋀𝜒𝜃 | Modus ponens 9284, 10896 | |
| 10898 | →¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗¬→𝜓¬⋀𝜒𝜃] into id | |
| 10899 | →→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜒→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1 | |
| 10900 | →¬𝜒→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃 | Modus ponens 10898, 10899 | |
| 10901 | →¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗¬→𝜓¬⋀𝜒𝜃] into notnotr | |
| 10902 | →¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1 | |
| 10903 | →→¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗→¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬¬¬→𝜓¬⋀𝜒𝜃] into ax-1 | |
| 10904 | →¬¬¬→𝜓¬⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃 | Modus ponens 10902, 10903 | |
| 10905 | →→¬¬¬→𝜓¬⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗¬¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬→𝜓¬⋀𝜒𝜃, 𝜒↗→¬𝜒¬→𝜓¬⋀𝜒𝜃] into ax-2 | |
| 10906 | →→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃 | Modus ponens 10904, 10905 | |
| 10907 | →¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃 | Modus ponens 10901, 10906 | |
| 10908 | →→¬𝜒→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗¬𝜒, 𝜓↗¬→𝜓¬⋀𝜒𝜃, 𝜒↗¬→𝜓¬⋀𝜒𝜃] into ax-2 | |
| 10909 | →→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃 | Modus ponens 10900, 10908 | |
| 10910 | →→→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗→→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬¬¬→𝜓¬⋀𝜒𝜃] into ax-1 | |
| 10911 | →¬¬¬→𝜓¬⋀𝜒𝜃→→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃 | Modus ponens 10909, 10910 | |
| 10912 | →→¬¬¬→𝜓¬⋀𝜒𝜃→→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗¬¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗→¬𝜒¬→𝜓¬⋀𝜒𝜃, 𝜒↗→¬𝜒¬→𝜓¬⋀𝜒𝜃] into ax-2 | |
| 10913 | →→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃 | Modus ponens 10911, 10912 | |
| 10914 | →¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→𝜓¬⋀𝜒𝜃] into ax-1 | |
| 10915 | →→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬𝜒→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒 | Subs [𝜑↗→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 10916 | →¬𝜒→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒 | Modus ponens 10914, 10915 | |
| 10917 | →→¬𝜒→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒] into ax-2 | |
| 10918 | →→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒 | Modus ponens 10916, 10917 | |
| 10919 | →→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗¬¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜒, 𝜒↗¬→𝜓¬⋀𝜒𝜃] into ax-2 | |
| 10920 | →→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃 | Modus ponens 10907, 10919 | |
| 10921 | →→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜒→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1 | |
| 10922 | →¬𝜒→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃 | Modus ponens 10920, 10921 | |
| 10923 | →→¬𝜒→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒, 𝜒↗→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃] into ax-2 | |
| 10924 | →→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃 | Modus ponens 10922, 10923 | |
| 10925 | →¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃 | Modus ponens 10914, 10924 | |
| 10926 | →→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗→𝜓¬⋀𝜒𝜃] into ax-3 | |
| 10927 | →→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃→¬𝜒→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1 | |
| 10928 | →¬𝜒→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃 | Modus ponens 10926, 10927 | |
| 10929 | →→¬𝜒→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃→→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜒→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃, 𝜒↗→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃] into ax-2 | |
| 10930 | →→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜒→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃 | Modus ponens 10928, 10929 | |
| 10931 | →¬𝜒→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃 | Modus ponens 10925, 10930 | |
| 10932 | →→¬𝜒→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃→→¬𝜒→𝜓¬⋀𝜒𝜃→¬𝜒¬¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗¬𝜒, 𝜓↗→𝜓¬⋀𝜒𝜃, 𝜒↗¬¬→𝜓¬⋀𝜒𝜃] into ax-2 | |
| 10933 | →→¬𝜒→𝜓¬⋀𝜒𝜃→¬𝜒¬¬→𝜓¬⋀𝜒𝜃 | Modus ponens 10931, 10932 | |
| 10934 | →¬𝜒¬¬→𝜓¬⋀𝜒𝜃 | Modus ponens 10897, 10933 | |
| 10935 | →→¬𝜒¬¬→𝜓¬⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃𝜒 | Subs [𝜑↗𝜒, 𝜓↗¬→𝜓¬⋀𝜒𝜃] into ax-3 | |
| 10936 | →¬→𝜓¬⋀𝜒𝜃𝜒 | Modus ponens 10934, 10935 | |
| 10937 | →↔⋀𝜓⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗¬→𝜓¬⋀𝜒𝜃] into biimp | |
| 10938 | →⋀𝜓⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃 | Modus ponens 10849, 10937 | |
| 10939 | →→¬→𝜓¬⋀𝜒𝜃𝜒→⋀𝜓⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃𝜒 | Subs [𝜑↗→¬→𝜓¬⋀𝜒𝜃𝜒, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 10940 | →⋀𝜓⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃𝜒 | Modus ponens 10936, 10939 | |
| 10941 | →→⋀𝜓⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃𝜒→→⋀𝜓⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃𝜒 | Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗¬→𝜓¬⋀𝜒𝜃] into ax-2 | |
| 10942 | →→⋀𝜓⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃𝜒 | Modus ponens 10940, 10941 | |
| 10943 | →⋀𝜓⋀𝜒𝜃𝜒 | Modus ponens 10938, 10942 | |
| 10944 | →→𝜒→𝜑𝜒→⋀𝜓⋀𝜒𝜃→𝜒→𝜑𝜒 | Subs [𝜑↗→𝜒→𝜑𝜒, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 10945 | →⋀𝜓⋀𝜒𝜃→𝜒→𝜑𝜒 | Modus ponens 1834, 10944 | |
| 10946 | →→⋀𝜓⋀𝜒𝜃→𝜒→𝜑𝜒→→⋀𝜓⋀𝜒𝜃𝜒→⋀𝜓⋀𝜒𝜃→𝜑𝜒 | Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗𝜒, 𝜒↗→𝜑𝜒] into ax-2 | |
| 10947 | →→⋀𝜓⋀𝜒𝜃𝜒→⋀𝜓⋀𝜒𝜃→𝜑𝜒 | Modus ponens 10945, 10946 | |
| 10948 | →⋀𝜓⋀𝜒𝜃→𝜑𝜒 | Modus ponens 10943, 10947 | |
| 10949 | ↔⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑] into df-an | |
| 10950 | →𝜑→⋀𝜓⋀𝜒𝜃𝜑 | Subs [𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 10951 | →→𝜑→⋀𝜓⋀𝜒𝜃𝜑→¬¬𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜑 | Subs [𝜑↗→𝜑→⋀𝜓⋀𝜒𝜃𝜑, 𝜓↗¬¬𝜑] into ax-1 | |
| 10952 | →¬¬𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜑 | Modus ponens 10950, 10951 | |
| 10953 | →→¬¬𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜑→→¬¬𝜑𝜑→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜑 | Subs [𝜑↗¬¬𝜑, 𝜓↗𝜑, 𝜒↗→⋀𝜓⋀𝜒𝜃𝜑] into ax-2 | |
| 10954 | →→¬¬𝜑𝜑→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜑 | Modus ponens 10952, 10953 | |
| 10955 | →¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜑 | Modus ponens notnotr, 10954 | |
| 10956 | →→⋀𝜓⋀𝜒𝜃→𝜑𝜒→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒 | Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑] into ax-2 | |
| 10957 | →→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒 | Modus ponens 10948, 10956 | |
| 10958 | →→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒→¬¬𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒 | Subs [𝜑↗→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒, 𝜓↗¬¬𝜑] into ax-1 | |
| 10959 | →¬¬𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒 | Modus ponens 10957, 10958 | |
| 10960 | →→¬¬𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒→→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜑→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜒 | Subs [𝜑↗¬¬𝜑, 𝜓↗→⋀𝜓⋀𝜒𝜃𝜑, 𝜒↗→⋀𝜓⋀𝜒𝜃𝜒] into ax-2 | |
| 10961 | →→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜑→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜒 | Modus ponens 10959, 10960 | |
| 10962 | →¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜒 | Modus ponens 10955, 10961 | |
| 10963 | →⋀𝜓⋀𝜒𝜃⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀𝜓⋀𝜒𝜃] into id | |
| 10964 | →⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗¬¬𝜑] into ax-1 | |
| 10965 | →→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 10966 | →⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃 | Modus ponens 10964, 10965 | |
| 10967 | →→⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃→→⋀𝜓⋀𝜒𝜃⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃, 𝜒↗→¬¬𝜑⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 10968 | →→⋀𝜓⋀𝜒𝜃⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃 | Modus ponens 10966, 10967 | |
| 10969 | →→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜒→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒 | Subs [𝜑↗¬¬𝜑, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 10970 | →→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒 | Modus ponens 10962, 10969 | |
| 10971 | →→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒→⋀𝜓⋀𝜒𝜃→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒 | Subs [𝜑↗→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 10972 | →⋀𝜓⋀𝜒𝜃→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒 | Modus ponens 10970, 10971 | |
| 10973 | →→⋀𝜓⋀𝜒𝜃→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒→→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒 | Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗→¬¬𝜑⋀𝜓⋀𝜒𝜃, 𝜒↗→¬¬𝜑𝜒] into ax-2 | |
| 10974 | →→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒 | Modus ponens 10972, 10973 | |
| 10975 | →⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒 | Modus ponens 10964, 10974 | |
| 10976 | →→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒→⋀𝜓⋀𝜒𝜃→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒 | Subs [𝜑↗→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 10977 | →⋀𝜓⋀𝜒𝜃→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒 | Modus ponens 9357, 10976 | |
| 10978 | →→⋀𝜓⋀𝜒𝜃→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒→→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜒 | Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗→¬¬𝜑𝜒, 𝜒↗→¬¬𝜑¬¬𝜒] into ax-2 | |
| 10979 | →→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜒 | Modus ponens 10977, 10978 | |
| 10980 | →⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜒 | Modus ponens 10975, 10979 | |
| 10981 | →→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑→⋀𝜓⋀𝜒𝜃→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑 | Subs [𝜑↗→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 10982 | →⋀𝜓⋀𝜒𝜃→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑 | Modus ponens 9363, 10981 | |
| 10983 | →→⋀𝜓⋀𝜒𝜃→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑→→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜒→⋀𝜓⋀𝜒𝜃→¬𝜒¬𝜑 | Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗→¬¬𝜑¬¬𝜒, 𝜒↗→¬𝜒¬𝜑] into ax-2 | |
| 10984 | →→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜒→⋀𝜓⋀𝜒𝜃→¬𝜒¬𝜑 | Modus ponens 10982, 10983 | |
| 10985 | →⋀𝜓⋀𝜒𝜃→¬𝜒¬𝜑 | Modus ponens 10980, 10984 | |
| 10986 | →¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 10987 | →→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒→¬𝜒→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒 | Subs [𝜑↗→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 10988 | →¬𝜒→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒 | Modus ponens 10986, 10987 | |
| 10989 | →→¬𝜒→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒→→¬𝜒¬𝜒→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→⋀𝜓⋀𝜒𝜃¬𝜒] into ax-2 | |
| 10990 | →→¬𝜒¬𝜒→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒 | Modus ponens 10988, 10989 | |
| 10991 | →→⋀𝜓⋀𝜒𝜃→¬𝜒¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜒, 𝜒↗¬𝜑] into ax-2 | |
| 10992 | →→⋀𝜓⋀𝜒𝜃¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 10985, 10991 | |
| 10993 | →→→⋀𝜓⋀𝜒𝜃¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒→→⋀𝜓⋀𝜒𝜃¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗→→⋀𝜓⋀𝜒𝜃¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜒] into ax-1 | |
| 10994 | →¬𝜒→→⋀𝜓⋀𝜒𝜃¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 10992, 10993 | |
| 10995 | →→¬𝜒→→⋀𝜓⋀𝜒𝜃¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜓⋀𝜒𝜃¬𝜒, 𝜒↗→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2 | |
| 10996 | →→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 10994, 10995 | |
| 10997 | →¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 10986, 10996 | |
| 10998 | →¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into id | |
| 10999 | →→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜒] into ax-1 | |
| 11000 | →¬𝜒→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 10998, 10999 | |
| 11001 | →¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into notnotr | |
| 11002 | →¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜒] into ax-1 | |
| 11003 | →→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-1 | |
| 11004 | →¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11002, 11003 | |
| 11005 | →→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2 | |
| 11006 | →→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11004, 11005 | |
| 11007 | →¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11001, 11006 | |
| 11008 | →→¬𝜒→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗¬𝜒, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2 | |
| 11009 | →→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11000, 11008 | |
| 11010 | →→→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗→→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-1 | |
| 11011 | →¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11009, 11010 | |
| 11012 | →→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2 | |
| 11013 | →→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11011, 11012 | |
| 11014 | →¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-1 | |
| 11015 | →→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬𝜒→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒 | Subs [𝜑↗→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 11016 | →¬𝜒→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒 | Modus ponens 11014, 11015 | |
| 11017 | →→¬𝜒→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒] into ax-2 | |
| 11018 | →→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒 | Modus ponens 11016, 11017 | |
| 11019 | →→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜒, 𝜒↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2 | |
| 11020 | →→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11007, 11019 | |
| 11021 | →→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜒] into ax-1 | |
| 11022 | →¬𝜒→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11020, 11021 | |
| 11023 | →→¬𝜒→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒, 𝜒↗→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2 | |
| 11024 | →→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11022, 11023 | |
| 11025 | →¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11014, 11024 | |
| 11026 | →→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-3 | |
| 11027 | →→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜒] into ax-1 | |
| 11028 | →¬𝜒→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11026, 11027 | |
| 11029 | →→¬𝜒→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2 | |
| 11030 | →→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11028, 11029 | |
| 11031 | →¬𝜒→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11025, 11030 | |
| 11032 | →→¬𝜒→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2 | |
| 11033 | →→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11031, 11032 | |
| 11034 | →¬𝜒¬¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 10997, 11033 | |
| 11035 | →→¬𝜒¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒 | Subs [𝜑↗𝜒, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-3 | |
| 11036 | →¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒 | Modus ponens 11034, 11035 | |
| 11037 | →↔⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗⋀⋀𝜓⋀𝜒𝜃𝜑, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into biimp | |
| 11038 | →⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 10949, 11037 | |
| 11039 | →→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒→⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒 | Subs [𝜑↗→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒, 𝜓↗⋀⋀𝜓⋀𝜒𝜃𝜑] into ax-1 | |
| 11040 | →⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒 | Modus ponens 11036, 11039 | |
| 11041 | →→⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒→→⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜒 | Subs [𝜑↗⋀⋀𝜓⋀𝜒𝜃𝜑, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2 | |
| 11042 | →→⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜒 | Modus ponens 11040, 11041 | |
| 11043 | →⋀⋀𝜓⋀𝜒𝜃𝜑𝜒 | Modus ponens 11038, 11042 | |
| 11044 | →↔⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑↔¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑 | Subs [𝜑↗⋀⋀𝜓⋀𝜒𝜃𝜑, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into bicom1 | |
| 11045 | ↔¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑 | Modus ponens 10949, 11044 | |
| 11046 | →↔¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑 | Subs [𝜑↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗⋀⋀𝜓⋀𝜒𝜃𝜑] into biimp | |
| 11047 | →¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑 | Modus ponens 11045, 11046 | |
| 11048 | →→⋀⋀𝜓⋀𝜒𝜃𝜑𝜒→¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜒 | Subs [𝜑↗→⋀⋀𝜓⋀𝜒𝜃𝜑𝜒, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-1 | |
| 11049 | →¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜒 | Modus ponens 11043, 11048 | |
| 11050 | →→¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜒→→¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒 | Subs [𝜑↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗⋀⋀𝜓⋀𝜒𝜃𝜑] into ax-2 | |
| 11051 | →→¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒 | Modus ponens 11049, 11050 | |
| 11052 | →⋀𝜓⋀𝜒𝜃→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑] into pm3.2im | |
| 11053 | →→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒→𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒 | Subs [𝜑↗→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒, 𝜓↗𝜑] into ax-1 | |
| 11054 | →𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒 | Modus ponens 11036, 11053 | |
| 11055 | →→𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜒 | Subs [𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2 | |
| 11056 | →→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜒 | Modus ponens 11054, 11055 | |
| 11057 | →→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜒→⋀𝜓⋀𝜒𝜃→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜒 | Subs [𝜑↗→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜒, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 11058 | →⋀𝜓⋀𝜒𝜃→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜒 | Modus ponens 11056, 11057 | |
| 11059 | →→⋀𝜓⋀𝜒𝜃→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜒→→⋀𝜓⋀𝜒𝜃→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀𝜓⋀𝜒𝜃→𝜑𝜒 | Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗→𝜑𝜒] into ax-2 | |
| 11060 | →→⋀𝜓⋀𝜒𝜃→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀𝜓⋀𝜒𝜃→𝜑𝜒 | Modus ponens 11058, 11059 | |
| 11061 | →→𝜑→⋀𝜓⋀𝜒𝜃𝜑→𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜑 | Subs [𝜑↗→𝜑→⋀𝜓⋀𝜒𝜃𝜑, 𝜓↗𝜑] into ax-1 | |
| 11062 | →𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜑 | Modus ponens 10950, 11061 | |
| 11063 | →→𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜑→→𝜑𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜑 | Subs [𝜓↗𝜑, 𝜒↗→⋀𝜓⋀𝜒𝜃𝜑] into ax-2 | |
| 11064 | →→𝜑𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜑 | Modus ponens 11062, 11063 | |
| 11065 | →→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒→𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒 | Subs [𝜑↗→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒, 𝜓↗𝜑] into ax-1 | |
| 11066 | →𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒 | Modus ponens 10957, 11065 | |
| 11067 | →→𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒→→𝜑→⋀𝜓⋀𝜒𝜃𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜒 | Subs [𝜓↗→⋀𝜓⋀𝜒𝜃𝜑, 𝜒↗→⋀𝜓⋀𝜒𝜃𝜒] into ax-2 | |
| 11068 | →→𝜑→⋀𝜓⋀𝜒𝜃𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜒 | Modus ponens 11066, 11067 | |
| 11069 | →𝜑→⋀𝜓⋀𝜒𝜃𝜒 | Modus ponens 10950, 11068 | |
| 11070 | ↔⋀𝜑⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜓↗⋀𝜓⋀𝜒𝜃] into df-an | |
| 11071 | →¬¬⋀𝜓⋀𝜒𝜃⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀𝜓⋀𝜒𝜃] into notnotr | |
| 11072 | →⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑] into ax-1 | |
| 11073 | →→⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃→¬¬⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗→⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗¬¬⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 11074 | →¬¬⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃 | Modus ponens 11072, 11073 | |
| 11075 | →→¬¬⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃→→¬¬⋀𝜓⋀𝜒𝜃⋀𝜓⋀𝜒𝜃→¬¬⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗¬¬⋀𝜓⋀𝜒𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃, 𝜒↗→𝜑⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 11076 | →→¬¬⋀𝜓⋀𝜒𝜃⋀𝜓⋀𝜒𝜃→¬¬⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃 | Modus ponens 11074, 11075 | |
| 11077 | →¬¬⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃 | Modus ponens 11071, 11076 | |
| 11078 | →→𝜑→⋀𝜓⋀𝜒𝜃𝜒→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜒 | Subs [𝜓↗⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 11079 | →→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜒 | Modus ponens 11069, 11078 | |
| 11080 | →→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜒→¬¬⋀𝜓⋀𝜒𝜃→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜒 | Subs [𝜑↗→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜒, 𝜓↗¬¬⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 11081 | →¬¬⋀𝜓⋀𝜒𝜃→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜒 | Modus ponens 11079, 11080 | |
| 11082 | →→¬¬⋀𝜓⋀𝜒𝜃→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜒→→¬¬⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃→¬¬⋀𝜓⋀𝜒𝜃→𝜑𝜒 | Subs [𝜑↗¬¬⋀𝜓⋀𝜒𝜃, 𝜓↗→𝜑⋀𝜓⋀𝜒𝜃, 𝜒↗→𝜑𝜒] into ax-2 | |
| 11083 | →→¬¬⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃→¬¬⋀𝜓⋀𝜒𝜃→𝜑𝜒 | Modus ponens 11081, 11082 | |
| 11084 | →¬¬⋀𝜓⋀𝜒𝜃→𝜑𝜒 | Modus ponens 11077, 11083 | |
| 11085 | →𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑 | Subs [𝜓↗¬¬⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 11086 | →→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑→𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑 | Subs [𝜑↗→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑, 𝜓↗𝜑] into ax-1 | |
| 11087 | →𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑 | Modus ponens 11085, 11086 | |
| 11088 | →→𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑→→𝜑𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑 | Subs [𝜓↗𝜑, 𝜒↗→¬¬⋀𝜓⋀𝜒𝜃𝜑] into ax-2 | |
| 11089 | →→𝜑𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑 | Modus ponens 11087, 11088 | |
| 11090 | →→¬¬⋀𝜓⋀𝜒𝜃→𝜑𝜒→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒 | Subs [𝜑↗¬¬⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑] into ax-2 | |
| 11091 | →→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒 | Modus ponens 11084, 11090 | |
| 11092 | →→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒 | Subs [𝜑↗→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒, 𝜓↗𝜑] into ax-1 | |
| 11093 | →𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒 | Modus ponens 11091, 11092 | |
| 11094 | →→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒→→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒 | Subs [𝜓↗→¬¬⋀𝜓⋀𝜒𝜃𝜑, 𝜒↗→¬¬⋀𝜓⋀𝜒𝜃𝜒] into ax-2 | |
| 11095 | →→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒 | Modus ponens 11093, 11094 | |
| 11096 | →𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒 | Modus ponens 11085, 11095 | |
| 11097 | →→𝜒¬¬𝜒→¬¬⋀𝜓⋀𝜒𝜃→𝜒¬¬𝜒 | Subs [𝜑↗→𝜒¬¬𝜒, 𝜓↗¬¬⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 11098 | →¬¬⋀𝜓⋀𝜒𝜃→𝜒¬¬𝜒 | Modus ponens 9172, 11097 | |
| 11099 | →→¬¬⋀𝜓⋀𝜒𝜃→𝜒¬¬𝜒→→¬¬⋀𝜓⋀𝜒𝜃𝜒→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒 | Subs [𝜑↗¬¬⋀𝜓⋀𝜒𝜃, 𝜓↗𝜒, 𝜒↗¬¬𝜒] into ax-2 | |
| 11100 | →→¬¬⋀𝜓⋀𝜒𝜃𝜒→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒 | Modus ponens 11098, 11099 | |
| 11101 | →→→¬¬⋀𝜓⋀𝜒𝜃𝜒→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜒→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒 | Subs [𝜑↗→→¬¬⋀𝜓⋀𝜒𝜃𝜒→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒, 𝜓↗𝜑] into ax-1 | |
| 11102 | →𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜒→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒 | Modus ponens 11100, 11101 | |
| 11103 | →→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜒→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒 | Subs [𝜓↗→¬¬⋀𝜓⋀𝜒𝜃𝜒, 𝜒↗→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒] into ax-2 | |
| 11104 | →→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒 | Modus ponens 11102, 11103 | |
| 11105 | →𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒 | Modus ponens 11096, 11104 | |
| 11106 | →→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-3 | |
| 11107 | →→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜓⋀𝜒𝜃→𝜑→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑] into ax-1 | |
| 11108 | →𝜑→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11106, 11107 | |
| 11109 | →→𝜑→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜓⋀𝜒𝜃→→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→𝜑→¬𝜒¬⋀𝜓⋀𝜒𝜃 | Subs [𝜓↗→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒, 𝜒↗→¬𝜒¬⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 11110 | →→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→𝜑→¬𝜒¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11108, 11109 | |
| 11111 | →𝜑→¬𝜒¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11105, 11110 | |
| 11112 | →→𝜑→¬𝜒¬⋀𝜓⋀𝜒𝜃→→𝜑¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜓↗¬𝜒, 𝜒↗¬⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 11113 | →→𝜑¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11111, 11112 | |
| 11114 | →→→𝜑¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒→→𝜑¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗→→𝜑¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1 | |
| 11115 | →¬𝜒→→𝜑¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11113, 11114 | |
| 11116 | →→¬𝜒→→𝜑¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜒→𝜑¬𝜒→¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗¬𝜒, 𝜓↗→𝜑¬𝜒, 𝜒↗→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 11117 | →→¬𝜒→𝜑¬𝜒→¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11115, 11116 | |
| 11118 | →¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 9465, 11117 | |
| 11119 | →¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into id | |
| 11120 | →→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1 | |
| 11121 | →¬𝜒→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11119, 11120 | |
| 11122 | →¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into notnotr | |
| 11123 | →¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1 | |
| 11124 | →→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 11125 | →¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11123, 11124 | |
| 11126 | →→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 11127 | →→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11125, 11126 | |
| 11128 | →¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11122, 11127 | |
| 11129 | →→¬𝜒→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗¬𝜒, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 11130 | →→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11121, 11129 | |
| 11131 | →→→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗→→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 11132 | →¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11130, 11131 | |
| 11133 | →→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 11134 | →→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11132, 11133 | |
| 11135 | →¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 11136 | →→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒 | Subs [𝜑↗→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒, 𝜓↗¬𝜒] into ax-1 | |
| 11137 | →¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒 | Modus ponens 11135, 11136 | |
| 11138 | →→¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒] into ax-2 | |
| 11139 | →→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒 | Modus ponens 11137, 11138 | |
| 11140 | →→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜒, 𝜒↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 11141 | →→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11128, 11140 | |
| 11142 | →→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1 | |
| 11143 | →¬𝜒→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11141, 11142 | |
| 11144 | →→¬𝜒→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒, 𝜒↗→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 11145 | →→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11143, 11144 | |
| 11146 | →¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11135, 11145 | |
| 11147 | →→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-3 | |
| 11148 | →→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1 | |
| 11149 | →¬𝜒→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11147, 11148 | |
| 11150 | →→¬𝜒→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 11151 | →→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11149, 11150 | |
| 11152 | →¬𝜒→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11146, 11151 | |
| 11153 | →→¬𝜒→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗¬𝜒, 𝜓↗→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 11154 | →→¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11152, 11153 | |
| 11155 | →¬𝜒¬¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11118, 11154 | |
| 11156 | →→¬𝜒¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜒 | Subs [𝜑↗𝜒, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-3 | |
| 11157 | →¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜒 | Modus ponens 11155, 11156 | |
| 11158 | →↔⋀𝜑⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into biimp | |
| 11159 | →⋀𝜑⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11070, 11158 | |
| 11160 | →→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜒→⋀𝜑⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜒 | Subs [𝜑↗→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜒, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 11161 | →⋀𝜑⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜒 | Modus ponens 11157, 11160 | |
| 11162 | →→⋀𝜑⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜒→→⋀𝜑⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃𝜒 | Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 11163 | →→⋀𝜑⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃𝜒 | Modus ponens 11161, 11162 | |
| 11164 | →⋀𝜑⋀𝜓⋀𝜒𝜃𝜒 | Modus ponens 11159, 11163 | simprrl |
| 11165 | →⋀𝜒𝜃𝜃 | Subs [𝜑↗𝜒, 𝜓↗𝜃] into simpr | |
| 11166 | →𝜃→𝜓𝜃 | Subs [𝜑↗𝜃] into ax-1 | |
| 11167 | →→𝜃→𝜓𝜃→⋀𝜒𝜃→𝜃→𝜓𝜃 | Subs [𝜑↗→𝜃→𝜓𝜃, 𝜓↗⋀𝜒𝜃] into ax-1 | |
| 11168 | →⋀𝜒𝜃→𝜃→𝜓𝜃 | Modus ponens 11166, 11167 | |
| 11169 | →→⋀𝜒𝜃→𝜃→𝜓𝜃→→⋀𝜒𝜃𝜃→⋀𝜒𝜃→𝜓𝜃 | Subs [𝜑↗⋀𝜒𝜃, 𝜓↗𝜃, 𝜒↗→𝜓𝜃] into ax-2 | |
| 11170 | →→⋀𝜒𝜃𝜃→⋀𝜒𝜃→𝜓𝜃 | Modus ponens 11168, 11169 | |
| 11171 | →⋀𝜒𝜃→𝜓𝜃 | Modus ponens 11165, 11170 | |
| 11172 | →→⋀𝜒𝜃→𝜓𝜃→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃 | Subs [𝜑↗⋀𝜒𝜃, 𝜒↗𝜃] into ax-2 | |
| 11173 | →→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃 | Modus ponens 11171, 11172 | |
| 11174 | →→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃→¬¬𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃 | Subs [𝜑↗→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃, 𝜓↗¬¬𝜓] into ax-1 | |
| 11175 | →¬¬𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃 | Modus ponens 11173, 11174 | |
| 11176 | →→¬¬𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃→→¬¬𝜓→⋀𝜒𝜃𝜓→¬¬𝜓→⋀𝜒𝜃𝜃 | Subs [𝜑↗¬¬𝜓, 𝜓↗→⋀𝜒𝜃𝜓, 𝜒↗→⋀𝜒𝜃𝜃] into ax-2 | |
| 11177 | →→¬¬𝜓→⋀𝜒𝜃𝜓→¬¬𝜓→⋀𝜒𝜃𝜃 | Modus ponens 11175, 11176 | |
| 11178 | →¬¬𝜓→⋀𝜒𝜃𝜃 | Modus ponens 10734, 11177 | |
| 11179 | →→¬¬𝜓→⋀𝜒𝜃𝜃→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜃 | Subs [𝜑↗¬¬𝜓, 𝜓↗⋀𝜒𝜃, 𝜒↗𝜃] into ax-2 | |
| 11180 | →→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜃 | Modus ponens 11178, 11179 | |
| 11181 | →→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜃→⋀𝜒𝜃→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜃 | Subs [𝜑↗→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜃, 𝜓↗⋀𝜒𝜃] into ax-1 | |
| 11182 | →⋀𝜒𝜃→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜃 | Modus ponens 11180, 11181 | |
| 11183 | →→⋀𝜒𝜃→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜃→→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓𝜃 | Subs [𝜑↗⋀𝜒𝜃, 𝜓↗→¬¬𝜓⋀𝜒𝜃, 𝜒↗→¬¬𝜓𝜃] into ax-2 | |
| 11184 | →→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓𝜃 | Modus ponens 11182, 11183 | |
| 11185 | →⋀𝜒𝜃→¬¬𝜓𝜃 | Modus ponens 10743, 11184 | |
| 11186 | →𝜃¬¬𝜃 | Subs [𝜑↗𝜃] into notnot | |
| 11187 | →→𝜃¬¬𝜃→¬¬𝜓→𝜃¬¬𝜃 | Subs [𝜑↗→𝜃¬¬𝜃, 𝜓↗¬¬𝜓] into ax-1 | |
| 11188 | →¬¬𝜓→𝜃¬¬𝜃 | Modus ponens 11186, 11187 | |
| 11189 | →→¬¬𝜓→𝜃¬¬𝜃→→¬¬𝜓𝜃→¬¬𝜓¬¬𝜃 | Subs [𝜑↗¬¬𝜓, 𝜓↗𝜃, 𝜒↗¬¬𝜃] into ax-2 | |
| 11190 | →→¬¬𝜓𝜃→¬¬𝜓¬¬𝜃 | Modus ponens 11188, 11189 | |
| 11191 | →→→¬¬𝜓𝜃→¬¬𝜓¬¬𝜃→⋀𝜒𝜃→→¬¬𝜓𝜃→¬¬𝜓¬¬𝜃 | Subs [𝜑↗→→¬¬𝜓𝜃→¬¬𝜓¬¬𝜃, 𝜓↗⋀𝜒𝜃] into ax-1 | |
| 11192 | →⋀𝜒𝜃→→¬¬𝜓𝜃→¬¬𝜓¬¬𝜃 | Modus ponens 11190, 11191 | |
| 11193 | →→⋀𝜒𝜃→→¬¬𝜓𝜃→¬¬𝜓¬¬𝜃→→⋀𝜒𝜃→¬¬𝜓𝜃→⋀𝜒𝜃→¬¬𝜓¬¬𝜃 | Subs [𝜑↗⋀𝜒𝜃, 𝜓↗→¬¬𝜓𝜃, 𝜒↗→¬¬𝜓¬¬𝜃] into ax-2 | |
| 11194 | →→⋀𝜒𝜃→¬¬𝜓𝜃→⋀𝜒𝜃→¬¬𝜓¬¬𝜃 | Modus ponens 11192, 11193 | |
| 11195 | →⋀𝜒𝜃→¬¬𝜓¬¬𝜃 | Modus ponens 11185, 11194 | |
| 11196 | →→¬¬𝜓¬¬𝜃→¬𝜃¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜃] into ax-3 | |
| 11197 | →→→¬¬𝜓¬¬𝜃→¬𝜃¬𝜓→⋀𝜒𝜃→→¬¬𝜓¬¬𝜃→¬𝜃¬𝜓 | Subs [𝜑↗→→¬¬𝜓¬¬𝜃→¬𝜃¬𝜓, 𝜓↗⋀𝜒𝜃] into ax-1 | |
| 11198 | →⋀𝜒𝜃→→¬¬𝜓¬¬𝜃→¬𝜃¬𝜓 | Modus ponens 11196, 11197 | |
| 11199 | →→⋀𝜒𝜃→→¬¬𝜓¬¬𝜃→¬𝜃¬𝜓→→⋀𝜒𝜃→¬¬𝜓¬¬𝜃→⋀𝜒𝜃→¬𝜃¬𝜓 | Subs [𝜑↗⋀𝜒𝜃, 𝜓↗→¬¬𝜓¬¬𝜃, 𝜒↗→¬𝜃¬𝜓] into ax-2 | |
| 11200 | →→⋀𝜒𝜃→¬¬𝜓¬¬𝜃→⋀𝜒𝜃→¬𝜃¬𝜓 | Modus ponens 11198, 11199 | |
| 11201 | →⋀𝜒𝜃→¬𝜃¬𝜓 | Modus ponens 11195, 11200 | |
| 11202 | →¬𝜃¬𝜃 | Subs [𝜑↗¬𝜃] into id | |
| 11203 | →¬𝜃→⋀𝜒𝜃¬𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗⋀𝜒𝜃] into ax-1 | |
| 11204 | →→¬𝜃→⋀𝜒𝜃¬𝜃→¬𝜃→¬𝜃→⋀𝜒𝜃¬𝜃 | Subs [𝜑↗→¬𝜃→⋀𝜒𝜃¬𝜃, 𝜓↗¬𝜃] into ax-1 | |
| 11205 | →¬𝜃→¬𝜃→⋀𝜒𝜃¬𝜃 | Modus ponens 11203, 11204 | |
| 11206 | →→¬𝜃→¬𝜃→⋀𝜒𝜃¬𝜃→→¬𝜃¬𝜃→¬𝜃→⋀𝜒𝜃¬𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗¬𝜃, 𝜒↗→⋀𝜒𝜃¬𝜃] into ax-2 | |
| 11207 | →→¬𝜃¬𝜃→¬𝜃→⋀𝜒𝜃¬𝜃 | Modus ponens 11205, 11206 | |
| 11208 | →→⋀𝜒𝜃→¬𝜃¬𝜓→→⋀𝜒𝜃¬𝜃→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗⋀𝜒𝜃, 𝜓↗¬𝜃, 𝜒↗¬𝜓] into ax-2 | |
| 11209 | →→⋀𝜒𝜃¬𝜃→⋀𝜒𝜃¬𝜓 | Modus ponens 11201, 11208 | |
| 11210 | →→→⋀𝜒𝜃¬𝜃→⋀𝜒𝜃¬𝜓→¬𝜃→→⋀𝜒𝜃¬𝜃→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗→→⋀𝜒𝜃¬𝜃→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜃] into ax-1 | |
| 11211 | →¬𝜃→→⋀𝜒𝜃¬𝜃→⋀𝜒𝜃¬𝜓 | Modus ponens 11209, 11210 | |
| 11212 | →→¬𝜃→→⋀𝜒𝜃¬𝜃→⋀𝜒𝜃¬𝜓→→¬𝜃→⋀𝜒𝜃¬𝜃→¬𝜃→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗¬𝜃, 𝜓↗→⋀𝜒𝜃¬𝜃, 𝜒↗→⋀𝜒𝜃¬𝜓] into ax-2 | |
| 11213 | →→¬𝜃→⋀𝜒𝜃¬𝜃→¬𝜃→⋀𝜒𝜃¬𝜓 | Modus ponens 11211, 11212 | |
| 11214 | →¬𝜃→⋀𝜒𝜃¬𝜓 | Modus ponens 11203, 11213 | |
| 11215 | →→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬𝜃→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜃] into ax-1 | |
| 11216 | →¬𝜃→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓 | Modus ponens 10777, 11215 | |
| 11217 | →¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜃] into ax-1 | |
| 11218 | →→¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗→¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬¬¬→⋀𝜒𝜃¬𝜓] into ax-1 | |
| 11219 | →¬¬¬→⋀𝜒𝜃¬𝜓→¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓 | Modus ponens 11217, 11218 | |
| 11220 | →→¬¬¬→⋀𝜒𝜃¬𝜓→¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗¬¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬→⋀𝜒𝜃¬𝜓, 𝜒↗→¬𝜃¬→⋀𝜒𝜃¬𝜓] into ax-2 | |
| 11221 | →→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓 | Modus ponens 11219, 11220 | |
| 11222 | →¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓 | Modus ponens 10780, 11221 | |
| 11223 | →→¬𝜃→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗¬𝜃, 𝜓↗¬→⋀𝜒𝜃¬𝜓, 𝜒↗¬→⋀𝜒𝜃¬𝜓] into ax-2 | |
| 11224 | →→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓 | Modus ponens 11216, 11223 | |
| 11225 | →→→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗→→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬¬¬→⋀𝜒𝜃¬𝜓] into ax-1 | |
| 11226 | →¬¬¬→⋀𝜒𝜃¬𝜓→→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓 | Modus ponens 11224, 11225 | |
| 11227 | →→¬¬¬→⋀𝜒𝜃¬𝜓→→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓→→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗¬¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗→¬𝜃¬→⋀𝜒𝜃¬𝜓, 𝜒↗→¬𝜃¬→⋀𝜒𝜃¬𝜓] into ax-2 | |
| 11228 | →→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓 | Modus ponens 11226, 11227 | |
| 11229 | →¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗¬¬¬→⋀𝜒𝜃¬𝜓] into ax-1 | |
| 11230 | →→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬𝜃→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃 | Subs [𝜑↗→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃, 𝜓↗¬𝜃] into ax-1 | |
| 11231 | →¬𝜃→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃 | Modus ponens 11229, 11230 | |
| 11232 | →→¬𝜃→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→→¬𝜃¬𝜃→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗¬𝜃, 𝜒↗→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃] into ax-2 | |
| 11233 | →→¬𝜃¬𝜃→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃 | Modus ponens 11231, 11232 | |
| 11234 | →→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗¬¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜃, 𝜒↗¬→⋀𝜒𝜃¬𝜓] into ax-2 | |
| 11235 | →→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓 | Modus ponens 11222, 11234 | |
| 11236 | →→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬𝜃→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜃] into ax-1 | |
| 11237 | →¬𝜃→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓 | Modus ponens 11235, 11236 | |
| 11238 | →→¬𝜃→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗¬𝜃, 𝜓↗→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃, 𝜒↗→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓] into ax-2 | |
| 11239 | →→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓 | Modus ponens 11237, 11238 | |
| 11240 | →¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓 | Modus ponens 11229, 11239 | |
| 11241 | →→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓→¬𝜃→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜃] into ax-1 | |
| 11242 | →¬𝜃→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓 | Modus ponens 10805, 11241 | |
| 11243 | →→¬𝜃→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓→→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬𝜃→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗¬𝜃, 𝜓↗→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓, 𝜒↗→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓] into ax-2 | |
| 11244 | →→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬𝜃→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓 | Modus ponens 11242, 11243 | |
| 11245 | →¬𝜃→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓 | Modus ponens 11240, 11244 | |
| 11246 | →→¬𝜃→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓→→¬𝜃→⋀𝜒𝜃¬𝜓→¬𝜃¬¬→⋀𝜒𝜃¬𝜓 | Subs [𝜑↗¬𝜃, 𝜓↗→⋀𝜒𝜃¬𝜓, 𝜒↗¬¬→⋀𝜒𝜃¬𝜓] into ax-2 | |
| 11247 | →→¬𝜃→⋀𝜒𝜃¬𝜓→¬𝜃¬¬→⋀𝜒𝜃¬𝜓 | Modus ponens 11245, 11246 | |
| 11248 | →¬𝜃¬¬→⋀𝜒𝜃¬𝜓 | Modus ponens 11214, 11247 | |
| 11249 | →→¬𝜃¬¬→⋀𝜒𝜃¬𝜓→¬→⋀𝜒𝜃¬𝜓𝜃 | Subs [𝜑↗𝜃, 𝜓↗¬→⋀𝜒𝜃¬𝜓] into ax-3 | |
| 11250 | →¬→⋀𝜒𝜃¬𝜓𝜃 | Modus ponens 11248, 11249 | |
| 11251 | →→¬→⋀𝜒𝜃¬𝜓𝜃→⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜃 | Subs [𝜑↗→¬→⋀𝜒𝜃¬𝜓𝜃, 𝜓↗⋀⋀𝜒𝜃𝜓] into ax-1 | |
| 11252 | →⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜃 | Modus ponens 11250, 11251 | |
| 11253 | →→⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜃→→⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜃 | Subs [𝜑↗⋀⋀𝜒𝜃𝜓, 𝜓↗¬→⋀𝜒𝜃¬𝜓, 𝜒↗𝜃] into ax-2 | |
| 11254 | →→⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜃 | Modus ponens 11252, 11253 | |
| 11255 | →⋀⋀𝜒𝜃𝜓𝜃 | Modus ponens 10817, 11254 | |
| 11256 | →→⋀⋀𝜒𝜃𝜓𝜃→¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜃 | Subs [𝜑↗→⋀⋀𝜒𝜃𝜓𝜃, 𝜓↗¬→⋀𝜒𝜃¬𝜓] into ax-1 | |
| 11257 | →¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜃 | Modus ponens 11255, 11256 | |
| 11258 | →→¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜃→→¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜃 | Subs [𝜑↗¬→⋀𝜒𝜃¬𝜓, 𝜓↗⋀⋀𝜒𝜃𝜓, 𝜒↗𝜃] into ax-2 | |
| 11259 | →→¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜃 | Modus ponens 11257, 11258 | |
| 11260 | →→¬→⋀𝜒𝜃¬𝜓𝜃→𝜓→¬→⋀𝜒𝜃¬𝜓𝜃 | Subs [𝜑↗→¬→⋀𝜒𝜃¬𝜓𝜃] into ax-1 | |
| 11261 | →𝜓→¬→⋀𝜒𝜃¬𝜓𝜃 | Modus ponens 11250, 11260 | |
| 11262 | →→𝜓→¬→⋀𝜒𝜃¬𝜓𝜃→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜃 | Subs [𝜑↗𝜓, 𝜓↗¬→⋀𝜒𝜃¬𝜓, 𝜒↗𝜃] into ax-2 | |
| 11263 | →→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜃 | Modus ponens 11261, 11262 | |
| 11264 | →→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜃→⋀𝜒𝜃→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜃 | Subs [𝜑↗→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜃, 𝜓↗⋀𝜒𝜃] into ax-1 | |
| 11265 | →⋀𝜒𝜃→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜃 | Modus ponens 11263, 11264 | |
| 11266 | →→⋀𝜒𝜃→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜃→→⋀𝜒𝜃→𝜓¬→⋀𝜒𝜃¬𝜓→⋀𝜒𝜃→𝜓𝜃 | Subs [𝜑↗⋀𝜒𝜃, 𝜓↗→𝜓¬→⋀𝜒𝜃¬𝜓, 𝜒↗→𝜓𝜃] into ax-2 | |
| 11267 | →→⋀𝜒𝜃→𝜓¬→⋀𝜒𝜃¬𝜓→⋀𝜒𝜃→𝜓𝜃 | Modus ponens 11265, 11266 | |
| 11268 | →→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃→𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃 | Subs [𝜑↗→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃] into ax-1 | |
| 11269 | →𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃 | Modus ponens 11173, 11268 | |
| 11270 | →→𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃→→𝜓→⋀𝜒𝜃𝜓→𝜓→⋀𝜒𝜃𝜃 | Subs [𝜑↗𝜓, 𝜓↗→⋀𝜒𝜃𝜓, 𝜒↗→⋀𝜒𝜃𝜃] into ax-2 | |
| 11271 | →→𝜓→⋀𝜒𝜃𝜓→𝜓→⋀𝜒𝜃𝜃 | Modus ponens 11269, 11270 | |
| 11272 | →𝜓→⋀𝜒𝜃𝜃 | Modus ponens 10729, 11271 | |
| 11273 | →→𝜓→⋀𝜒𝜃𝜃→→𝜓⋀𝜒𝜃→𝜓𝜃 | Subs [𝜑↗𝜓, 𝜓↗⋀𝜒𝜃, 𝜒↗𝜃] into ax-2 | |
| 11274 | →→𝜓⋀𝜒𝜃→𝜓𝜃 | Modus ponens 11272, 11273 | |
| 11275 | →→→𝜓⋀𝜒𝜃→𝜓𝜃→¬¬⋀𝜒𝜃→→𝜓⋀𝜒𝜃→𝜓𝜃 | Subs [𝜑↗→→𝜓⋀𝜒𝜃→𝜓𝜃, 𝜓↗¬¬⋀𝜒𝜃] into ax-1 | |
| 11276 | →¬¬⋀𝜒𝜃→→𝜓⋀𝜒𝜃→𝜓𝜃 | Modus ponens 11274, 11275 | |
| 11277 | →→¬¬⋀𝜒𝜃→→𝜓⋀𝜒𝜃→𝜓𝜃→→¬¬⋀𝜒𝜃→𝜓⋀𝜒𝜃→¬¬⋀𝜒𝜃→𝜓𝜃 | Subs [𝜑↗¬¬⋀𝜒𝜃, 𝜓↗→𝜓⋀𝜒𝜃, 𝜒↗→𝜓𝜃] into ax-2 | |
| 11278 | →→¬¬⋀𝜒𝜃→𝜓⋀𝜒𝜃→¬¬⋀𝜒𝜃→𝜓𝜃 | Modus ponens 11276, 11277 | |
| 11279 | →¬¬⋀𝜒𝜃→𝜓𝜃 | Modus ponens 10856, 11278 | |
| 11280 | →→¬¬⋀𝜒𝜃→𝜓𝜃→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜃 | Subs [𝜑↗¬¬⋀𝜒𝜃, 𝜒↗𝜃] into ax-2 | |
| 11281 | →→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜃 | Modus ponens 11279, 11280 | |
| 11282 | →→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜃→𝜓→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜃 | Subs [𝜑↗→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜃] into ax-1 | |
| 11283 | →𝜓→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜃 | Modus ponens 11281, 11282 | |
| 11284 | →→𝜓→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜃→→𝜓→¬¬⋀𝜒𝜃𝜓→𝜓→¬¬⋀𝜒𝜃𝜃 | Subs [𝜑↗𝜓, 𝜓↗→¬¬⋀𝜒𝜃𝜓, 𝜒↗→¬¬⋀𝜒𝜃𝜃] into ax-2 | |
| 11285 | →→𝜓→¬¬⋀𝜒𝜃𝜓→𝜓→¬¬⋀𝜒𝜃𝜃 | Modus ponens 11283, 11284 | |
| 11286 | →𝜓→¬¬⋀𝜒𝜃𝜃 | Modus ponens 10864, 11285 | |
| 11287 | →→𝜃¬¬𝜃→¬¬⋀𝜒𝜃→𝜃¬¬𝜃 | Subs [𝜑↗→𝜃¬¬𝜃, 𝜓↗¬¬⋀𝜒𝜃] into ax-1 | |
| 11288 | →¬¬⋀𝜒𝜃→𝜃¬¬𝜃 | Modus ponens 11186, 11287 | |
| 11289 | →→¬¬⋀𝜒𝜃→𝜃¬¬𝜃→→¬¬⋀𝜒𝜃𝜃→¬¬⋀𝜒𝜃¬¬𝜃 | Subs [𝜑↗¬¬⋀𝜒𝜃, 𝜓↗𝜃, 𝜒↗¬¬𝜃] into ax-2 | |
| 11290 | →→¬¬⋀𝜒𝜃𝜃→¬¬⋀𝜒𝜃¬¬𝜃 | Modus ponens 11288, 11289 | |
| 11291 | →→→¬¬⋀𝜒𝜃𝜃→¬¬⋀𝜒𝜃¬¬𝜃→𝜓→→¬¬⋀𝜒𝜃𝜃→¬¬⋀𝜒𝜃¬¬𝜃 | Subs [𝜑↗→→¬¬⋀𝜒𝜃𝜃→¬¬⋀𝜒𝜃¬¬𝜃] into ax-1 | |
| 11292 | →𝜓→→¬¬⋀𝜒𝜃𝜃→¬¬⋀𝜒𝜃¬¬𝜃 | Modus ponens 11290, 11291 | |
| 11293 | →→𝜓→→¬¬⋀𝜒𝜃𝜃→¬¬⋀𝜒𝜃¬¬𝜃→→𝜓→¬¬⋀𝜒𝜃𝜃→𝜓→¬¬⋀𝜒𝜃¬¬𝜃 | Subs [𝜑↗𝜓, 𝜓↗→¬¬⋀𝜒𝜃𝜃, 𝜒↗→¬¬⋀𝜒𝜃¬¬𝜃] into ax-2 | |
| 11294 | →→𝜓→¬¬⋀𝜒𝜃𝜃→𝜓→¬¬⋀𝜒𝜃¬¬𝜃 | Modus ponens 11292, 11293 | |
| 11295 | →𝜓→¬¬⋀𝜒𝜃¬¬𝜃 | Modus ponens 11286, 11294 | |
| 11296 | →→¬¬⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜒𝜃 | Subs [𝜑↗¬⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-3 | |
| 11297 | →→→¬¬⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜒𝜃→𝜓→→¬¬⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜒𝜃 | Subs [𝜑↗→→¬¬⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜒𝜃] into ax-1 | |
| 11298 | →𝜓→→¬¬⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜒𝜃 | Modus ponens 11296, 11297 | |
| 11299 | →→𝜓→→¬¬⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜒𝜃→→𝜓→¬¬⋀𝜒𝜃¬¬𝜃→𝜓→¬𝜃¬⋀𝜒𝜃 | Subs [𝜑↗𝜓, 𝜓↗→¬¬⋀𝜒𝜃¬¬𝜃, 𝜒↗→¬𝜃¬⋀𝜒𝜃] into ax-2 | |
| 11300 | →→𝜓→¬¬⋀𝜒𝜃¬¬𝜃→𝜓→¬𝜃¬⋀𝜒𝜃 | Modus ponens 11298, 11299 | |
| 11301 | →𝜓→¬𝜃¬⋀𝜒𝜃 | Modus ponens 11295, 11300 | |
| 11302 | →¬𝜃→𝜓¬𝜃 | Subs [𝜑↗¬𝜃] into ax-1 | |
| 11303 | →→¬𝜃→𝜓¬𝜃→¬𝜃→¬𝜃→𝜓¬𝜃 | Subs [𝜑↗→¬𝜃→𝜓¬𝜃, 𝜓↗¬𝜃] into ax-1 | |
| 11304 | →¬𝜃→¬𝜃→𝜓¬𝜃 | Modus ponens 11302, 11303 | |
| 11305 | →→¬𝜃→¬𝜃→𝜓¬𝜃→→¬𝜃¬𝜃→¬𝜃→𝜓¬𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗¬𝜃, 𝜒↗→𝜓¬𝜃] into ax-2 | |
| 11306 | →→¬𝜃¬𝜃→¬𝜃→𝜓¬𝜃 | Modus ponens 11304, 11305 | |
| 11307 | →→𝜓→¬𝜃¬⋀𝜒𝜃→→𝜓¬𝜃→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗𝜓, 𝜓↗¬𝜃, 𝜒↗¬⋀𝜒𝜃] into ax-2 | |
| 11308 | →→𝜓¬𝜃→𝜓¬⋀𝜒𝜃 | Modus ponens 11301, 11307 | |
| 11309 | →→→𝜓¬𝜃→𝜓¬⋀𝜒𝜃→¬𝜃→→𝜓¬𝜃→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗→→𝜓¬𝜃→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1 | |
| 11310 | →¬𝜃→→𝜓¬𝜃→𝜓¬⋀𝜒𝜃 | Modus ponens 11308, 11309 | |
| 11311 | →→¬𝜃→→𝜓¬𝜃→𝜓¬⋀𝜒𝜃→→¬𝜃→𝜓¬𝜃→¬𝜃→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗→𝜓¬𝜃, 𝜒↗→𝜓¬⋀𝜒𝜃] into ax-2 | |
| 11312 | →→¬𝜃→𝜓¬𝜃→¬𝜃→𝜓¬⋀𝜒𝜃 | Modus ponens 11310, 11311 | |
| 11313 | →¬𝜃→𝜓¬⋀𝜒𝜃 | Modus ponens 11302, 11312 | |
| 11314 | →→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1 | |
| 11315 | →¬𝜃→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃 | Modus ponens 10898, 11314 | |
| 11316 | →¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1 | |
| 11317 | →→¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗→¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬¬¬→𝜓¬⋀𝜒𝜃] into ax-1 | |
| 11318 | →¬¬¬→𝜓¬⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃 | Modus ponens 11316, 11317 | |
| 11319 | →→¬¬¬→𝜓¬⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗¬¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬→𝜓¬⋀𝜒𝜃, 𝜒↗→¬𝜃¬→𝜓¬⋀𝜒𝜃] into ax-2 | |
| 11320 | →→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃 | Modus ponens 11318, 11319 | |
| 11321 | →¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃 | Modus ponens 10901, 11320 | |
| 11322 | →→¬𝜃→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗¬→𝜓¬⋀𝜒𝜃, 𝜒↗¬→𝜓¬⋀𝜒𝜃] into ax-2 | |
| 11323 | →→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃 | Modus ponens 11315, 11322 | |
| 11324 | →→→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗→→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬¬¬→𝜓¬⋀𝜒𝜃] into ax-1 | |
| 11325 | →¬¬¬→𝜓¬⋀𝜒𝜃→→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃 | Modus ponens 11323, 11324 | |
| 11326 | →→¬¬¬→𝜓¬⋀𝜒𝜃→→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗¬¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗→¬𝜃¬→𝜓¬⋀𝜒𝜃, 𝜒↗→¬𝜃¬→𝜓¬⋀𝜒𝜃] into ax-2 | |
| 11327 | →→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃 | Modus ponens 11325, 11326 | |
| 11328 | →¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗¬¬¬→𝜓¬⋀𝜒𝜃] into ax-1 | |
| 11329 | →→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬𝜃→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃 | Subs [𝜑↗→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃, 𝜓↗¬𝜃] into ax-1 | |
| 11330 | →¬𝜃→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃 | Modus ponens 11328, 11329 | |
| 11331 | →→¬𝜃→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→→¬𝜃¬𝜃→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗¬𝜃, 𝜒↗→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃] into ax-2 | |
| 11332 | →→¬𝜃¬𝜃→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃 | Modus ponens 11330, 11331 | |
| 11333 | →→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗¬¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜃, 𝜒↗¬→𝜓¬⋀𝜒𝜃] into ax-2 | |
| 11334 | →→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃 | Modus ponens 11321, 11333 | |
| 11335 | →→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1 | |
| 11336 | →¬𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃 | Modus ponens 11334, 11335 | |
| 11337 | →→¬𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃, 𝜒↗→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃] into ax-2 | |
| 11338 | →→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃 | Modus ponens 11336, 11337 | |
| 11339 | →¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃 | Modus ponens 11328, 11338 | |
| 11340 | →→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃→¬𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1 | |
| 11341 | →¬𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃 | Modus ponens 10926, 11340 | |
| 11342 | →→¬𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃→→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃, 𝜒↗→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃] into ax-2 | |
| 11343 | →→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃 | Modus ponens 11341, 11342 | |
| 11344 | →¬𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃 | Modus ponens 11339, 11343 | |
| 11345 | →→¬𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃→→¬𝜃→𝜓¬⋀𝜒𝜃→¬𝜃¬¬→𝜓¬⋀𝜒𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗→𝜓¬⋀𝜒𝜃, 𝜒↗¬¬→𝜓¬⋀𝜒𝜃] into ax-2 | |
| 11346 | →→¬𝜃→𝜓¬⋀𝜒𝜃→¬𝜃¬¬→𝜓¬⋀𝜒𝜃 | Modus ponens 11344, 11345 | |
| 11347 | →¬𝜃¬¬→𝜓¬⋀𝜒𝜃 | Modus ponens 11313, 11346 | |
| 11348 | →→¬𝜃¬¬→𝜓¬⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃𝜃 | Subs [𝜑↗𝜃, 𝜓↗¬→𝜓¬⋀𝜒𝜃] into ax-3 | |
| 11349 | →¬→𝜓¬⋀𝜒𝜃𝜃 | Modus ponens 11347, 11348 | |
| 11350 | →→¬→𝜓¬⋀𝜒𝜃𝜃→⋀𝜓⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃𝜃 | Subs [𝜑↗→¬→𝜓¬⋀𝜒𝜃𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 11351 | →⋀𝜓⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃𝜃 | Modus ponens 11349, 11350 | |
| 11352 | →→⋀𝜓⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃𝜃→→⋀𝜓⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃𝜃 | Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗¬→𝜓¬⋀𝜒𝜃, 𝜒↗𝜃] into ax-2 | |
| 11353 | →→⋀𝜓⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃𝜃 | Modus ponens 11351, 11352 | |
| 11354 | →⋀𝜓⋀𝜒𝜃𝜃 | Modus ponens 10938, 11353 | |
| 11355 | →𝜃→𝜑𝜃 | Subs [𝜑↗𝜃, 𝜓↗𝜑] into ax-1 | |
| 11356 | →→𝜃→𝜑𝜃→⋀𝜓⋀𝜒𝜃→𝜃→𝜑𝜃 | Subs [𝜑↗→𝜃→𝜑𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 11357 | →⋀𝜓⋀𝜒𝜃→𝜃→𝜑𝜃 | Modus ponens 11355, 11356 | |
| 11358 | →→⋀𝜓⋀𝜒𝜃→𝜃→𝜑𝜃→→⋀𝜓⋀𝜒𝜃𝜃→⋀𝜓⋀𝜒𝜃→𝜑𝜃 | Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗𝜃, 𝜒↗→𝜑𝜃] into ax-2 | |
| 11359 | →→⋀𝜓⋀𝜒𝜃𝜃→⋀𝜓⋀𝜒𝜃→𝜑𝜃 | Modus ponens 11357, 11358 | |
| 11360 | →⋀𝜓⋀𝜒𝜃→𝜑𝜃 | Modus ponens 11354, 11359 | |
| 11361 | →→⋀𝜓⋀𝜒𝜃→𝜑𝜃→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃 | Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑, 𝜒↗𝜃] into ax-2 | |
| 11362 | →→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃 | Modus ponens 11360, 11361 | |
| 11363 | →→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃→¬¬𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃 | Subs [𝜑↗→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃, 𝜓↗¬¬𝜑] into ax-1 | |
| 11364 | →¬¬𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃 | Modus ponens 11362, 11363 | |
| 11365 | →→¬¬𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃→→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜑→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜃 | Subs [𝜑↗¬¬𝜑, 𝜓↗→⋀𝜓⋀𝜒𝜃𝜑, 𝜒↗→⋀𝜓⋀𝜒𝜃𝜃] into ax-2 | |
| 11366 | →→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜑→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜃 | Modus ponens 11364, 11365 | |
| 11367 | →¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜃 | Modus ponens 10955, 11366 | |
| 11368 | →→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜃→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃 | Subs [𝜑↗¬¬𝜑, 𝜓↗⋀𝜓⋀𝜒𝜃, 𝜒↗𝜃] into ax-2 | |
| 11369 | →→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃 | Modus ponens 11367, 11368 | |
| 11370 | →→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃→⋀𝜓⋀𝜒𝜃→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃 | Subs [𝜑↗→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 11371 | →⋀𝜓⋀𝜒𝜃→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃 | Modus ponens 11369, 11370 | |
| 11372 | →→⋀𝜓⋀𝜒𝜃→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃→→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃 | Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗→¬¬𝜑⋀𝜓⋀𝜒𝜃, 𝜒↗→¬¬𝜑𝜃] into ax-2 | |
| 11373 | →→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃 | Modus ponens 11371, 11372 | |
| 11374 | →⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃 | Modus ponens 10964, 11373 | |
| 11375 | →→𝜃¬¬𝜃→¬¬𝜑→𝜃¬¬𝜃 | Subs [𝜑↗→𝜃¬¬𝜃, 𝜓↗¬¬𝜑] into ax-1 | |
| 11376 | →¬¬𝜑→𝜃¬¬𝜃 | Modus ponens 11186, 11375 | |
| 11377 | →→¬¬𝜑→𝜃¬¬𝜃→→¬¬𝜑𝜃→¬¬𝜑¬¬𝜃 | Subs [𝜑↗¬¬𝜑, 𝜓↗𝜃, 𝜒↗¬¬𝜃] into ax-2 | |
| 11378 | →→¬¬𝜑𝜃→¬¬𝜑¬¬𝜃 | Modus ponens 11376, 11377 | |
| 11379 | →→→¬¬𝜑𝜃→¬¬𝜑¬¬𝜃→⋀𝜓⋀𝜒𝜃→→¬¬𝜑𝜃→¬¬𝜑¬¬𝜃 | Subs [𝜑↗→→¬¬𝜑𝜃→¬¬𝜑¬¬𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 11380 | →⋀𝜓⋀𝜒𝜃→→¬¬𝜑𝜃→¬¬𝜑¬¬𝜃 | Modus ponens 11378, 11379 | |
| 11381 | →→⋀𝜓⋀𝜒𝜃→→¬¬𝜑𝜃→¬¬𝜑¬¬𝜃→→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜃 | Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗→¬¬𝜑𝜃, 𝜒↗→¬¬𝜑¬¬𝜃] into ax-2 | |
| 11382 | →→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜃 | Modus ponens 11380, 11381 | |
| 11383 | →⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜃 | Modus ponens 11374, 11382 | |
| 11384 | →→¬¬𝜑¬¬𝜃→¬𝜃¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜃] into ax-3 | |
| 11385 | →→→¬¬𝜑¬¬𝜃→¬𝜃¬𝜑→⋀𝜓⋀𝜒𝜃→→¬¬𝜑¬¬𝜃→¬𝜃¬𝜑 | Subs [𝜑↗→→¬¬𝜑¬¬𝜃→¬𝜃¬𝜑, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 11386 | →⋀𝜓⋀𝜒𝜃→→¬¬𝜑¬¬𝜃→¬𝜃¬𝜑 | Modus ponens 11384, 11385 | |
| 11387 | →→⋀𝜓⋀𝜒𝜃→→¬¬𝜑¬¬𝜃→¬𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜃→⋀𝜓⋀𝜒𝜃→¬𝜃¬𝜑 | Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗→¬¬𝜑¬¬𝜃, 𝜒↗→¬𝜃¬𝜑] into ax-2 | |
| 11388 | →→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜃→⋀𝜓⋀𝜒𝜃→¬𝜃¬𝜑 | Modus ponens 11386, 11387 | |
| 11389 | →⋀𝜓⋀𝜒𝜃→¬𝜃¬𝜑 | Modus ponens 11383, 11388 | |
| 11390 | →¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 11391 | →→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃→¬𝜃→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃 | Subs [𝜑↗→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃, 𝜓↗¬𝜃] into ax-1 | |
| 11392 | →¬𝜃→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃 | Modus ponens 11390, 11391 | |
| 11393 | →→¬𝜃→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃→→¬𝜃¬𝜃→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗¬𝜃, 𝜒↗→⋀𝜓⋀𝜒𝜃¬𝜃] into ax-2 | |
| 11394 | →→¬𝜃¬𝜃→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃 | Modus ponens 11392, 11393 | |
| 11395 | →→⋀𝜓⋀𝜒𝜃→¬𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜃, 𝜒↗¬𝜑] into ax-2 | |
| 11396 | →→⋀𝜓⋀𝜒𝜃¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11389, 11395 | |
| 11397 | →→→⋀𝜓⋀𝜒𝜃¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃→→⋀𝜓⋀𝜒𝜃¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗→→⋀𝜓⋀𝜒𝜃¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜃] into ax-1 | |
| 11398 | →¬𝜃→→⋀𝜓⋀𝜒𝜃¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11396, 11397 | |
| 11399 | →→¬𝜃→→⋀𝜓⋀𝜒𝜃¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗¬𝜃, 𝜓↗→⋀𝜓⋀𝜒𝜃¬𝜃, 𝜒↗→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2 | |
| 11400 | →→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11398, 11399 | |
| 11401 | →¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11390, 11400 | |
| 11402 | →→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜃] into ax-1 | |
| 11403 | →¬𝜃→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 10998, 11402 | |
| 11404 | →¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜃] into ax-1 | |
| 11405 | →→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-1 | |
| 11406 | →¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11404, 11405 | |
| 11407 | →→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2 | |
| 11408 | →→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11406, 11407 | |
| 11409 | →¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11001, 11408 | |
| 11410 | →→¬𝜃→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗¬𝜃, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2 | |
| 11411 | →→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11403, 11410 | |
| 11412 | →→→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗→→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-1 | |
| 11413 | →¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11411, 11412 | |
| 11414 | →→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2 | |
| 11415 | →→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11413, 11414 | |
| 11416 | →¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-1 | |
| 11417 | →→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬𝜃→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃 | Subs [𝜑↗→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃, 𝜓↗¬𝜃] into ax-1 | |
| 11418 | →¬𝜃→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃 | Modus ponens 11416, 11417 | |
| 11419 | →→¬𝜃→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→→¬𝜃¬𝜃→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗¬𝜃, 𝜒↗→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃] into ax-2 | |
| 11420 | →→¬𝜃¬𝜃→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃 | Modus ponens 11418, 11419 | |
| 11421 | →→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜃, 𝜒↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2 | |
| 11422 | →→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11409, 11421 | |
| 11423 | →→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜃] into ax-1 | |
| 11424 | →¬𝜃→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11422, 11423 | |
| 11425 | →→¬𝜃→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗¬𝜃, 𝜓↗→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃, 𝜒↗→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2 | |
| 11426 | →→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11424, 11425 | |
| 11427 | →¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11416, 11426 | |
| 11428 | →→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜃] into ax-1 | |
| 11429 | →¬𝜃→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11026, 11428 | |
| 11430 | →→¬𝜃→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗¬𝜃, 𝜓↗→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2 | |
| 11431 | →→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11429, 11430 | |
| 11432 | →¬𝜃→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11427, 11431 | |
| 11433 | →→¬𝜃→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Subs [𝜑↗¬𝜃, 𝜓↗→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2 | |
| 11434 | →→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11432, 11433 | |
| 11435 | →¬𝜃¬¬→⋀𝜓⋀𝜒𝜃¬𝜑 | Modus ponens 11401, 11434 | |
| 11436 | →→¬𝜃¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃 | Subs [𝜑↗𝜃, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-3 | |
| 11437 | →¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃 | Modus ponens 11435, 11436 | |
| 11438 | →→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃→⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃 | Subs [𝜑↗→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃, 𝜓↗⋀⋀𝜓⋀𝜒𝜃𝜑] into ax-1 | |
| 11439 | →⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃 | Modus ponens 11437, 11438 | |
| 11440 | →→⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃→→⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜃 | Subs [𝜑↗⋀⋀𝜓⋀𝜒𝜃𝜑, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗𝜃] into ax-2 | |
| 11441 | →→⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜃 | Modus ponens 11439, 11440 | |
| 11442 | →⋀⋀𝜓⋀𝜒𝜃𝜑𝜃 | Modus ponens 11038, 11441 | |
| 11443 | →→⋀⋀𝜓⋀𝜒𝜃𝜑𝜃→¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜃 | Subs [𝜑↗→⋀⋀𝜓⋀𝜒𝜃𝜑𝜃, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-1 | |
| 11444 | →¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜃 | Modus ponens 11442, 11443 | |
| 11445 | →→¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜃→→¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃 | Subs [𝜑↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗⋀⋀𝜓⋀𝜒𝜃𝜑, 𝜒↗𝜃] into ax-2 | |
| 11446 | →→¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃 | Modus ponens 11444, 11445 | |
| 11447 | →→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃→𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃 | Subs [𝜑↗→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃, 𝜓↗𝜑] into ax-1 | |
| 11448 | →𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃 | Modus ponens 11437, 11447 | |
| 11449 | →→𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜃 | Subs [𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗𝜃] into ax-2 | |
| 11450 | →→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜃 | Modus ponens 11448, 11449 | |
| 11451 | →→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜃→⋀𝜓⋀𝜒𝜃→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜃 | Subs [𝜑↗→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 11452 | →⋀𝜓⋀𝜒𝜃→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜃 | Modus ponens 11450, 11451 | |
| 11453 | →→⋀𝜓⋀𝜒𝜃→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜃→→⋀𝜓⋀𝜒𝜃→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀𝜓⋀𝜒𝜃→𝜑𝜃 | Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗→𝜑𝜃] into ax-2 | |
| 11454 | →→⋀𝜓⋀𝜒𝜃→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀𝜓⋀𝜒𝜃→𝜑𝜃 | Modus ponens 11452, 11453 | |
| 11455 | →→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃→𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃 | Subs [𝜑↗→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃, 𝜓↗𝜑] into ax-1 | |
| 11456 | →𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃 | Modus ponens 11362, 11455 | |
| 11457 | →→𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃→→𝜑→⋀𝜓⋀𝜒𝜃𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜃 | Subs [𝜓↗→⋀𝜓⋀𝜒𝜃𝜑, 𝜒↗→⋀𝜓⋀𝜒𝜃𝜃] into ax-2 | |
| 11458 | →→𝜑→⋀𝜓⋀𝜒𝜃𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜃 | Modus ponens 11456, 11457 | |
| 11459 | →𝜑→⋀𝜓⋀𝜒𝜃𝜃 | Modus ponens 10950, 11458 | |
| 11460 | →→𝜑→⋀𝜓⋀𝜒𝜃𝜃→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜃 | Subs [𝜓↗⋀𝜓⋀𝜒𝜃, 𝜒↗𝜃] into ax-2 | |
| 11461 | →→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜃 | Modus ponens 11459, 11460 | |
| 11462 | →→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜃→¬¬⋀𝜓⋀𝜒𝜃→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜃 | Subs [𝜑↗→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜃, 𝜓↗¬¬⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 11463 | →¬¬⋀𝜓⋀𝜒𝜃→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜃 | Modus ponens 11461, 11462 | |
| 11464 | →→¬¬⋀𝜓⋀𝜒𝜃→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜃→→¬¬⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃→¬¬⋀𝜓⋀𝜒𝜃→𝜑𝜃 | Subs [𝜑↗¬¬⋀𝜓⋀𝜒𝜃, 𝜓↗→𝜑⋀𝜓⋀𝜒𝜃, 𝜒↗→𝜑𝜃] into ax-2 | |
| 11465 | →→¬¬⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃→¬¬⋀𝜓⋀𝜒𝜃→𝜑𝜃 | Modus ponens 11463, 11464 | |
| 11466 | →¬¬⋀𝜓⋀𝜒𝜃→𝜑𝜃 | Modus ponens 11077, 11465 | |
| 11467 | →→¬¬⋀𝜓⋀𝜒𝜃→𝜑𝜃→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃 | Subs [𝜑↗¬¬⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑, 𝜒↗𝜃] into ax-2 | |
| 11468 | →→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃 | Modus ponens 11466, 11467 | |
| 11469 | →→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃 | Subs [𝜑↗→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃, 𝜓↗𝜑] into ax-1 | |
| 11470 | →𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃 | Modus ponens 11468, 11469 | |
| 11471 | →→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃→→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃 | Subs [𝜓↗→¬¬⋀𝜓⋀𝜒𝜃𝜑, 𝜒↗→¬¬⋀𝜓⋀𝜒𝜃𝜃] into ax-2 | |
| 11472 | →→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃 | Modus ponens 11470, 11471 | |
| 11473 | →𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃 | Modus ponens 11085, 11472 | |
| 11474 | →→𝜃¬¬𝜃→¬¬⋀𝜓⋀𝜒𝜃→𝜃¬¬𝜃 | Subs [𝜑↗→𝜃¬¬𝜃, 𝜓↗¬¬⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 11475 | →¬¬⋀𝜓⋀𝜒𝜃→𝜃¬¬𝜃 | Modus ponens 11186, 11474 | |
| 11476 | →→¬¬⋀𝜓⋀𝜒𝜃→𝜃¬¬𝜃→→¬¬⋀𝜓⋀𝜒𝜃𝜃→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃 | Subs [𝜑↗¬¬⋀𝜓⋀𝜒𝜃, 𝜓↗𝜃, 𝜒↗¬¬𝜃] into ax-2 | |
| 11477 | →→¬¬⋀𝜓⋀𝜒𝜃𝜃→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃 | Modus ponens 11475, 11476 | |
| 11478 | →→→¬¬⋀𝜓⋀𝜒𝜃𝜃→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜃→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃 | Subs [𝜑↗→→¬¬⋀𝜓⋀𝜒𝜃𝜃→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃, 𝜓↗𝜑] into ax-1 | |
| 11479 | →𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜃→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃 | Modus ponens 11477, 11478 | |
| 11480 | →→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜃→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃 | Subs [𝜓↗→¬¬⋀𝜓⋀𝜒𝜃𝜃, 𝜒↗→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃] into ax-2 | |
| 11481 | →→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃 | Modus ponens 11479, 11480 | |
| 11482 | →𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃 | Modus ponens 11473, 11481 | |
| 11483 | →→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-3 | |
| 11484 | →→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜓⋀𝜒𝜃→𝜑→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑] into ax-1 | |
| 11485 | →𝜑→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11483, 11484 | |
| 11486 | →→𝜑→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜓⋀𝜒𝜃→→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→𝜑→¬𝜃¬⋀𝜓⋀𝜒𝜃 | Subs [𝜓↗→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃, 𝜒↗→¬𝜃¬⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 11487 | →→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→𝜑→¬𝜃¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11485, 11486 | |
| 11488 | →𝜑→¬𝜃¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11482, 11487 | |
| 11489 | →¬𝜃→𝜑¬𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗𝜑] into ax-1 | |
| 11490 | →→¬𝜃→𝜑¬𝜃→¬𝜃→¬𝜃→𝜑¬𝜃 | Subs [𝜑↗→¬𝜃→𝜑¬𝜃, 𝜓↗¬𝜃] into ax-1 | |
| 11491 | →¬𝜃→¬𝜃→𝜑¬𝜃 | Modus ponens 11489, 11490 | |
| 11492 | →→¬𝜃→¬𝜃→𝜑¬𝜃→→¬𝜃¬𝜃→¬𝜃→𝜑¬𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗¬𝜃, 𝜒↗→𝜑¬𝜃] into ax-2 | |
| 11493 | →→¬𝜃¬𝜃→¬𝜃→𝜑¬𝜃 | Modus ponens 11491, 11492 | |
| 11494 | →→𝜑→¬𝜃¬⋀𝜓⋀𝜒𝜃→→𝜑¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜓↗¬𝜃, 𝜒↗¬⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 11495 | →→𝜑¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11488, 11494 | |
| 11496 | →→→𝜑¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃→→𝜑¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗→→𝜑¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1 | |
| 11497 | →¬𝜃→→𝜑¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11495, 11496 | |
| 11498 | →→¬𝜃→→𝜑¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜃→𝜑¬𝜃→¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗→𝜑¬𝜃, 𝜒↗→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 11499 | →→¬𝜃→𝜑¬𝜃→¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11497, 11498 | |
| 11500 | →¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11489, 11499 | |
| 11501 | →→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1 | |
| 11502 | →¬𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11119, 11501 | |
| 11503 | →¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1 | |
| 11504 | →→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 11505 | →¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11503, 11504 | |
| 11506 | →→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 11507 | →→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11505, 11506 | |
| 11508 | →¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11122, 11507 | |
| 11509 | →→¬𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 11510 | →→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11502, 11509 | |
| 11511 | →→→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗→→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 11512 | →¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11510, 11511 | |
| 11513 | →→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 11514 | →→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11512, 11513 | |
| 11515 | →¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 11516 | →→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬𝜃→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃 | Subs [𝜑↗→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃, 𝜓↗¬𝜃] into ax-1 | |
| 11517 | →¬𝜃→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃 | Modus ponens 11515, 11516 | |
| 11518 | →→¬𝜃→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→→¬𝜃¬𝜃→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗¬𝜃, 𝜒↗→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃] into ax-2 | |
| 11519 | →→¬𝜃¬𝜃→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃 | Modus ponens 11517, 11518 | |
| 11520 | →→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜃, 𝜒↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 11521 | →→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11508, 11520 | |
| 11522 | →→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1 | |
| 11523 | →¬𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11521, 11522 | |
| 11524 | →→¬𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃, 𝜒↗→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 11525 | →→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11523, 11524 | |
| 11526 | →¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11515, 11525 | |
| 11527 | →→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1 | |
| 11528 | →¬𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11147, 11527 | |
| 11529 | →→¬𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 11530 | →→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11528, 11529 | |
| 11531 | →¬𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11526, 11530 | |
| 11532 | →→¬𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Subs [𝜑↗¬𝜃, 𝜓↗→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2 | |
| 11533 | →→¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11531, 11532 | |
| 11534 | →¬𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃 | Modus ponens 11500, 11533 | |
| 11535 | →→¬𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜃 | Subs [𝜑↗𝜃, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-3 | |
| 11536 | →¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜃 | Modus ponens 11534, 11535 | |
| 11537 | →→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜃 | Subs [𝜑↗→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜃, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃] into ax-1 | |
| 11538 | →⋀𝜑⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜃 | Modus ponens 11536, 11537 | |
| 11539 | →→⋀𝜑⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜃→→⋀𝜑⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃𝜃 | Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗𝜃] into ax-2 | |
| 11540 | →→⋀𝜑⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃𝜃 | Modus ponens 11538, 11539 | |
| 11541 | →⋀𝜑⋀𝜓⋀𝜒𝜃𝜃 | Modus ponens 11159, 11540 | simprrr |
| 11542 | →𝜑→𝜏𝜑 | Subs [𝜓↗𝜏] into ax-1 | |
| 11543 | →→𝜑→𝜏𝜑→⋀⋀𝜑𝜓𝜒→𝜑→𝜏𝜑 | Subs [𝜑↗→𝜑→𝜏𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 11544 | →⋀⋀𝜑𝜓𝜒→𝜑→𝜏𝜑 | Modus ponens 11542, 11543 | |
| 11545 | →→⋀⋀𝜑𝜓𝜒→𝜑→𝜏𝜑→→⋀⋀𝜑𝜓𝜒𝜑→⋀⋀𝜑𝜓𝜒→𝜏𝜑 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑, 𝜒↗→𝜏𝜑] into ax-2 | |
| 11546 | →→⋀⋀𝜑𝜓𝜒𝜑→⋀⋀𝜑𝜓𝜒→𝜏𝜑 | Modus ponens 11544, 11545 | |
| 11547 | →⋀⋀𝜑𝜓𝜒→𝜏𝜑 | Modus ponens simpll, 11546 | |
| 11548 | ↔⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜏] into df-an | |
| 11549 | →¬¬𝜏𝜏 | Subs [𝜑↗𝜏] into notnotr | |
| 11550 | →𝜏→⋀⋀𝜑𝜓𝜒𝜏 | Subs [𝜑↗𝜏, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 11551 | →→𝜏→⋀⋀𝜑𝜓𝜒𝜏→¬¬𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜏 | Subs [𝜑↗→𝜏→⋀⋀𝜑𝜓𝜒𝜏, 𝜓↗¬¬𝜏] into ax-1 | |
| 11552 | →¬¬𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜏 | Modus ponens 11550, 11551 | |
| 11553 | →→¬¬𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜏→→¬¬𝜏𝜏→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜏 | Subs [𝜑↗¬¬𝜏, 𝜓↗𝜏, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜏] into ax-2 | |
| 11554 | →→¬¬𝜏𝜏→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜏 | Modus ponens 11552, 11553 | |
| 11555 | →¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜏 | Modus ponens 11549, 11554 | |
| 11556 | →→⋀⋀𝜑𝜓𝜒→𝜏𝜑→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜏, 𝜒↗𝜑] into ax-2 | |
| 11557 | →→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑 | Modus ponens 11547, 11556 | |
| 11558 | →→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑→¬¬𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑 | Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑, 𝜓↗¬¬𝜏] into ax-1 | |
| 11559 | →¬¬𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑 | Modus ponens 11557, 11558 | |
| 11560 | →→¬¬𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑→→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜏→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜑 | Subs [𝜑↗¬¬𝜏, 𝜓↗→⋀⋀𝜑𝜓𝜒𝜏, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜑] into ax-2 | |
| 11561 | →→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜏→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜑 | Modus ponens 11559, 11560 | |
| 11562 | →¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜑 | Modus ponens 11555, 11561 | |
| 11563 | →⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬¬𝜏] into ax-1 | |
| 11564 | →→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 11565 | →⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒 | Modus ponens 11563, 11564 | |
| 11566 | →→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬𝜏⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 11567 | →→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒 | Modus ponens 11565, 11566 | |
| 11568 | →→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜑→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑 | Subs [𝜑↗¬¬𝜏, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜑] into ax-2 | |
| 11569 | →→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑 | Modus ponens 11562, 11568 | |
| 11570 | →→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑→⋀⋀𝜑𝜓𝜒→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑 | Subs [𝜑↗→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 11571 | →⋀⋀𝜑𝜓𝜒→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑 | Modus ponens 11569, 11570 | |
| 11572 | →→⋀⋀𝜑𝜓𝜒→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑→→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜏⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬𝜏𝜑] into ax-2 | |
| 11573 | →→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑 | Modus ponens 11571, 11572 | |
| 11574 | →⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑 | Modus ponens 11563, 11573 | |
| 11575 | →→𝜑¬¬𝜑→¬¬𝜏→𝜑¬¬𝜑 | Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜏] into ax-1 | |
| 11576 | →¬¬𝜏→𝜑¬¬𝜑 | Modus ponens notnot, 11575 | |
| 11577 | →→¬¬𝜏→𝜑¬¬𝜑→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑 | Subs [𝜑↗¬¬𝜏, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2 | |
| 11578 | →→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑 | Modus ponens 11576, 11577 | |
| 11579 | →→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑→⋀⋀𝜑𝜓𝜒→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑 | Subs [𝜑↗→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 11580 | →⋀⋀𝜑𝜓𝜒→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑 | Modus ponens 11578, 11579 | |
| 11581 | →→⋀⋀𝜑𝜓𝜒→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑→→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜑 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜏𝜑, 𝜒↗→¬¬𝜏¬¬𝜑] into ax-2 | |
| 11582 | →→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜑 | Modus ponens 11580, 11581 | |
| 11583 | →⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜑 | Modus ponens 11574, 11582 | |
| 11584 | →→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏 | Subs [𝜑↗¬𝜏, 𝜓↗¬𝜑] into ax-3 | |
| 11585 | →→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏→⋀⋀𝜑𝜓𝜒→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏 | Subs [𝜑↗→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 11586 | →⋀⋀𝜑𝜓𝜒→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏 | Modus ponens 11584, 11585 | |
| 11587 | →→⋀⋀𝜑𝜓𝜒→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏→→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜑→⋀⋀𝜑𝜓𝜒→¬𝜑¬𝜏 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜏¬¬𝜑, 𝜒↗→¬𝜑¬𝜏] into ax-2 | |
| 11588 | →→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜑→⋀⋀𝜑𝜓𝜒→¬𝜑¬𝜏 | Modus ponens 11586, 11587 | |
| 11589 | →⋀⋀𝜑𝜓𝜒→¬𝜑¬𝜏 | Modus ponens 11583, 11588 | |
| 11590 | →→⋀⋀𝜑𝜓𝜒→¬𝜑¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬𝜑, 𝜒↗¬𝜏] into ax-2 | |
| 11591 | →→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11589, 11590 | |
| 11592 | →→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜑] into ax-1 | |
| 11593 | →¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11591, 11592 | |
| 11594 | →→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜑, 𝜒↗→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2 | |
| 11595 | →→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11593, 11594 | |
| 11596 | →¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 9716, 11595 | |
| 11597 | →¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into id | |
| 11598 | →→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜑] into ax-1 | |
| 11599 | →¬𝜑→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11597, 11598 | |
| 11600 | →¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into notnotr | |
| 11601 | →¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜑] into ax-1 | |
| 11602 | →→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-1 | |
| 11603 | →¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11601, 11602 | |
| 11604 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2 | |
| 11605 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11603, 11604 | |
| 11606 | →¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11600, 11605 | |
| 11607 | →→¬𝜑→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2 | |
| 11608 | →→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11599, 11607 | |
| 11609 | →→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-1 | |
| 11610 | →¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11608, 11609 | |
| 11611 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2 | |
| 11612 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11610, 11611 | |
| 11613 | →¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-1 | |
| 11614 | →→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 11615 | →¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑 | Modus ponens 11613, 11614 | |
| 11616 | →→¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑] into ax-2 | |
| 11617 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑 | Modus ponens 11615, 11616 | |
| 11618 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2 | |
| 11619 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11606, 11618 | |
| 11620 | →→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜑] into ax-1 | |
| 11621 | →¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11619, 11620 | |
| 11622 | →→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑, 𝜒↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2 | |
| 11623 | →→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11621, 11622 | |
| 11624 | →¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11613, 11623 | |
| 11625 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-3 | |
| 11626 | →→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜑] into ax-1 | |
| 11627 | →¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11625, 11626 | |
| 11628 | →→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2 | |
| 11629 | →→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11627, 11628 | |
| 11630 | →¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11624, 11629 | |
| 11631 | →→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2 | |
| 11632 | →→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11630, 11631 | |
| 11633 | →¬𝜑¬¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11596, 11632 | |
| 11634 | →→¬𝜑¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑 | Subs [𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-3 | |
| 11635 | →¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑 | Modus ponens 11633, 11634 | |
| 11636 | →↔⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜏, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into biimp | |
| 11637 | →⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11548, 11636 | |
| 11638 | →→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑→⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑 | Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜏] into ax-1 | |
| 11639 | →⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑 | Modus ponens 11635, 11638 | |
| 11640 | →→⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜑 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜏, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗𝜑] into ax-2 | |
| 11641 | →→⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜑 | Modus ponens 11639, 11640 | |
| 11642 | →⋀⋀⋀𝜑𝜓𝜒𝜏𝜑 | Modus ponens 11637, 11641 | |
| 11643 | →⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜃] into simpl | |
| 11644 | →↔⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏↔¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜏, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into bicom1 | |
| 11645 | ↔¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏 | Modus ponens 11548, 11644 | |
| 11646 | →↔¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏 | Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜏] into biimp | |
| 11647 | →¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏 | Modus ponens 11645, 11646 | |
| 11648 | →→⋀⋀⋀𝜑𝜓𝜒𝜏𝜑→¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜑 | Subs [𝜑↗→⋀⋀⋀𝜑𝜓𝜒𝜏𝜑, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-1 | |
| 11649 | →¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜑 | Modus ponens 11642, 11648 | |
| 11650 | →→¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜑→→¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑 | Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜏, 𝜒↗𝜑] into ax-2 | |
| 11651 | →→¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑 | Modus ponens 11649, 11650 | |
| 11652 | →⋀⋀𝜑𝜓𝜒→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜏] into pm3.2im | |
| 11653 | →→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑→𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑 | Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑, 𝜓↗𝜏] into ax-1 | |
| 11654 | →𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑 | Modus ponens 11635, 11653 | |
| 11655 | →→𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜑 | Subs [𝜑↗𝜏, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗𝜑] into ax-2 | |
| 11656 | →→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜑 | Modus ponens 11654, 11655 | |
| 11657 | →→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜑→⋀⋀𝜑𝜓𝜒→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜑 | Subs [𝜑↗→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 11658 | →⋀⋀𝜑𝜓𝜒→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜑 | Modus ponens 11656, 11657 | |
| 11659 | →→⋀⋀𝜑𝜓𝜒→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜑→→⋀⋀𝜑𝜓𝜒→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀𝜑𝜓𝜒→𝜏𝜑 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗→𝜏𝜑] into ax-2 | |
| 11660 | →→⋀⋀𝜑𝜓𝜒→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀𝜑𝜓𝜒→𝜏𝜑 | Modus ponens 11658, 11659 | |
| 11661 | →𝜏𝜏 | Subs [𝜑↗𝜏] into id | |
| 11662 | →→𝜏→⋀⋀𝜑𝜓𝜒𝜏→𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜏 | Subs [𝜑↗→𝜏→⋀⋀𝜑𝜓𝜒𝜏, 𝜓↗𝜏] into ax-1 | |
| 11663 | →𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜏 | Modus ponens 11550, 11662 | |
| 11664 | →→𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜏→→𝜏𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜏 | Subs [𝜑↗𝜏, 𝜓↗𝜏, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜏] into ax-2 | |
| 11665 | →→𝜏𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜏 | Modus ponens 11663, 11664 | |
| 11666 | →→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑→𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑 | Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑, 𝜓↗𝜏] into ax-1 | |
| 11667 | →𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑 | Modus ponens 11557, 11666 | |
| 11668 | →→𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑→→𝜏→⋀⋀𝜑𝜓𝜒𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜑 | Subs [𝜑↗𝜏, 𝜓↗→⋀⋀𝜑𝜓𝜒𝜏, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜑] into ax-2 | |
| 11669 | →→𝜏→⋀⋀𝜑𝜓𝜒𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜑 | Modus ponens 11667, 11668 | |
| 11670 | →𝜏→⋀⋀𝜑𝜓𝜒𝜑 | Modus ponens 11550, 11669 | |
| 11671 | →⋀⋀𝜑𝜓𝜒→𝜏⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜏] into ax-1 | |
| 11672 | →→⋀⋀𝜑𝜓𝜒→𝜏⋀⋀𝜑𝜓𝜒→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒→𝜏⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗→⋀⋀𝜑𝜓𝜒→𝜏⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 11673 | →⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒→𝜏⋀⋀𝜑𝜓𝜒 | Modus ponens 11671, 11672 | |
| 11674 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒→𝜏⋀⋀𝜑𝜓𝜒→→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀𝜑𝜓𝜒→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜏⋀⋀𝜑𝜓𝜒] into ax-2 | |
| 11675 | →→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀𝜑𝜓𝜒→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀𝜑𝜓𝜒 | Modus ponens 11673, 11674 | |
| 11676 | →⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀𝜑𝜓𝜒 | Modus ponens 11643, 11675 | |
| 11677 | →→𝜏→⋀⋀𝜑𝜓𝜒𝜑→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜑 | Subs [𝜑↗𝜏, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜑] into ax-2 | |
| 11678 | →→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜑 | Modus ponens 11670, 11677 | |
| 11679 | →→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜑 | Subs [𝜑↗→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 11680 | →⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜑 | Modus ponens 11678, 11679 | |
| 11681 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀𝜑𝜓𝜒→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→𝜏⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜏𝜑] into ax-2 | |
| 11682 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀𝜑𝜓𝜒→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑 | Modus ponens 11680, 11681 | |
| 11683 | →⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑 | Modus ponens 11676, 11682 | |
| 11684 | →𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Subs [𝜑↗𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 11685 | →→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Subs [𝜑↗→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜏] into ax-1 | |
| 11686 | →𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Modus ponens 11684, 11685 | |
| 11687 | →→𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜏𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Subs [𝜑↗𝜏, 𝜓↗𝜏, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-2 | |
| 11688 | →→𝜏𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Modus ponens 11686, 11687 | |
| 11689 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜏, 𝜒↗𝜑] into ax-2 | |
| 11690 | →→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Modus ponens 11683, 11689 | |
| 11691 | →→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑, 𝜓↗𝜏] into ax-1 | |
| 11692 | →𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Modus ponens 11690, 11691 | |
| 11693 | →→𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Subs [𝜑↗𝜏, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑] into ax-2 | |
| 11694 | →→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Modus ponens 11692, 11693 | |
| 11695 | →𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Modus ponens 11684, 11694 | |
| 11696 | →⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀⋀𝜑𝜓𝜒𝜃 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃] into id | |
| 11697 | →⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜏] into ax-1 | |
| 11698 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃 | Subs [𝜑↗→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 11699 | →⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃 | Modus ponens 11697, 11698 | |
| 11700 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-2 | |
| 11701 | →→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃 | Modus ponens 11699, 11700 | |
| 11702 | →→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑 | Subs [𝜑↗𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗𝜑] into ax-2 | |
| 11703 | →→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑 | Modus ponens 11695, 11702 | |
| 11704 | →→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑 | Subs [𝜑↗→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 11705 | →⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑 | Modus ponens 11703, 11704 | |
| 11706 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→𝜏𝜑] into ax-2 | |
| 11707 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑 | Modus ponens 11705, 11706 | |
| 11708 | ↔⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜏] into df-an | |
| 11709 | →→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Subs [𝜑↗→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬¬𝜏] into ax-1 | |
| 11710 | →¬¬𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Modus ponens 11684, 11709 | |
| 11711 | →→¬¬𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜏𝜏→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Subs [𝜑↗¬¬𝜏, 𝜓↗𝜏, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-2 | |
| 11712 | →→¬¬𝜏𝜏→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Modus ponens 11710, 11711 | |
| 11713 | →¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Modus ponens 11549, 11712 | |
| 11714 | →→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→¬¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑, 𝜓↗¬¬𝜏] into ax-1 | |
| 11715 | →¬¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Modus ponens 11690, 11714 | |
| 11716 | →→¬¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Subs [𝜑↗¬¬𝜏, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑] into ax-2 | |
| 11717 | →→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Modus ponens 11715, 11716 | |
| 11718 | →¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Modus ponens 11713, 11717 | |
| 11719 | →⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬¬𝜏] into ax-1 | |
| 11720 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃 | Subs [𝜑↗→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 11721 | →⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃 | Modus ponens 11719, 11720 | |
| 11722 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-2 | |
| 11723 | →→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃 | Modus ponens 11721, 11722 | |
| 11724 | →→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑 | Subs [𝜑↗¬¬𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗𝜑] into ax-2 | |
| 11725 | →→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑 | Modus ponens 11718, 11724 | |
| 11726 | →→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑 | Subs [𝜑↗→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 11727 | →⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑 | Modus ponens 11725, 11726 | |
| 11728 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→¬¬𝜏𝜑] into ax-2 | |
| 11729 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑 | Modus ponens 11727, 11728 | |
| 11730 | →⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑 | Modus ponens 11719, 11729 | |
| 11731 | →→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑 | Subs [𝜑↗→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 11732 | →⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑 | Modus ponens 11578, 11731 | |
| 11733 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜑 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜏𝜑, 𝜒↗→¬¬𝜏¬¬𝜑] into ax-2 | |
| 11734 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜑 | Modus ponens 11732, 11733 | |
| 11735 | →⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜑 | Modus ponens 11730, 11734 | |
| 11736 | →→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏 | Subs [𝜑↗→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 11737 | →⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏 | Modus ponens 11584, 11736 | |
| 11738 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜑¬𝜏 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜏¬¬𝜑, 𝜒↗→¬𝜑¬𝜏] into ax-2 | |
| 11739 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜑¬𝜏 | Modus ponens 11737, 11738 | |
| 11740 | →⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜑¬𝜏 | Modus ponens 11735, 11739 | |
| 11741 | →¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 11742 | →→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 11743 | →¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑 | Modus ponens 11741, 11742 | |
| 11744 | →→¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑] into ax-2 | |
| 11745 | →→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑 | Modus ponens 11743, 11744 | |
| 11746 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜑¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬𝜑, 𝜒↗¬𝜏] into ax-2 | |
| 11747 | →→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11740, 11746 | |
| 11748 | →→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜑] into ax-1 | |
| 11749 | →¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11747, 11748 | |
| 11750 | →→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2 | |
| 11751 | →→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11749, 11750 | |
| 11752 | →¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11741, 11751 | |
| 11753 | →¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into id | |
| 11754 | →→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜑] into ax-1 | |
| 11755 | →¬𝜑→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11753, 11754 | |
| 11756 | →¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into notnotr | |
| 11757 | →¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜑] into ax-1 | |
| 11758 | →→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-1 | |
| 11759 | →¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11757, 11758 | |
| 11760 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2 | |
| 11761 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11759, 11760 | |
| 11762 | →¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11756, 11761 | |
| 11763 | →→¬𝜑→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2 | |
| 11764 | →→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11755, 11763 | |
| 11765 | →→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-1 | |
| 11766 | →¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11764, 11765 | |
| 11767 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2 | |
| 11768 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11766, 11767 | |
| 11769 | →¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-1 | |
| 11770 | →→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 11771 | →¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑 | Modus ponens 11769, 11770 | |
| 11772 | →→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑] into ax-2 | |
| 11773 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑 | Modus ponens 11771, 11772 | |
| 11774 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2 | |
| 11775 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11762, 11774 | |
| 11776 | →→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜑] into ax-1 | |
| 11777 | →¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11775, 11776 | |
| 11778 | →→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2 | |
| 11779 | →→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11777, 11778 | |
| 11780 | →¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11769, 11779 | |
| 11781 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-3 | |
| 11782 | →→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜑] into ax-1 | |
| 11783 | →¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11781, 11782 | |
| 11784 | →→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2 | |
| 11785 | →→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11783, 11784 | |
| 11786 | →¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11780, 11785 | |
| 11787 | →→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2 | |
| 11788 | →→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11786, 11787 | |
| 11789 | →¬𝜑¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11752, 11788 | |
| 11790 | →→¬𝜑¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜑 | Subs [𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-3 | |
| 11791 | →¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜑 | Modus ponens 11789, 11790 | |
| 11792 | →↔⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into biimp | |
| 11793 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11708, 11792 | |
| 11794 | →→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜑 | Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 11795 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜑 | Modus ponens 11791, 11794 | |
| 11796 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗𝜑] into ax-2 | |
| 11797 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Modus ponens 11795, 11796 | |
| 11798 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Modus ponens 11793, 11797 | simp-4l |
| 11799 | →𝜓→𝜏𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜏] into ax-1 | |
| 11800 | →→𝜓→𝜏𝜓→⋀⋀𝜑𝜓𝜒→𝜓→𝜏𝜓 | Subs [𝜑↗→𝜓→𝜏𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 11801 | →⋀⋀𝜑𝜓𝜒→𝜓→𝜏𝜓 | Modus ponens 11799, 11800 | |
| 11802 | →→⋀⋀𝜑𝜓𝜒→𝜓→𝜏𝜓→→⋀⋀𝜑𝜓𝜒𝜓→⋀⋀𝜑𝜓𝜒→𝜏𝜓 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜏𝜓] into ax-2 | |
| 11803 | →→⋀⋀𝜑𝜓𝜒𝜓→⋀⋀𝜑𝜓𝜒→𝜏𝜓 | Modus ponens 11801, 11802 | |
| 11804 | →⋀⋀𝜑𝜓𝜒→𝜏𝜓 | Modus ponens simplr, 11803 | |
| 11805 | →→⋀⋀𝜑𝜓𝜒→𝜏𝜓→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜏, 𝜒↗𝜓] into ax-2 | |
| 11806 | →→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓 | Modus ponens 11804, 11805 | |
| 11807 | →→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓→¬¬𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓 | Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓, 𝜓↗¬¬𝜏] into ax-1 | |
| 11808 | →¬¬𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓 | Modus ponens 11806, 11807 | |
| 11809 | →→¬¬𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓→→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜏→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜓 | Subs [𝜑↗¬¬𝜏, 𝜓↗→⋀⋀𝜑𝜓𝜒𝜏, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜓] into ax-2 | |
| 11810 | →→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜏→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜓 | Modus ponens 11808, 11809 | |
| 11811 | →¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜓 | Modus ponens 11555, 11810 | |
| 11812 | →→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜓→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓 | Subs [𝜑↗¬¬𝜏, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜓] into ax-2 | |
| 11813 | →→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓 | Modus ponens 11811, 11812 | |
| 11814 | →→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓→⋀⋀𝜑𝜓𝜒→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓 | Subs [𝜑↗→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 11815 | →⋀⋀𝜑𝜓𝜒→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓 | Modus ponens 11813, 11814 | |
| 11816 | →→⋀⋀𝜑𝜓𝜒→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓→→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜏⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬𝜏𝜓] into ax-2 | |
| 11817 | →→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓 | Modus ponens 11815, 11816 | |
| 11818 | →⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓 | Modus ponens 11563, 11817 | |
| 11819 | →→𝜓¬¬𝜓→¬¬𝜏→𝜓¬¬𝜓 | Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜏] into ax-1 | |
| 11820 | →¬¬𝜏→𝜓¬¬𝜓 | Modus ponens 448, 11819 | |
| 11821 | →→¬¬𝜏→𝜓¬¬𝜓→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓 | Subs [𝜑↗¬¬𝜏, 𝜒↗¬¬𝜓] into ax-2 | |
| 11822 | →→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓 | Modus ponens 11820, 11821 | |
| 11823 | →→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓→⋀⋀𝜑𝜓𝜒→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓 | Subs [𝜑↗→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 11824 | →⋀⋀𝜑𝜓𝜒→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓 | Modus ponens 11822, 11823 | |
| 11825 | →→⋀⋀𝜑𝜓𝜒→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓→→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜓 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜏𝜓, 𝜒↗→¬¬𝜏¬¬𝜓] into ax-2 | |
| 11826 | →→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜓 | Modus ponens 11824, 11825 | |
| 11827 | →⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜓 | Modus ponens 11818, 11826 | |
| 11828 | →→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏 | Subs [𝜑↗¬𝜏, 𝜓↗¬𝜓] into ax-3 | |
| 11829 | →→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏→⋀⋀𝜑𝜓𝜒→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏 | Subs [𝜑↗→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 11830 | →⋀⋀𝜑𝜓𝜒→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏 | Modus ponens 11828, 11829 | |
| 11831 | →→⋀⋀𝜑𝜓𝜒→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏→→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜓→⋀⋀𝜑𝜓𝜒→¬𝜓¬𝜏 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜏¬¬𝜓, 𝜒↗→¬𝜓¬𝜏] into ax-2 | |
| 11832 | →→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜓→⋀⋀𝜑𝜓𝜒→¬𝜓¬𝜏 | Modus ponens 11830, 11831 | |
| 11833 | →⋀⋀𝜑𝜓𝜒→¬𝜓¬𝜏 | Modus ponens 11827, 11832 | |
| 11834 | →→⋀⋀𝜑𝜓𝜒→¬𝜓¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬𝜓, 𝜒↗¬𝜏] into ax-2 | |
| 11835 | →→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11833, 11834 | |
| 11836 | →→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜓] into ax-1 | |
| 11837 | →¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11835, 11836 | |
| 11838 | →→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜓, 𝜒↗→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2 | |
| 11839 | →→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11837, 11838 | |
| 11840 | →¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 9916, 11839 | |
| 11841 | →→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜓] into ax-1 | |
| 11842 | →¬𝜓→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11597, 11841 | |
| 11843 | →¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜓] into ax-1 | |
| 11844 | →→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-1 | |
| 11845 | →¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11843, 11844 | |
| 11846 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2 | |
| 11847 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11845, 11846 | |
| 11848 | →¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11600, 11847 | |
| 11849 | →→¬𝜓→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2 | |
| 11850 | →→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11842, 11849 | |
| 11851 | →→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-1 | |
| 11852 | →¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11850, 11851 | |
| 11853 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2 | |
| 11854 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11852, 11853 | |
| 11855 | →¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-1 | |
| 11856 | →→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 11857 | →¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓 | Modus ponens 11855, 11856 | |
| 11858 | →→¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓] into ax-2 | |
| 11859 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓 | Modus ponens 11857, 11858 | |
| 11860 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2 | |
| 11861 | →→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11848, 11860 | |
| 11862 | →→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜓] into ax-1 | |
| 11863 | →¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11861, 11862 | |
| 11864 | →→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓, 𝜒↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2 | |
| 11865 | →→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11863, 11864 | |
| 11866 | →¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11855, 11865 | |
| 11867 | →→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜓] into ax-1 | |
| 11868 | →¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11625, 11867 | |
| 11869 | →→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2 | |
| 11870 | →→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11868, 11869 | |
| 11871 | →¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11866, 11870 | |
| 11872 | →→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2 | |
| 11873 | →→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11871, 11872 | |
| 11874 | →¬𝜓¬¬→⋀⋀𝜑𝜓𝜒¬𝜏 | Modus ponens 11840, 11873 | |
| 11875 | →→¬𝜓¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-3 | |
| 11876 | →¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓 | Modus ponens 11874, 11875 | |
| 11877 | →→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓→⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓 | Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜏] into ax-1 | |
| 11878 | →⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓 | Modus ponens 11876, 11877 | |
| 11879 | →→⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜓 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜏, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗𝜓] into ax-2 | |
| 11880 | →→⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜓 | Modus ponens 11878, 11879 | |
| 11881 | →⋀⋀⋀𝜑𝜓𝜒𝜏𝜓 | Modus ponens 11637, 11880 | |
| 11882 | →→⋀⋀⋀𝜑𝜓𝜒𝜏𝜓→¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜓 | Subs [𝜑↗→⋀⋀⋀𝜑𝜓𝜒𝜏𝜓, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-1 | |
| 11883 | →¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜓 | Modus ponens 11881, 11882 | |
| 11884 | →→¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜓→→¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓 | Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜏, 𝜒↗𝜓] into ax-2 | |
| 11885 | →→¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓 | Modus ponens 11883, 11884 | |
| 11886 | →→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓→𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓 | Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓, 𝜓↗𝜏] into ax-1 | |
| 11887 | →𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓 | Modus ponens 11876, 11886 | |
| 11888 | →→𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜓 | Subs [𝜑↗𝜏, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗𝜓] into ax-2 | |
| 11889 | →→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜓 | Modus ponens 11887, 11888 | |
| 11890 | →→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜓→⋀⋀𝜑𝜓𝜒→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜓 | Subs [𝜑↗→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 11891 | →⋀⋀𝜑𝜓𝜒→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜓 | Modus ponens 11889, 11890 | |
| 11892 | →→⋀⋀𝜑𝜓𝜒→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜓→→⋀⋀𝜑𝜓𝜒→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀𝜑𝜓𝜒→𝜏𝜓 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗→𝜏𝜓] into ax-2 | |
| 11893 | →→⋀⋀𝜑𝜓𝜒→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀𝜑𝜓𝜒→𝜏𝜓 | Modus ponens 11891, 11892 | |
| 11894 | →→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓→𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓 | Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓, 𝜓↗𝜏] into ax-1 | |
| 11895 | →𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓 | Modus ponens 11806, 11894 | |
| 11896 | →→𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓→→𝜏→⋀⋀𝜑𝜓𝜒𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜓 | Subs [𝜑↗𝜏, 𝜓↗→⋀⋀𝜑𝜓𝜒𝜏, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜓] into ax-2 | |
| 11897 | →→𝜏→⋀⋀𝜑𝜓𝜒𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜓 | Modus ponens 11895, 11896 | |
| 11898 | →𝜏→⋀⋀𝜑𝜓𝜒𝜓 | Modus ponens 11550, 11897 | |
| 11899 | →→𝜏→⋀⋀𝜑𝜓𝜒𝜓→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜓 | Subs [𝜑↗𝜏, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜓] into ax-2 | |
| 11900 | →→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜓 | Modus ponens 11898, 11899 | |
| 11901 | →→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜓 | Subs [𝜑↗→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 11902 | →⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜓 | Modus ponens 11900, 11901 | |
| 11903 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀𝜑𝜓𝜒→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→𝜏⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜏𝜓] into ax-2 | |
| 11904 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀𝜑𝜓𝜒→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓 | Modus ponens 11902, 11903 | |
| 11905 | →⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓 | Modus ponens 11676, 11904 | |
| 11906 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜏, 𝜒↗𝜓] into ax-2 | |
| 11907 | →→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Modus ponens 11905, 11906 | |
| 11908 | →→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓, 𝜓↗𝜏] into ax-1 | |
| 11909 | →𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Modus ponens 11907, 11908 | |
| 11910 | →→𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Subs [𝜑↗𝜏, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓] into ax-2 | |
| 11911 | →→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Modus ponens 11909, 11910 | |
| 11912 | →𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Modus ponens 11684, 11911 | |
| 11913 | →→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓 | Subs [𝜑↗𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗𝜓] into ax-2 | |
| 11914 | →→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓 | Modus ponens 11912, 11913 | |
| 11915 | →→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓 | Subs [𝜑↗→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 11916 | →⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓 | Modus ponens 11914, 11915 | |
| 11917 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→𝜏𝜓] into ax-2 | |
| 11918 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓 | Modus ponens 11916, 11917 | |
| 11919 | →→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→¬¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓, 𝜓↗¬¬𝜏] into ax-1 | |
| 11920 | →¬¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Modus ponens 11907, 11919 | |
| 11921 | →→¬¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Subs [𝜑↗¬¬𝜏, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓] into ax-2 | |
| 11922 | →→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Modus ponens 11920, 11921 | |
| 11923 | →¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Modus ponens 11713, 11922 | |
| 11924 | →→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓 | Subs [𝜑↗¬¬𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗𝜓] into ax-2 | |
| 11925 | →→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓 | Modus ponens 11923, 11924 | |
| 11926 | →→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓 | Subs [𝜑↗→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 11927 | →⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓 | Modus ponens 11925, 11926 | |
| 11928 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→¬¬𝜏𝜓] into ax-2 | |
| 11929 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓 | Modus ponens 11927, 11928 | |
| 11930 | →⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓 | Modus ponens 11719, 11929 | |
| 11931 | →→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓 | Subs [𝜑↗→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 11932 | →⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓 | Modus ponens 11822, 11931 | |
| 11933 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜓 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜏𝜓, 𝜒↗→¬¬𝜏¬¬𝜓] into ax-2 | |
| 11934 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜓 | Modus ponens 11932, 11933 | |
| 11935 | →⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜓 | Modus ponens 11930, 11934 | |
| 11936 | →→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏 | Subs [𝜑↗→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 11937 | →⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏 | Modus ponens 11828, 11936 | |
| 11938 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜓¬𝜏 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜏¬¬𝜓, 𝜒↗→¬𝜓¬𝜏] into ax-2 | |
| 11939 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜓¬𝜏 | Modus ponens 11937, 11938 | |
| 11940 | →⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜓¬𝜏 | Modus ponens 11935, 11939 | |
| 11941 | →¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 11942 | →→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓 | Subs [𝜑↗→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 11943 | →¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓 | Modus ponens 11941, 11942 | |
| 11944 | →→¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓] into ax-2 | |
| 11945 | →→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓 | Modus ponens 11943, 11944 | |
| 11946 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜓¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬𝜓, 𝜒↗¬𝜏] into ax-2 | |
| 11947 | →→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11940, 11946 | |
| 11948 | →→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜓] into ax-1 | |
| 11949 | →¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11947, 11948 | |
| 11950 | →→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2 | |
| 11951 | →→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11949, 11950 | |
| 11952 | →¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11941, 11951 | |
| 11953 | →→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜓] into ax-1 | |
| 11954 | →¬𝜓→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11753, 11953 | |
| 11955 | →¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜓] into ax-1 | |
| 11956 | →→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-1 | |
| 11957 | →¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11955, 11956 | |
| 11958 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2 | |
| 11959 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11957, 11958 | |
| 11960 | →¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11756, 11959 | |
| 11961 | →→¬𝜓→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2 | |
| 11962 | →→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11954, 11961 | |
| 11963 | →→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-1 | |
| 11964 | →¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11962, 11963 | |
| 11965 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2 | |
| 11966 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11964, 11965 | |
| 11967 | →¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-1 | |
| 11968 | →→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 11969 | →¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓 | Modus ponens 11967, 11968 | |
| 11970 | →→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓] into ax-2 | |
| 11971 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓 | Modus ponens 11969, 11970 | |
| 11972 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2 | |
| 11973 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11960, 11972 | |
| 11974 | →→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜓] into ax-1 | |
| 11975 | →¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11973, 11974 | |
| 11976 | →→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2 | |
| 11977 | →→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11975, 11976 | |
| 11978 | →¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11967, 11977 | |
| 11979 | →→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜓] into ax-1 | |
| 11980 | →¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11781, 11979 | |
| 11981 | →→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2 | |
| 11982 | →→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11980, 11981 | |
| 11983 | →¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11978, 11982 | |
| 11984 | →→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2 | |
| 11985 | →→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11983, 11984 | |
| 11986 | →¬𝜓¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏 | Modus ponens 11952, 11985 | |
| 11987 | →→¬𝜓¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-3 | |
| 11988 | →¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜓 | Modus ponens 11986, 11987 | |
| 11989 | →→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜓 | Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 11990 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜓 | Modus ponens 11988, 11989 | |
| 11991 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗𝜓] into ax-2 | |
| 11992 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Modus ponens 11990, 11991 | |
| 11993 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Modus ponens 11793, 11992 | simp-4r |
| 11994 | →→𝜑→𝜃𝜑→⋀⋀𝜑𝜓𝜒→𝜑→𝜃𝜑 | Subs [𝜑↗→𝜑→𝜃𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 11995 | →⋀⋀𝜑𝜓𝜒→𝜑→𝜃𝜑 | Modus ponens 9518, 11994 | |
| 11996 | →→⋀⋀𝜑𝜓𝜒→𝜑→𝜃𝜑→→⋀⋀𝜑𝜓𝜒𝜑→⋀⋀𝜑𝜓𝜒→𝜃𝜑 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑, 𝜒↗→𝜃𝜑] into ax-2 | |
| 11997 | →→⋀⋀𝜑𝜓𝜒𝜑→⋀⋀𝜑𝜓𝜒→𝜃𝜑 | Modus ponens 11995, 11996 | |
| 11998 | →𝜑→𝜂𝜑 | Subs [𝜓↗𝜂] into ax-1 | |
| 11999 | →→𝜑→𝜂𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜑→𝜂𝜑 | Subs [𝜑↗→𝜑→𝜂𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 12000 | →⋀⋀⋀𝜑𝜓𝜒𝜃→𝜑→𝜂𝜑 | Modus ponens 11998, 11999 | |
| 12001 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜑→𝜂𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜑, 𝜒↗→𝜂𝜑] into ax-2 | |
| 12002 | →→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑 | Modus ponens 12000, 12001 | |
| 12003 | →⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑 | Modus ponens simplll, 12002 | |
| 12004 | ↔⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜂] into df-an | |
| 12005 | →¬¬𝜂𝜂 | Subs [𝜑↗𝜂] into notnotr | |
| 12006 | →𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂 | Subs [𝜑↗𝜂, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 12007 | →→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬¬𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂 | Subs [𝜑↗→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜓↗¬¬𝜂] into ax-1 | |
| 12008 | →¬¬𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂 | Modus ponens 12006, 12007 | |
| 12009 | →→¬¬𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→→¬¬𝜂𝜂→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂 | Subs [𝜑↗¬¬𝜂, 𝜓↗𝜂, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂] into ax-2 | |
| 12010 | →→¬¬𝜂𝜂→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂 | Modus ponens 12008, 12009 | |
| 12011 | →¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂 | Modus ponens 12005, 12010 | |
| 12012 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜂, 𝜒↗𝜑] into ax-2 | |
| 12013 | →→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Modus ponens 12003, 12012 | |
| 12014 | →→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→¬¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑, 𝜓↗¬¬𝜂] into ax-1 | |
| 12015 | →¬¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Modus ponens 12013, 12014 | |
| 12016 | →→¬¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Subs [𝜑↗¬¬𝜂, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑] into ax-2 | |
| 12017 | →→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Modus ponens 12015, 12016 | |
| 12018 | →¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Modus ponens 12011, 12017 | |
| 12019 | →⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬¬𝜂] into ax-1 | |
| 12020 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃 | Subs [𝜑↗→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 12021 | →⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃 | Modus ponens 12019, 12020 | |
| 12022 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-2 | |
| 12023 | →→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃 | Modus ponens 12021, 12022 | |
| 12024 | →→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑 | Subs [𝜑↗¬¬𝜂, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗𝜑] into ax-2 | |
| 12025 | →→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑 | Modus ponens 12018, 12024 | |
| 12026 | →→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑 | Subs [𝜑↗→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 12027 | →⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑 | Modus ponens 12025, 12026 | |
| 12028 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→¬¬𝜂𝜑] into ax-2 | |
| 12029 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑 | Modus ponens 12027, 12028 | |
| 12030 | →⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑 | Modus ponens 12019, 12029 | |
| 12031 | →→𝜑¬¬𝜑→¬¬𝜂→𝜑¬¬𝜑 | Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜂] into ax-1 | |
| 12032 | →¬¬𝜂→𝜑¬¬𝜑 | Modus ponens notnot, 12031 | |
| 12033 | →→¬¬𝜂→𝜑¬¬𝜑→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑 | Subs [𝜑↗¬¬𝜂, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2 | |
| 12034 | →→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑 | Modus ponens 12032, 12033 | |
| 12035 | →→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑 | Subs [𝜑↗→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 12036 | →⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑 | Modus ponens 12034, 12035 | |
| 12037 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜑 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜂𝜑, 𝜒↗→¬¬𝜂¬¬𝜑] into ax-2 | |
| 12038 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜑 | Modus ponens 12036, 12037 | |
| 12039 | →⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜑 | Modus ponens 12030, 12038 | |
| 12040 | →→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂 | Subs [𝜑↗¬𝜂, 𝜓↗¬𝜑] into ax-3 | |
| 12041 | →→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂 | Subs [𝜑↗→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 12042 | →⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂 | Modus ponens 12040, 12041 | |
| 12043 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜑¬𝜂 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜂¬¬𝜑, 𝜒↗→¬𝜑¬𝜂] into ax-2 | |
| 12044 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜑¬𝜂 | Modus ponens 12042, 12043 | |
| 12045 | →⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜑¬𝜂 | Modus ponens 12039, 12044 | |
| 12046 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜑¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬𝜑, 𝜒↗¬𝜂] into ax-2 | |
| 12047 | →→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12045, 12046 | |
| 12048 | →→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜑] into ax-1 | |
| 12049 | →¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12047, 12048 | |
| 12050 | →→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2 | |
| 12051 | →→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12049, 12050 | |
| 12052 | →¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 11741, 12051 | |
| 12053 | →¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into id | |
| 12054 | →→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜑] into ax-1 | |
| 12055 | →¬𝜑→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12053, 12054 | |
| 12056 | →¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into notnotr | |
| 12057 | →¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜑] into ax-1 | |
| 12058 | →→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-1 | |
| 12059 | →¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12057, 12058 | |
| 12060 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2 | |
| 12061 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12059, 12060 | |
| 12062 | →¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12056, 12061 | |
| 12063 | →→¬𝜑→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2 | |
| 12064 | →→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12055, 12063 | |
| 12065 | →→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-1 | |
| 12066 | →¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12064, 12065 | |
| 12067 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2 | |
| 12068 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12066, 12067 | |
| 12069 | →¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-1 | |
| 12070 | →→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 12071 | →¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑 | Modus ponens 12069, 12070 | |
| 12072 | →→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑] into ax-2 | |
| 12073 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑 | Modus ponens 12071, 12072 | |
| 12074 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2 | |
| 12075 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12062, 12074 | |
| 12076 | →→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜑] into ax-1 | |
| 12077 | →¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12075, 12076 | |
| 12078 | →→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2 | |
| 12079 | →→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12077, 12078 | |
| 12080 | →¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12069, 12079 | |
| 12081 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-3 | |
| 12082 | →→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜑] into ax-1 | |
| 12083 | →¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12081, 12082 | |
| 12084 | →→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2 | |
| 12085 | →→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12083, 12084 | |
| 12086 | →¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12080, 12085 | |
| 12087 | →→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2 | |
| 12088 | →→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12086, 12087 | |
| 12089 | →¬𝜑¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12052, 12088 | |
| 12090 | →→¬𝜑¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑 | Subs [𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-3 | |
| 12091 | →¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑 | Modus ponens 12089, 12090 | |
| 12092 | →↔⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into biimp | |
| 12093 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12004, 12092 | |
| 12094 | →→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑 | Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂] into ax-1 | |
| 12095 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑 | Modus ponens 12091, 12094 | |
| 12096 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜑 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗𝜑] into ax-2 | |
| 12097 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜑 | Modus ponens 12095, 12096 | |
| 12098 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜑 | Modus ponens 12093, 12097 | |
| 12099 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀𝜑𝜓𝜒𝜃 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜏] into simpl | |
| 12100 | →↔⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂↔¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into bicom1 | |
| 12101 | ↔¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂 | Modus ponens 12004, 12100 | |
| 12102 | →↔¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂 | Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂] into biimp | |
| 12103 | →¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂 | Modus ponens 12101, 12102 | |
| 12104 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜑→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜑 | Subs [𝜑↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜑, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-1 | |
| 12105 | →¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜑 | Modus ponens 12098, 12104 | |
| 12106 | →→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜑→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑 | Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜒↗𝜑] into ax-2 | |
| 12107 | →→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑 | Modus ponens 12105, 12106 | |
| 12108 | →⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜂] into pm3.2im | |
| 12109 | →→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑→𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑 | Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑, 𝜓↗𝜂] into ax-1 | |
| 12110 | →𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑 | Modus ponens 12091, 12109 | |
| 12111 | →→𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜑 | Subs [𝜑↗𝜂, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗𝜑] into ax-2 | |
| 12112 | →→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜑 | Modus ponens 12110, 12111 | |
| 12113 | →→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜑 | Subs [𝜑↗→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 12114 | →⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜑 | Modus ponens 12112, 12113 | |
| 12115 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗→𝜂𝜑] into ax-2 | |
| 12116 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑 | Modus ponens 12114, 12115 | |
| 12117 | →𝜂𝜂 | Subs [𝜑↗𝜂] into id | |
| 12118 | →→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂 | Subs [𝜑↗→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜓↗𝜂] into ax-1 | |
| 12119 | →𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂 | Modus ponens 12006, 12118 | |
| 12120 | →→𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→→𝜂𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂 | Subs [𝜑↗𝜂, 𝜓↗𝜂, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂] into ax-2 | |
| 12121 | →→𝜂𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂 | Modus ponens 12119, 12120 | |
| 12122 | →→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑, 𝜓↗𝜂] into ax-1 | |
| 12123 | →𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Modus ponens 12013, 12122 | |
| 12124 | →→𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Subs [𝜑↗𝜂, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑] into ax-2 | |
| 12125 | →→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Modus ponens 12123, 12124 | |
| 12126 | →𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑 | Modus ponens 12006, 12125 | |
| 12127 | →⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜂] into ax-1 | |
| 12128 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃 | Subs [𝜑↗→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12129 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃 | Modus ponens 12127, 12128 | |
| 12130 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-2 | |
| 12131 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃 | Modus ponens 12129, 12130 | |
| 12132 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃 | Modus ponens 12099, 12131 | |
| 12133 | →→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑 | Subs [𝜑↗𝜂, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗𝜑] into ax-2 | |
| 12134 | →→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑 | Modus ponens 12126, 12133 | |
| 12135 | →→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑 | Subs [𝜑↗→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12136 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑 | Modus ponens 12134, 12135 | |
| 12137 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→𝜂𝜑] into ax-2 | |
| 12138 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑 | Modus ponens 12136, 12137 | |
| 12139 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑 | Modus ponens 12132, 12138 | |
| 12140 | →𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Subs [𝜑↗𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12141 | →→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Subs [𝜑↗→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜂] into ax-1 | |
| 12142 | →𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Modus ponens 12140, 12141 | |
| 12143 | →→𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜂𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Subs [𝜑↗𝜂, 𝜓↗𝜂, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-2 | |
| 12144 | →→𝜂𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Modus ponens 12142, 12143 | |
| 12145 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜂, 𝜒↗𝜑] into ax-2 | |
| 12146 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Modus ponens 12139, 12145 | |
| 12147 | →→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑, 𝜓↗𝜂] into ax-1 | |
| 12148 | →𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Modus ponens 12146, 12147 | |
| 12149 | →→𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Subs [𝜑↗𝜂, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑] into ax-2 | |
| 12150 | →→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Modus ponens 12148, 12149 | |
| 12151 | →𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Modus ponens 12140, 12150 | |
| 12152 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into id | |
| 12153 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜂] into ax-1 | |
| 12154 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Subs [𝜑↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12155 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Modus ponens 12153, 12154 | |
| 12156 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-2 | |
| 12157 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Modus ponens 12155, 12156 | |
| 12158 | →→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑 | Subs [𝜑↗𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗𝜑] into ax-2 | |
| 12159 | →→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑 | Modus ponens 12151, 12158 | |
| 12160 | →→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑 | Subs [𝜑↗→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12161 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑 | Modus ponens 12159, 12160 | |
| 12162 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→𝜂𝜑] into ax-2 | |
| 12163 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑 | Modus ponens 12161, 12162 | |
| 12164 | ↔⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜂] into df-an | |
| 12165 | →→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Subs [𝜑↗→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬¬𝜂] into ax-1 | |
| 12166 | →¬¬𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Modus ponens 12140, 12165 | |
| 12167 | →→¬¬𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜂𝜂→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Subs [𝜑↗¬¬𝜂, 𝜓↗𝜂, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-2 | |
| 12168 | →→¬¬𝜂𝜂→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Modus ponens 12166, 12167 | |
| 12169 | →¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Modus ponens 12005, 12168 | |
| 12170 | →→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→¬¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑, 𝜓↗¬¬𝜂] into ax-1 | |
| 12171 | →¬¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Modus ponens 12146, 12170 | |
| 12172 | →→¬¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Subs [𝜑↗¬¬𝜂, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑] into ax-2 | |
| 12173 | →→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Modus ponens 12171, 12172 | |
| 12174 | →¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Modus ponens 12169, 12173 | |
| 12175 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬¬𝜂] into ax-1 | |
| 12176 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Subs [𝜑↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12177 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Modus ponens 12175, 12176 | |
| 12178 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-2 | |
| 12179 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Modus ponens 12177, 12178 | |
| 12180 | →→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑 | Subs [𝜑↗¬¬𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗𝜑] into ax-2 | |
| 12181 | →→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑 | Modus ponens 12174, 12180 | |
| 12182 | →→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑 | Subs [𝜑↗→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12183 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑 | Modus ponens 12181, 12182 | |
| 12184 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→¬¬𝜂𝜑] into ax-2 | |
| 12185 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑 | Modus ponens 12183, 12184 | |
| 12186 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑 | Modus ponens 12175, 12185 | |
| 12187 | →→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑 | Subs [𝜑↗→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12188 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑 | Modus ponens 12034, 12187 | |
| 12189 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜑 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜂𝜑, 𝜒↗→¬¬𝜂¬¬𝜑] into ax-2 | |
| 12190 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜑 | Modus ponens 12188, 12189 | |
| 12191 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜑 | Modus ponens 12186, 12190 | |
| 12192 | →→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂 | Subs [𝜑↗→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12193 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂 | Modus ponens 12040, 12192 | |
| 12194 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜑¬𝜂 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜂¬¬𝜑, 𝜒↗→¬𝜑¬𝜂] into ax-2 | |
| 12195 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜑¬𝜂 | Modus ponens 12193, 12194 | |
| 12196 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜑¬𝜂 | Modus ponens 12191, 12195 | |
| 12197 | →¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12198 | →→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑 | Subs [𝜑↗→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 12199 | →¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑 | Modus ponens 12197, 12198 | |
| 12200 | →→¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑] into ax-2 | |
| 12201 | →→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑 | Modus ponens 12199, 12200 | |
| 12202 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜑¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬𝜑, 𝜒↗¬𝜂] into ax-2 | |
| 12203 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12196, 12202 | |
| 12204 | →→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜑] into ax-1 | |
| 12205 | →¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12203, 12204 | |
| 12206 | →→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2 | |
| 12207 | →→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12205, 12206 | |
| 12208 | →¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12197, 12207 | |
| 12209 | →¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into id | |
| 12210 | →→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜑] into ax-1 | |
| 12211 | →¬𝜑→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12209, 12210 | |
| 12212 | →¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into notnotr | |
| 12213 | →¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜑] into ax-1 | |
| 12214 | →→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-1 | |
| 12215 | →¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12213, 12214 | |
| 12216 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2 | |
| 12217 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12215, 12216 | |
| 12218 | →¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12212, 12217 | |
| 12219 | →→¬𝜑→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2 | |
| 12220 | →→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12211, 12219 | |
| 12221 | →→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-1 | |
| 12222 | →¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12220, 12221 | |
| 12223 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2 | |
| 12224 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12222, 12223 | |
| 12225 | →¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-1 | |
| 12226 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 12227 | →¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑 | Modus ponens 12225, 12226 | |
| 12228 | →→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑] into ax-2 | |
| 12229 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑 | Modus ponens 12227, 12228 | |
| 12230 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2 | |
| 12231 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12218, 12230 | |
| 12232 | →→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜑] into ax-1 | |
| 12233 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12231, 12232 | |
| 12234 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2 | |
| 12235 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12233, 12234 | |
| 12236 | →¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12225, 12235 | |
| 12237 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-3 | |
| 12238 | →→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜑] into ax-1 | |
| 12239 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12237, 12238 | |
| 12240 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2 | |
| 12241 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12239, 12240 | |
| 12242 | →¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12236, 12241 | |
| 12243 | →→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2 | |
| 12244 | →→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12242, 12243 | |
| 12245 | →¬𝜑¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12208, 12244 | |
| 12246 | →→¬𝜑¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜑 | Subs [𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-3 | |
| 12247 | →¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜑 | Modus ponens 12245, 12246 | |
| 12248 | →↔⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into biimp | |
| 12249 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12164, 12248 | |
| 12250 | →→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜑 | Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 12251 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜑 | Modus ponens 12247, 12250 | |
| 12252 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗𝜑] into ax-2 | |
| 12253 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Modus ponens 12251, 12252 | |
| 12254 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Modus ponens 12249, 12253 | simp-5l |
| 12255 | →→𝜓→𝜃𝜓→⋀⋀𝜑𝜓𝜒→𝜓→𝜃𝜓 | Subs [𝜑↗→𝜓→𝜃𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1 | |
| 12256 | →⋀⋀𝜑𝜓𝜒→𝜓→𝜃𝜓 | Modus ponens 9774, 12255 | |
| 12257 | →→⋀⋀𝜑𝜓𝜒→𝜓→𝜃𝜓→→⋀⋀𝜑𝜓𝜒𝜓→⋀⋀𝜑𝜓𝜒→𝜃𝜓 | Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜃𝜓] into ax-2 | |
| 12258 | →→⋀⋀𝜑𝜓𝜒𝜓→⋀⋀𝜑𝜓𝜒→𝜃𝜓 | Modus ponens 12256, 12257 | |
| 12259 | →𝜓→𝜂𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜂] into ax-1 | |
| 12260 | →→𝜓→𝜂𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜓→𝜂𝜓 | Subs [𝜑↗→𝜓→𝜂𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 12261 | →⋀⋀⋀𝜑𝜓𝜒𝜃→𝜓→𝜂𝜓 | Modus ponens 12259, 12260 | |
| 12262 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜓→𝜂𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→𝜂𝜓] into ax-2 | |
| 12263 | →→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓 | Modus ponens 12261, 12262 | |
| 12264 | →⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓 | Modus ponens simpllr, 12263 | |
| 12265 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜂, 𝜒↗𝜓] into ax-2 | |
| 12266 | →→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Modus ponens 12264, 12265 | |
| 12267 | →→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→¬¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓, 𝜓↗¬¬𝜂] into ax-1 | |
| 12268 | →¬¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Modus ponens 12266, 12267 | |
| 12269 | →→¬¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Subs [𝜑↗¬¬𝜂, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓] into ax-2 | |
| 12270 | →→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Modus ponens 12268, 12269 | |
| 12271 | →¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Modus ponens 12011, 12270 | |
| 12272 | →→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓 | Subs [𝜑↗¬¬𝜂, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗𝜓] into ax-2 | |
| 12273 | →→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓 | Modus ponens 12271, 12272 | |
| 12274 | →→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓 | Subs [𝜑↗→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 12275 | →⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓 | Modus ponens 12273, 12274 | |
| 12276 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→¬¬𝜂𝜓] into ax-2 | |
| 12277 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓 | Modus ponens 12275, 12276 | |
| 12278 | →⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓 | Modus ponens 12019, 12277 | |
| 12279 | →→𝜓¬¬𝜓→¬¬𝜂→𝜓¬¬𝜓 | Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜂] into ax-1 | |
| 12280 | →¬¬𝜂→𝜓¬¬𝜓 | Modus ponens 448, 12279 | |
| 12281 | →→¬¬𝜂→𝜓¬¬𝜓→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓 | Subs [𝜑↗¬¬𝜂, 𝜒↗¬¬𝜓] into ax-2 | |
| 12282 | →→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓 | Modus ponens 12280, 12281 | |
| 12283 | →→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓 | Subs [𝜑↗→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 12284 | →⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓 | Modus ponens 12282, 12283 | |
| 12285 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜓 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜂𝜓, 𝜒↗→¬¬𝜂¬¬𝜓] into ax-2 | |
| 12286 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜓 | Modus ponens 12284, 12285 | |
| 12287 | →⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜓 | Modus ponens 12278, 12286 | |
| 12288 | →→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂 | Subs [𝜑↗¬𝜂, 𝜓↗¬𝜓] into ax-3 | |
| 12289 | →→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂 | Subs [𝜑↗→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 12290 | →⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂 | Modus ponens 12288, 12289 | |
| 12291 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜓¬𝜂 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜂¬¬𝜓, 𝜒↗→¬𝜓¬𝜂] into ax-2 | |
| 12292 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜓¬𝜂 | Modus ponens 12290, 12291 | |
| 12293 | →⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜓¬𝜂 | Modus ponens 12287, 12292 | |
| 12294 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜓¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬𝜓, 𝜒↗¬𝜂] into ax-2 | |
| 12295 | →→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12293, 12294 | |
| 12296 | →→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜓] into ax-1 | |
| 12297 | →¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12295, 12296 | |
| 12298 | →→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2 | |
| 12299 | →→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12297, 12298 | |
| 12300 | →¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 11941, 12299 | |
| 12301 | →→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜓] into ax-1 | |
| 12302 | →¬𝜓→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12053, 12301 | |
| 12303 | →¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜓] into ax-1 | |
| 12304 | →→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-1 | |
| 12305 | →¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12303, 12304 | |
| 12306 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2 | |
| 12307 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12305, 12306 | |
| 12308 | →¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12056, 12307 | |
| 12309 | →→¬𝜓→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2 | |
| 12310 | →→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12302, 12309 | |
| 12311 | →→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-1 | |
| 12312 | →¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12310, 12311 | |
| 12313 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2 | |
| 12314 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12312, 12313 | |
| 12315 | →¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-1 | |
| 12316 | →→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 12317 | →¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓 | Modus ponens 12315, 12316 | |
| 12318 | →→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓] into ax-2 | |
| 12319 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓 | Modus ponens 12317, 12318 | |
| 12320 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2 | |
| 12321 | →→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12308, 12320 | |
| 12322 | →→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜓] into ax-1 | |
| 12323 | →¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12321, 12322 | |
| 12324 | →→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2 | |
| 12325 | →→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12323, 12324 | |
| 12326 | →¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12315, 12325 | |
| 12327 | →→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜓] into ax-1 | |
| 12328 | →¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12081, 12327 | |
| 12329 | →→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2 | |
| 12330 | →→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12328, 12329 | |
| 12331 | →¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12326, 12330 | |
| 12332 | →→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2 | |
| 12333 | →→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12331, 12332 | |
| 12334 | →¬𝜓¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂 | Modus ponens 12300, 12333 | |
| 12335 | →→¬𝜓¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-3 | |
| 12336 | →¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓 | Modus ponens 12334, 12335 | |
| 12337 | →→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓 | Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂] into ax-1 | |
| 12338 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓 | Modus ponens 12336, 12337 | |
| 12339 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜓 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗𝜓] into ax-2 | |
| 12340 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜓 | Modus ponens 12338, 12339 | |
| 12341 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜓 | Modus ponens 12093, 12340 | |
| 12342 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜓→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜓 | Subs [𝜑↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜓, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-1 | |
| 12343 | →¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜓 | Modus ponens 12341, 12342 | |
| 12344 | →→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜓→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓 | Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜒↗𝜓] into ax-2 | |
| 12345 | →→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓 | Modus ponens 12343, 12344 | |
| 12346 | →→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓→𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓 | Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓, 𝜓↗𝜂] into ax-1 | |
| 12347 | →𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓 | Modus ponens 12336, 12346 | |
| 12348 | →→𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜓 | Subs [𝜑↗𝜂, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗𝜓] into ax-2 | |
| 12349 | →→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜓 | Modus ponens 12347, 12348 | |
| 12350 | →→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜓 | Subs [𝜑↗→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 12351 | →⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜓 | Modus ponens 12349, 12350 | |
| 12352 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗→𝜂𝜓] into ax-2 | |
| 12353 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓 | Modus ponens 12351, 12352 | |
| 12354 | →→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓, 𝜓↗𝜂] into ax-1 | |
| 12355 | →𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Modus ponens 12266, 12354 | |
| 12356 | →→𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Subs [𝜑↗𝜂, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓] into ax-2 | |
| 12357 | →→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Modus ponens 12355, 12356 | |
| 12358 | →𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓 | Modus ponens 12006, 12357 | |
| 12359 | →→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓 | Subs [𝜑↗𝜂, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗𝜓] into ax-2 | |
| 12360 | →→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓 | Modus ponens 12358, 12359 | |
| 12361 | →→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓 | Subs [𝜑↗→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12362 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓 | Modus ponens 12360, 12361 | |
| 12363 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→𝜂𝜓] into ax-2 | |
| 12364 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓 | Modus ponens 12362, 12363 | |
| 12365 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓 | Modus ponens 12132, 12364 | |
| 12366 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜂, 𝜒↗𝜓] into ax-2 | |
| 12367 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Modus ponens 12365, 12366 | |
| 12368 | →→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓, 𝜓↗𝜂] into ax-1 | |
| 12369 | →𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Modus ponens 12367, 12368 | |
| 12370 | →→𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Subs [𝜑↗𝜂, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓] into ax-2 | |
| 12371 | →→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Modus ponens 12369, 12370 | |
| 12372 | →𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Modus ponens 12140, 12371 | |
| 12373 | →→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓 | Subs [𝜑↗𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗𝜓] into ax-2 | |
| 12374 | →→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓 | Modus ponens 12372, 12373 | |
| 12375 | →→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓 | Subs [𝜑↗→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12376 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓 | Modus ponens 12374, 12375 | |
| 12377 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→𝜂𝜓] into ax-2 | |
| 12378 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓 | Modus ponens 12376, 12377 | |
| 12379 | →→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→¬¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓, 𝜓↗¬¬𝜂] into ax-1 | |
| 12380 | →¬¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Modus ponens 12367, 12379 | |
| 12381 | →→¬¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Subs [𝜑↗¬¬𝜂, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓] into ax-2 | |
| 12382 | →→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Modus ponens 12380, 12381 | |
| 12383 | →¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Modus ponens 12169, 12382 | |
| 12384 | →→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓 | Subs [𝜑↗¬¬𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗𝜓] into ax-2 | |
| 12385 | →→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓 | Modus ponens 12383, 12384 | |
| 12386 | →→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓 | Subs [𝜑↗→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12387 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓 | Modus ponens 12385, 12386 | |
| 12388 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→¬¬𝜂𝜓] into ax-2 | |
| 12389 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓 | Modus ponens 12387, 12388 | |
| 12390 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓 | Modus ponens 12175, 12389 | |
| 12391 | →→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓 | Subs [𝜑↗→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12392 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓 | Modus ponens 12282, 12391 | |
| 12393 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜓 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜂𝜓, 𝜒↗→¬¬𝜂¬¬𝜓] into ax-2 | |
| 12394 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜓 | Modus ponens 12392, 12393 | |
| 12395 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜓 | Modus ponens 12390, 12394 | |
| 12396 | →→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂 | Subs [𝜑↗→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12397 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂 | Modus ponens 12288, 12396 | |
| 12398 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜓¬𝜂 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜂¬¬𝜓, 𝜒↗→¬𝜓¬𝜂] into ax-2 | |
| 12399 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜓¬𝜂 | Modus ponens 12397, 12398 | |
| 12400 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜓¬𝜂 | Modus ponens 12395, 12399 | |
| 12401 | →¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12402 | →→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓 | Subs [𝜑↗→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 12403 | →¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓 | Modus ponens 12401, 12402 | |
| 12404 | →→¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓] into ax-2 | |
| 12405 | →→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓 | Modus ponens 12403, 12404 | |
| 12406 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜓¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬𝜓, 𝜒↗¬𝜂] into ax-2 | |
| 12407 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12400, 12406 | |
| 12408 | →→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜓] into ax-1 | |
| 12409 | →¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12407, 12408 | |
| 12410 | →→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2 | |
| 12411 | →→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12409, 12410 | |
| 12412 | →¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12401, 12411 | |
| 12413 | →→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜓] into ax-1 | |
| 12414 | →¬𝜓→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12209, 12413 | |
| 12415 | →¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜓] into ax-1 | |
| 12416 | →→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-1 | |
| 12417 | →¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12415, 12416 | |
| 12418 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2 | |
| 12419 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12417, 12418 | |
| 12420 | →¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12212, 12419 | |
| 12421 | →→¬𝜓→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2 | |
| 12422 | →→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12414, 12421 | |
| 12423 | →→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-1 | |
| 12424 | →¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12422, 12423 | |
| 12425 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2 | |
| 12426 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12424, 12425 | |
| 12427 | →¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-1 | |
| 12428 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 12429 | →¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓 | Modus ponens 12427, 12428 | |
| 12430 | →→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓] into ax-2 | |
| 12431 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓 | Modus ponens 12429, 12430 | |
| 12432 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2 | |
| 12433 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12420, 12432 | |
| 12434 | →→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜓] into ax-1 | |
| 12435 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12433, 12434 | |
| 12436 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2 | |
| 12437 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12435, 12436 | |
| 12438 | →¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12427, 12437 | |
| 12439 | →→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜓] into ax-1 | |
| 12440 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12237, 12439 | |
| 12441 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2 | |
| 12442 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12440, 12441 | |
| 12443 | →¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12438, 12442 | |
| 12444 | →→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2 | |
| 12445 | →→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12443, 12444 | |
| 12446 | →¬𝜓¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂 | Modus ponens 12412, 12445 | |
| 12447 | →→¬𝜓¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-3 | |
| 12448 | →¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜓 | Modus ponens 12446, 12447 | |
| 12449 | →→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜓 | Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 12450 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜓 | Modus ponens 12448, 12449 | |
| 12451 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗𝜓] into ax-2 | |
| 12452 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Modus ponens 12450, 12451 | |
| 12453 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Modus ponens 12249, 12452 | simp-5r |
| 12454 | →→𝜑→𝜏𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜑→𝜏𝜑 | Subs [𝜑↗→𝜑→𝜏𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 12455 | →⋀⋀⋀𝜑𝜓𝜒𝜃→𝜑→𝜏𝜑 | Modus ponens 11542, 12454 | |
| 12456 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜑→𝜏𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜑, 𝜒↗→𝜏𝜑] into ax-2 | |
| 12457 | →→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑 | Modus ponens 12455, 12456 | |
| 12458 | →𝜑→𝜁𝜑 | Subs [𝜓↗𝜁] into ax-1 | |
| 12459 | →→𝜑→𝜁𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜑→𝜁𝜑 | Subs [𝜑↗→𝜑→𝜁𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12460 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜑→𝜁𝜑 | Modus ponens 12458, 12459 | |
| 12461 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜑→𝜁𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜑, 𝜒↗→𝜁𝜑] into ax-2 | |
| 12462 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑 | Modus ponens 12460, 12461 | |
| 12463 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑 | Modus ponens simp-4l, 12462 | |
| 12464 | ↔⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜁] into df-an | |
| 12465 | →¬¬𝜁𝜁 | Subs [𝜑↗𝜁] into notnotr | |
| 12466 | →𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁 | Subs [𝜑↗𝜁, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12467 | →→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬¬𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁 | Subs [𝜑↗→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜓↗¬¬𝜁] into ax-1 | |
| 12468 | →¬¬𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁 | Modus ponens 12466, 12467 | |
| 12469 | →→¬¬𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→→¬¬𝜁𝜁→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁 | Subs [𝜑↗¬¬𝜁, 𝜓↗𝜁, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁] into ax-2 | |
| 12470 | →→¬¬𝜁𝜁→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁 | Modus ponens 12468, 12469 | |
| 12471 | →¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁 | Modus ponens 12465, 12470 | |
| 12472 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜁, 𝜒↗𝜑] into ax-2 | |
| 12473 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Modus ponens 12463, 12472 | |
| 12474 | →→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→¬¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑, 𝜓↗¬¬𝜁] into ax-1 | |
| 12475 | →¬¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Modus ponens 12473, 12474 | |
| 12476 | →→¬¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Subs [𝜑↗¬¬𝜁, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑] into ax-2 | |
| 12477 | →→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Modus ponens 12475, 12476 | |
| 12478 | →¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Modus ponens 12471, 12477 | |
| 12479 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬¬𝜁] into ax-1 | |
| 12480 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Subs [𝜑↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12481 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Modus ponens 12479, 12480 | |
| 12482 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-2 | |
| 12483 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Modus ponens 12481, 12482 | |
| 12484 | →→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑 | Subs [𝜑↗¬¬𝜁, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗𝜑] into ax-2 | |
| 12485 | →→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑 | Modus ponens 12478, 12484 | |
| 12486 | →→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑 | Subs [𝜑↗→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12487 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑 | Modus ponens 12485, 12486 | |
| 12488 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→¬¬𝜁𝜑] into ax-2 | |
| 12489 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑 | Modus ponens 12487, 12488 | |
| 12490 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑 | Modus ponens 12479, 12489 | |
| 12491 | →→𝜑¬¬𝜑→¬¬𝜁→𝜑¬¬𝜑 | Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜁] into ax-1 | |
| 12492 | →¬¬𝜁→𝜑¬¬𝜑 | Modus ponens notnot, 12491 | |
| 12493 | →→¬¬𝜁→𝜑¬¬𝜑→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑 | Subs [𝜑↗¬¬𝜁, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2 | |
| 12494 | →→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑 | Modus ponens 12492, 12493 | |
| 12495 | →→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑 | Subs [𝜑↗→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12496 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑 | Modus ponens 12494, 12495 | |
| 12497 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜑 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜁𝜑, 𝜒↗→¬¬𝜁¬¬𝜑] into ax-2 | |
| 12498 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜑 | Modus ponens 12496, 12497 | |
| 12499 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜑 | Modus ponens 12490, 12498 | |
| 12500 | →→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁 | Subs [𝜑↗¬𝜁, 𝜓↗¬𝜑] into ax-3 | |
| 12501 | →→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁 | Subs [𝜑↗→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12502 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁 | Modus ponens 12500, 12501 | |
| 12503 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜑¬𝜁 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜁¬¬𝜑, 𝜒↗→¬𝜑¬𝜁] into ax-2 | |
| 12504 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜑¬𝜁 | Modus ponens 12502, 12503 | |
| 12505 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜑¬𝜁 | Modus ponens 12499, 12504 | |
| 12506 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜑¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬𝜑, 𝜒↗¬𝜁] into ax-2 | |
| 12507 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12505, 12506 | |
| 12508 | →→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜑] into ax-1 | |
| 12509 | →¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12507, 12508 | |
| 12510 | →→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2 | |
| 12511 | →→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12509, 12510 | |
| 12512 | →¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12197, 12511 | |
| 12513 | →¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into id | |
| 12514 | →→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜑] into ax-1 | |
| 12515 | →¬𝜑→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12513, 12514 | |
| 12516 | →¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into notnotr | |
| 12517 | →¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜑] into ax-1 | |
| 12518 | →→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-1 | |
| 12519 | →¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12517, 12518 | |
| 12520 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2 | |
| 12521 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12519, 12520 | |
| 12522 | →¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12516, 12521 | |
| 12523 | →→¬𝜑→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2 | |
| 12524 | →→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12515, 12523 | |
| 12525 | →→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-1 | |
| 12526 | →¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12524, 12525 | |
| 12527 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2 | |
| 12528 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12526, 12527 | |
| 12529 | →¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-1 | |
| 12530 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 12531 | →¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑 | Modus ponens 12529, 12530 | |
| 12532 | →→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑] into ax-2 | |
| 12533 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑 | Modus ponens 12531, 12532 | |
| 12534 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2 | |
| 12535 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12522, 12534 | |
| 12536 | →→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜑] into ax-1 | |
| 12537 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12535, 12536 | |
| 12538 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2 | |
| 12539 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12537, 12538 | |
| 12540 | →¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12529, 12539 | |
| 12541 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-3 | |
| 12542 | →→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜑] into ax-1 | |
| 12543 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12541, 12542 | |
| 12544 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2 | |
| 12545 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12543, 12544 | |
| 12546 | →¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12540, 12545 | |
| 12547 | →→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2 | |
| 12548 | →→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12546, 12547 | |
| 12549 | →¬𝜑¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12512, 12548 | |
| 12550 | →→¬𝜑¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑 | Subs [𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-3 | |
| 12551 | →¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑 | Modus ponens 12549, 12550 | |
| 12552 | →↔⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into biimp | |
| 12553 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12464, 12552 | |
| 12554 | →→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑 | Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁] into ax-1 | |
| 12555 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑 | Modus ponens 12551, 12554 | |
| 12556 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗𝜑] into ax-2 | |
| 12557 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜑 | Modus ponens 12555, 12556 | |
| 12558 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜑 | Modus ponens 12553, 12557 | |
| 12559 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜂] into simpl | |
| 12560 | →↔⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁↔¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into bicom1 | |
| 12561 | ↔¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁 | Modus ponens 12464, 12560 | |
| 12562 | →↔¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁 | Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁] into biimp | |
| 12563 | →¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁 | Modus ponens 12561, 12562 | |
| 12564 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜑→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜑 | Subs [𝜑↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜑, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-1 | |
| 12565 | →¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜑 | Modus ponens 12558, 12564 | |
| 12566 | →→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜑→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑 | Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜒↗𝜑] into ax-2 | |
| 12567 | →→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑 | Modus ponens 12565, 12566 | |
| 12568 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜁] into pm3.2im | |
| 12569 | →→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑→𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑 | Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑, 𝜓↗𝜁] into ax-1 | |
| 12570 | →𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑 | Modus ponens 12551, 12569 | |
| 12571 | →→𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜑 | Subs [𝜑↗𝜁, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗𝜑] into ax-2 | |
| 12572 | →→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜑 | Modus ponens 12570, 12571 | |
| 12573 | →→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜑 | Subs [𝜑↗→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12574 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜑 | Modus ponens 12572, 12573 | |
| 12575 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗→𝜁𝜑] into ax-2 | |
| 12576 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑 | Modus ponens 12574, 12575 | |
| 12577 | →𝜁𝜁 | Subs [𝜑↗𝜁] into id | |
| 12578 | →→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁 | Subs [𝜑↗→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜓↗𝜁] into ax-1 | |
| 12579 | →𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁 | Modus ponens 12466, 12578 | |
| 12580 | →→𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→→𝜁𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁 | Subs [𝜑↗𝜁, 𝜓↗𝜁, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁] into ax-2 | |
| 12581 | →→𝜁𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁 | Modus ponens 12579, 12580 | |
| 12582 | →→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑, 𝜓↗𝜁] into ax-1 | |
| 12583 | →𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Modus ponens 12473, 12582 | |
| 12584 | →→𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Subs [𝜑↗𝜁, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑] into ax-2 | |
| 12585 | →→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Modus ponens 12583, 12584 | |
| 12586 | →𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑 | Modus ponens 12466, 12585 | |
| 12587 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜁] into ax-1 | |
| 12588 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Subs [𝜑↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 12589 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Modus ponens 12587, 12588 | |
| 12590 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-2 | |
| 12591 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Modus ponens 12589, 12590 | |
| 12592 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏 | Modus ponens 12559, 12591 | |
| 12593 | →→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑 | Subs [𝜑↗𝜁, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗𝜑] into ax-2 | |
| 12594 | →→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑 | Modus ponens 12586, 12593 | |
| 12595 | →→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑 | Subs [𝜑↗→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 12596 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑 | Modus ponens 12594, 12595 | |
| 12597 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→𝜁𝜑] into ax-2 | |
| 12598 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑 | Modus ponens 12596, 12597 | |
| 12599 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑 | Modus ponens 12592, 12598 | |
| 12600 | →𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Subs [𝜑↗𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 12601 | →→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Subs [𝜑↗→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜁] into ax-1 | |
| 12602 | →𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Modus ponens 12600, 12601 | |
| 12603 | →→𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜁𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Subs [𝜑↗𝜁, 𝜓↗𝜁, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-2 | |
| 12604 | →→𝜁𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Modus ponens 12602, 12603 | |
| 12605 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜁, 𝜒↗𝜑] into ax-2 | |
| 12606 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Modus ponens 12599, 12605 | |
| 12607 | →→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑, 𝜓↗𝜁] into ax-1 | |
| 12608 | →𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Modus ponens 12606, 12607 | |
| 12609 | →→𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Subs [𝜑↗𝜁, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑] into ax-2 | |
| 12610 | →→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Modus ponens 12608, 12609 | |
| 12611 | →𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Modus ponens 12600, 12610 | |
| 12612 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into id | |
| 12613 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜁] into ax-1 | |
| 12614 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Subs [𝜑↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 12615 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Modus ponens 12613, 12614 | |
| 12616 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-2 | |
| 12617 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Modus ponens 12615, 12616 | |
| 12618 | →→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑 | Subs [𝜑↗𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗𝜑] into ax-2 | |
| 12619 | →→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑 | Modus ponens 12611, 12618 | |
| 12620 | →→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑 | Subs [𝜑↗→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 12621 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑 | Modus ponens 12619, 12620 | |
| 12622 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→𝜁𝜑] into ax-2 | |
| 12623 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑 | Modus ponens 12621, 12622 | |
| 12624 | ↔⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜁] into df-an | |
| 12625 | →→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Subs [𝜑↗→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬¬𝜁] into ax-1 | |
| 12626 | →¬¬𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Modus ponens 12600, 12625 | |
| 12627 | →→¬¬𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜁𝜁→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Subs [𝜑↗¬¬𝜁, 𝜓↗𝜁, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-2 | |
| 12628 | →→¬¬𝜁𝜁→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Modus ponens 12626, 12627 | |
| 12629 | →¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Modus ponens 12465, 12628 | |
| 12630 | →→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→¬¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑, 𝜓↗¬¬𝜁] into ax-1 | |
| 12631 | →¬¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Modus ponens 12606, 12630 | |
| 12632 | →→¬¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Subs [𝜑↗¬¬𝜁, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑] into ax-2 | |
| 12633 | →→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Modus ponens 12631, 12632 | |
| 12634 | →¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Modus ponens 12629, 12633 | |
| 12635 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬¬𝜁] into ax-1 | |
| 12636 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Subs [𝜑↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 12637 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Modus ponens 12635, 12636 | |
| 12638 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-2 | |
| 12639 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Modus ponens 12637, 12638 | |
| 12640 | →→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑 | Subs [𝜑↗¬¬𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗𝜑] into ax-2 | |
| 12641 | →→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑 | Modus ponens 12634, 12640 | |
| 12642 | →→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑 | Subs [𝜑↗→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 12643 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑 | Modus ponens 12641, 12642 | |
| 12644 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→¬¬𝜁𝜑] into ax-2 | |
| 12645 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑 | Modus ponens 12643, 12644 | |
| 12646 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑 | Modus ponens 12635, 12645 | |
| 12647 | →→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑 | Subs [𝜑↗→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 12648 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑 | Modus ponens 12494, 12647 | |
| 12649 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜁𝜑, 𝜒↗→¬¬𝜁¬¬𝜑] into ax-2 | |
| 12650 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜑 | Modus ponens 12648, 12649 | |
| 12651 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜑 | Modus ponens 12646, 12650 | |
| 12652 | →→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁 | Subs [𝜑↗→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 12653 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁 | Modus ponens 12500, 12652 | |
| 12654 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜑¬𝜁 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜁¬¬𝜑, 𝜒↗→¬𝜑¬𝜁] into ax-2 | |
| 12655 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜑¬𝜁 | Modus ponens 12653, 12654 | |
| 12656 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜑¬𝜁 | Modus ponens 12651, 12655 | |
| 12657 | →¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 12658 | →→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑 | Subs [𝜑↗→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 12659 | →¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑 | Modus ponens 12657, 12658 | |
| 12660 | →→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑] into ax-2 | |
| 12661 | →→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑 | Modus ponens 12659, 12660 | |
| 12662 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜑¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬𝜑, 𝜒↗¬𝜁] into ax-2 | |
| 12663 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12656, 12662 | |
| 12664 | →→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜑] into ax-1 | |
| 12665 | →¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12663, 12664 | |
| 12666 | →→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2 | |
| 12667 | →→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12665, 12666 | |
| 12668 | →¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12657, 12667 | |
| 12669 | →¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into id | |
| 12670 | →→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜑] into ax-1 | |
| 12671 | →¬𝜑→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12669, 12670 | |
| 12672 | →¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into notnotr | |
| 12673 | →¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜑] into ax-1 | |
| 12674 | →→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-1 | |
| 12675 | →¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12673, 12674 | |
| 12676 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2 | |
| 12677 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12675, 12676 | |
| 12678 | →¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12672, 12677 | |
| 12679 | →→¬𝜑→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2 | |
| 12680 | →→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12671, 12679 | |
| 12681 | →→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-1 | |
| 12682 | →¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12680, 12681 | |
| 12683 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2 | |
| 12684 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12682, 12683 | |
| 12685 | →¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-1 | |
| 12686 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 12687 | →¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑 | Modus ponens 12685, 12686 | |
| 12688 | →→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑] into ax-2 | |
| 12689 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑 | Modus ponens 12687, 12688 | |
| 12690 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2 | |
| 12691 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12678, 12690 | |
| 12692 | →→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜑] into ax-1 | |
| 12693 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12691, 12692 | |
| 12694 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2 | |
| 12695 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12693, 12694 | |
| 12696 | →¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12685, 12695 | |
| 12697 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-3 | |
| 12698 | →→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜑] into ax-1 | |
| 12699 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12697, 12698 | |
| 12700 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2 | |
| 12701 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12699, 12700 | |
| 12702 | →¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12696, 12701 | |
| 12703 | →→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2 | |
| 12704 | →→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12702, 12703 | |
| 12705 | →¬𝜑¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12668, 12704 | |
| 12706 | →→¬𝜑¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜑 | Subs [𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-3 | |
| 12707 | →¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜑 | Modus ponens 12705, 12706 | |
| 12708 | →↔⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into biimp | |
| 12709 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12624, 12708 | |
| 12710 | →→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜑 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 12711 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜑 | Modus ponens 12707, 12710 | |
| 12712 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗𝜑] into ax-2 | |
| 12713 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Modus ponens 12711, 12712 | |
| 12714 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Modus ponens 12709, 12713 | simp-6l |
| 12715 | →→𝜓→𝜏𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜓→𝜏𝜓 | Subs [𝜑↗→𝜓→𝜏𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1 | |
| 12716 | →⋀⋀⋀𝜑𝜓𝜒𝜃→𝜓→𝜏𝜓 | Modus ponens 11799, 12715 | |
| 12717 | →→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜓→𝜏𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓 | Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→𝜏𝜓] into ax-2 | |
| 12718 | →→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓 | Modus ponens 12716, 12717 | |
| 12719 | →𝜓→𝜁𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜁] into ax-1 | |
| 12720 | →→𝜓→𝜁𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜓→𝜁𝜓 | Subs [𝜑↗→𝜓→𝜁𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12721 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜓→𝜁𝜓 | Modus ponens 12719, 12720 | |
| 12722 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜓→𝜁𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→𝜁𝜓] into ax-2 | |
| 12723 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓 | Modus ponens 12721, 12722 | |
| 12724 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓 | Modus ponens simp-4r, 12723 | |
| 12725 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜁, 𝜒↗𝜓] into ax-2 | |
| 12726 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Modus ponens 12724, 12725 | |
| 12727 | →→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→¬¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓, 𝜓↗¬¬𝜁] into ax-1 | |
| 12728 | →¬¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Modus ponens 12726, 12727 | |
| 12729 | →→¬¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Subs [𝜑↗¬¬𝜁, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓] into ax-2 | |
| 12730 | →→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Modus ponens 12728, 12729 | |
| 12731 | →¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Modus ponens 12471, 12730 | |
| 12732 | →→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓 | Subs [𝜑↗¬¬𝜁, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗𝜓] into ax-2 | |
| 12733 | →→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓 | Modus ponens 12731, 12732 | |
| 12734 | →→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓 | Subs [𝜑↗→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12735 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓 | Modus ponens 12733, 12734 | |
| 12736 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→¬¬𝜁𝜓] into ax-2 | |
| 12737 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓 | Modus ponens 12735, 12736 | |
| 12738 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓 | Modus ponens 12479, 12737 | |
| 12739 | →→𝜓¬¬𝜓→¬¬𝜁→𝜓¬¬𝜓 | Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜁] into ax-1 | |
| 12740 | →¬¬𝜁→𝜓¬¬𝜓 | Modus ponens 448, 12739 | |
| 12741 | →→¬¬𝜁→𝜓¬¬𝜓→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓 | Subs [𝜑↗¬¬𝜁, 𝜒↗¬¬𝜓] into ax-2 | |
| 12742 | →→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓 | Modus ponens 12740, 12741 | |
| 12743 | →→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓 | Subs [𝜑↗→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12744 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓 | Modus ponens 12742, 12743 | |
| 12745 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜓 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜁𝜓, 𝜒↗→¬¬𝜁¬¬𝜓] into ax-2 | |
| 12746 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜓 | Modus ponens 12744, 12745 | |
| 12747 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜓 | Modus ponens 12738, 12746 | |
| 12748 | →→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁 | Subs [𝜑↗¬𝜁, 𝜓↗¬𝜓] into ax-3 | |
| 12749 | →→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁 | Subs [𝜑↗→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12750 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁 | Modus ponens 12748, 12749 | |
| 12751 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜓¬𝜁 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜁¬¬𝜓, 𝜒↗→¬𝜓¬𝜁] into ax-2 | |
| 12752 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜓¬𝜁 | Modus ponens 12750, 12751 | |
| 12753 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜓¬𝜁 | Modus ponens 12747, 12752 | |
| 12754 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜓¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬𝜓, 𝜒↗¬𝜁] into ax-2 | |
| 12755 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12753, 12754 | |
| 12756 | →→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜓] into ax-1 | |
| 12757 | →¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12755, 12756 | |
| 12758 | →→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2 | |
| 12759 | →→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12757, 12758 | |
| 12760 | →¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12401, 12759 | |
| 12761 | →→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜓] into ax-1 | |
| 12762 | →¬𝜓→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12513, 12761 | |
| 12763 | →¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜓] into ax-1 | |
| 12764 | →→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-1 | |
| 12765 | →¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12763, 12764 | |
| 12766 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2 | |
| 12767 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12765, 12766 | |
| 12768 | →¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12516, 12767 | |
| 12769 | →→¬𝜓→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2 | |
| 12770 | →→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12762, 12769 | |
| 12771 | →→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-1 | |
| 12772 | →¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12770, 12771 | |
| 12773 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2 | |
| 12774 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12772, 12773 | |
| 12775 | →¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-1 | |
| 12776 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 12777 | →¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓 | Modus ponens 12775, 12776 | |
| 12778 | →→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓] into ax-2 | |
| 12779 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓 | Modus ponens 12777, 12778 | |
| 12780 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2 | |
| 12781 | →→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12768, 12780 | |
| 12782 | →→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜓] into ax-1 | |
| 12783 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12781, 12782 | |
| 12784 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2 | |
| 12785 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12783, 12784 | |
| 12786 | →¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12775, 12785 | |
| 12787 | →→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜓] into ax-1 | |
| 12788 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12541, 12787 | |
| 12789 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2 | |
| 12790 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12788, 12789 | |
| 12791 | →¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12786, 12790 | |
| 12792 | →→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2 | |
| 12793 | →→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12791, 12792 | |
| 12794 | →¬𝜓¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁 | Modus ponens 12760, 12793 | |
| 12795 | →→¬𝜓¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-3 | |
| 12796 | →¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓 | Modus ponens 12794, 12795 | |
| 12797 | →→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓 | Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁] into ax-1 | |
| 12798 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓 | Modus ponens 12796, 12797 | |
| 12799 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗𝜓] into ax-2 | |
| 12800 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜓 | Modus ponens 12798, 12799 | |
| 12801 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜓 | Modus ponens 12553, 12800 | |
| 12802 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜓→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜓 | Subs [𝜑↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜓, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-1 | |
| 12803 | →¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜓 | Modus ponens 12801, 12802 | |
| 12804 | →→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜓→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓 | Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜒↗𝜓] into ax-2 | |
| 12805 | →→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓 | Modus ponens 12803, 12804 | |
| 12806 | →→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓→𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓 | Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓, 𝜓↗𝜁] into ax-1 | |
| 12807 | →𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓 | Modus ponens 12796, 12806 | |
| 12808 | →→𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜓 | Subs [𝜑↗𝜁, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗𝜓] into ax-2 | |
| 12809 | →→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜓 | Modus ponens 12807, 12808 | |
| 12810 | →→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜓 | Subs [𝜑↗→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12811 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜓 | Modus ponens 12809, 12810 | |
| 12812 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗→𝜁𝜓] into ax-2 | |
| 12813 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓 | Modus ponens 12811, 12812 | |
| 12814 | →→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓, 𝜓↗𝜁] into ax-1 | |
| 12815 | →𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Modus ponens 12726, 12814 | |
| 12816 | →→𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Subs [𝜑↗𝜁, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓] into ax-2 | |
| 12817 | →→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Modus ponens 12815, 12816 | |
| 12818 | →𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓 | Modus ponens 12466, 12817 | |
| 12819 | →→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓 | Subs [𝜑↗𝜁, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗𝜓] into ax-2 | |
| 12820 | →→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓 | Modus ponens 12818, 12819 | |
| 12821 | →→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓 | Subs [𝜑↗→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 12822 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓 | Modus ponens 12820, 12821 | |
| 12823 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→𝜁𝜓] into ax-2 | |
| 12824 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓 | Modus ponens 12822, 12823 | |
| 12825 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓 | Modus ponens 12592, 12824 | |
| 12826 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜁, 𝜒↗𝜓] into ax-2 | |
| 12827 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Modus ponens 12825, 12826 | |
| 12828 | →→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓, 𝜓↗𝜁] into ax-1 | |
| 12829 | →𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Modus ponens 12827, 12828 | |
| 12830 | →→𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Subs [𝜑↗𝜁, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓] into ax-2 | |
| 12831 | →→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Modus ponens 12829, 12830 | |
| 12832 | →𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Modus ponens 12600, 12831 | |
| 12833 | →→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓 | Subs [𝜑↗𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗𝜓] into ax-2 | |
| 12834 | →→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓 | Modus ponens 12832, 12833 | |
| 12835 | →→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓 | Subs [𝜑↗→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 12836 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓 | Modus ponens 12834, 12835 | |
| 12837 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→𝜁𝜓] into ax-2 | |
| 12838 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓 | Modus ponens 12836, 12837 | |
| 12839 | →→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→¬¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓, 𝜓↗¬¬𝜁] into ax-1 | |
| 12840 | →¬¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Modus ponens 12827, 12839 | |
| 12841 | →→¬¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Subs [𝜑↗¬¬𝜁, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓] into ax-2 | |
| 12842 | →→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Modus ponens 12840, 12841 | |
| 12843 | →¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Modus ponens 12629, 12842 | |
| 12844 | →→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓 | Subs [𝜑↗¬¬𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗𝜓] into ax-2 | |
| 12845 | →→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓 | Modus ponens 12843, 12844 | |
| 12846 | →→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓 | Subs [𝜑↗→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 12847 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓 | Modus ponens 12845, 12846 | |
| 12848 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→¬¬𝜁𝜓] into ax-2 | |
| 12849 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓 | Modus ponens 12847, 12848 | |
| 12850 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓 | Modus ponens 12635, 12849 | |
| 12851 | →→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓 | Subs [𝜑↗→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 12852 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓 | Modus ponens 12742, 12851 | |
| 12853 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜁𝜓, 𝜒↗→¬¬𝜁¬¬𝜓] into ax-2 | |
| 12854 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜓 | Modus ponens 12852, 12853 | |
| 12855 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜓 | Modus ponens 12850, 12854 | |
| 12856 | →→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁 | Subs [𝜑↗→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 12857 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁 | Modus ponens 12748, 12856 | |
| 12858 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜓¬𝜁 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜁¬¬𝜓, 𝜒↗→¬𝜓¬𝜁] into ax-2 | |
| 12859 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜓¬𝜁 | Modus ponens 12857, 12858 | |
| 12860 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜓¬𝜁 | Modus ponens 12855, 12859 | |
| 12861 | →¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 12862 | →→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓 | Subs [𝜑↗→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 12863 | →¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓 | Modus ponens 12861, 12862 | |
| 12864 | →→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓] into ax-2 | |
| 12865 | →→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓 | Modus ponens 12863, 12864 | |
| 12866 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜓¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬𝜓, 𝜒↗¬𝜁] into ax-2 | |
| 12867 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12860, 12866 | |
| 12868 | →→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜓] into ax-1 | |
| 12869 | →¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12867, 12868 | |
| 12870 | →→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2 | |
| 12871 | →→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12869, 12870 | |
| 12872 | →¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12861, 12871 | |
| 12873 | →→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜓] into ax-1 | |
| 12874 | →¬𝜓→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12669, 12873 | |
| 12875 | →¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜓] into ax-1 | |
| 12876 | →→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-1 | |
| 12877 | →¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12875, 12876 | |
| 12878 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2 | |
| 12879 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12877, 12878 | |
| 12880 | →¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12672, 12879 | |
| 12881 | →→¬𝜓→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2 | |
| 12882 | →→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12874, 12881 | |
| 12883 | →→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-1 | |
| 12884 | →¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12882, 12883 | |
| 12885 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2 | |
| 12886 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12884, 12885 | |
| 12887 | →¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-1 | |
| 12888 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 12889 | →¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓 | Modus ponens 12887, 12888 | |
| 12890 | →→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓] into ax-2 | |
| 12891 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓 | Modus ponens 12889, 12890 | |
| 12892 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2 | |
| 12893 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12880, 12892 | |
| 12894 | →→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜓] into ax-1 | |
| 12895 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12893, 12894 | |
| 12896 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2 | |
| 12897 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12895, 12896 | |
| 12898 | →¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12887, 12897 | |
| 12899 | →→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜓] into ax-1 | |
| 12900 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12697, 12899 | |
| 12901 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2 | |
| 12902 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12900, 12901 | |
| 12903 | →¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12898, 12902 | |
| 12904 | →→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2 | |
| 12905 | →→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12903, 12904 | |
| 12906 | →¬𝜓¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁 | Modus ponens 12872, 12905 | |
| 12907 | →→¬𝜓¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-3 | |
| 12908 | →¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜓 | Modus ponens 12906, 12907 | |
| 12909 | →→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜓 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 12910 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜓 | Modus ponens 12908, 12909 | |
| 12911 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗𝜓] into ax-2 | |
| 12912 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Modus ponens 12910, 12911 | |
| 12913 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Modus ponens 12709, 12912 | simp-6r |
| 12914 | →→𝜑→𝜂𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜑→𝜂𝜑 | Subs [𝜑↗→𝜑→𝜂𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 12915 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜑→𝜂𝜑 | Modus ponens 11998, 12914 | |
| 12916 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜑→𝜂𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜑, 𝜒↗→𝜂𝜑] into ax-2 | |
| 12917 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑 | Modus ponens 12915, 12916 | |
| 12918 | →𝜑→𝜎𝜑 | Subs [𝜓↗𝜎] into ax-1 | |
| 12919 | →→𝜑→𝜎𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜑→𝜎𝜑 | Subs [𝜑↗→𝜑→𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 12920 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜑→𝜎𝜑 | Modus ponens 12918, 12919 | |
| 12921 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜑→𝜎𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜑, 𝜒↗→𝜎𝜑] into ax-2 | |
| 12922 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑 | Modus ponens 12920, 12921 | |
| 12923 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑 | Modus ponens simp-5l, 12922 | |
| 12924 | ↔⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜎] into df-an | |
| 12925 | →¬¬𝜎𝜎 | Subs [𝜑↗𝜎] into notnotr | |
| 12926 | →𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎 | Subs [𝜑↗𝜎, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 12927 | →→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬¬𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎 | Subs [𝜑↗→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜓↗¬¬𝜎] into ax-1 | |
| 12928 | →¬¬𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎 | Modus ponens 12926, 12927 | |
| 12929 | →→¬¬𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→→¬¬𝜎𝜎→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎 | Subs [𝜑↗¬¬𝜎, 𝜓↗𝜎, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎] into ax-2 | |
| 12930 | →→¬¬𝜎𝜎→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎 | Modus ponens 12928, 12929 | |
| 12931 | →¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎 | Modus ponens 12925, 12930 | |
| 12932 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜎, 𝜒↗𝜑] into ax-2 | |
| 12933 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Modus ponens 12923, 12932 | |
| 12934 | →→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→¬¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑, 𝜓↗¬¬𝜎] into ax-1 | |
| 12935 | →¬¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Modus ponens 12933, 12934 | |
| 12936 | →→¬¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Subs [𝜑↗¬¬𝜎, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑] into ax-2 | |
| 12937 | →→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Modus ponens 12935, 12936 | |
| 12938 | →¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Modus ponens 12931, 12937 | |
| 12939 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬¬𝜎] into ax-1 | |
| 12940 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Subs [𝜑↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 12941 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Modus ponens 12939, 12940 | |
| 12942 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-2 | |
| 12943 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Modus ponens 12941, 12942 | |
| 12944 | →→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑 | Subs [𝜑↗¬¬𝜎, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗𝜑] into ax-2 | |
| 12945 | →→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑 | Modus ponens 12938, 12944 | |
| 12946 | →→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑 | Subs [𝜑↗→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 12947 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑 | Modus ponens 12945, 12946 | |
| 12948 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→¬¬𝜎𝜑] into ax-2 | |
| 12949 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑 | Modus ponens 12947, 12948 | |
| 12950 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑 | Modus ponens 12939, 12949 | |
| 12951 | →→𝜑¬¬𝜑→¬¬𝜎→𝜑¬¬𝜑 | Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜎] into ax-1 | |
| 12952 | →¬¬𝜎→𝜑¬¬𝜑 | Modus ponens notnot, 12951 | |
| 12953 | →→¬¬𝜎→𝜑¬¬𝜑→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑 | Subs [𝜑↗¬¬𝜎, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2 | |
| 12954 | →→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑 | Modus ponens 12952, 12953 | |
| 12955 | →→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑 | Subs [𝜑↗→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 12956 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑 | Modus ponens 12954, 12955 | |
| 12957 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜎𝜑, 𝜒↗→¬¬𝜎¬¬𝜑] into ax-2 | |
| 12958 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜑 | Modus ponens 12956, 12957 | |
| 12959 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜑 | Modus ponens 12950, 12958 | |
| 12960 | →→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎 | Subs [𝜑↗¬𝜎, 𝜓↗¬𝜑] into ax-3 | |
| 12961 | →→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎 | Subs [𝜑↗→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 12962 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎 | Modus ponens 12960, 12961 | |
| 12963 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜑¬𝜎 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜎¬¬𝜑, 𝜒↗→¬𝜑¬𝜎] into ax-2 | |
| 12964 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜑¬𝜎 | Modus ponens 12962, 12963 | |
| 12965 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜑¬𝜎 | Modus ponens 12959, 12964 | |
| 12966 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜑¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬𝜑, 𝜒↗¬𝜎] into ax-2 | |
| 12967 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 12965, 12966 | |
| 12968 | →→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜑] into ax-1 | |
| 12969 | →¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 12967, 12968 | |
| 12970 | →→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2 | |
| 12971 | →→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 12969, 12970 | |
| 12972 | →¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 12657, 12971 | |
| 12973 | →¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into id | |
| 12974 | →→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜑] into ax-1 | |
| 12975 | →¬𝜑→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 12973, 12974 | |
| 12976 | →¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into notnotr | |
| 12977 | →¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜑] into ax-1 | |
| 12978 | →→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-1 | |
| 12979 | →¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 12977, 12978 | |
| 12980 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2 | |
| 12981 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 12979, 12980 | |
| 12982 | →¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 12976, 12981 | |
| 12983 | →→¬𝜑→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2 | |
| 12984 | →→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 12975, 12983 | |
| 12985 | →→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-1 | |
| 12986 | →¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 12984, 12985 | |
| 12987 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2 | |
| 12988 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 12986, 12987 | |
| 12989 | →¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-1 | |
| 12990 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 12991 | →¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑 | Modus ponens 12989, 12990 | |
| 12992 | →→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑] into ax-2 | |
| 12993 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑 | Modus ponens 12991, 12992 | |
| 12994 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2 | |
| 12995 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 12982, 12994 | |
| 12996 | →→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜑] into ax-1 | |
| 12997 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 12995, 12996 | |
| 12998 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2 | |
| 12999 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 12997, 12998 | |
| 13000 | →¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 12989, 12999 | |
| 13001 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-3 | |
| 13002 | →→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜑] into ax-1 | |
| 13003 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 13001, 13002 | |
| 13004 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2 | |
| 13005 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 13003, 13004 | |
| 13006 | →¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 13000, 13005 | |
| 13007 | →→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2 | |
| 13008 | →→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 13006, 13007 | |
| 13009 | →¬𝜑¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 12972, 13008 | |
| 13010 | →→¬𝜑¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑 | Subs [𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-3 | |
| 13011 | →¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑 | Modus ponens 13009, 13010 | |
| 13012 | →↔⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into biimp | |
| 13013 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 12924, 13012 | |
| 13014 | →→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎] into ax-1 | |
| 13015 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑 | Modus ponens 13011, 13014 | |
| 13016 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗𝜑] into ax-2 | |
| 13017 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜑 | Modus ponens 13015, 13016 | |
| 13018 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜑 | Modus ponens 13013, 13017 | |
| 13019 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜁] into simpl | |
| 13020 | →↔⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎↔¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into bicom1 | |
| 13021 | ↔¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎 | Modus ponens 12924, 13020 | |
| 13022 | →↔¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎] into biimp | |
| 13023 | →¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎 | Modus ponens 13021, 13022 | |
| 13024 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜑→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜑 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-1 | |
| 13025 | →¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜑 | Modus ponens 13018, 13024 | |
| 13026 | →→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜑→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜒↗𝜑] into ax-2 | |
| 13027 | →→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑 | Modus ponens 13025, 13026 | |
| 13028 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜎] into pm3.2im | |
| 13029 | →→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑→𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑, 𝜓↗𝜎] into ax-1 | |
| 13030 | →𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑 | Modus ponens 13011, 13029 | |
| 13031 | →→𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜑 | Subs [𝜑↗𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗𝜑] into ax-2 | |
| 13032 | →→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜑 | Modus ponens 13030, 13031 | |
| 13033 | →→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜑 | Subs [𝜑↗→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 13034 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜑 | Modus ponens 13032, 13033 | |
| 13035 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗→𝜎𝜑] into ax-2 | |
| 13036 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑 | Modus ponens 13034, 13035 | |
| 13037 | →𝜎𝜎 | Subs [𝜑↗𝜎] into id | |
| 13038 | →→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎 | Subs [𝜑↗→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜓↗𝜎] into ax-1 | |
| 13039 | →𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎 | Modus ponens 12926, 13038 | |
| 13040 | →→𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→→𝜎𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎 | Subs [𝜑↗𝜎, 𝜓↗𝜎, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎] into ax-2 | |
| 13041 | →→𝜎𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎 | Modus ponens 13039, 13040 | |
| 13042 | →→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑, 𝜓↗𝜎] into ax-1 | |
| 13043 | →𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Modus ponens 12933, 13042 | |
| 13044 | →→𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Subs [𝜑↗𝜎, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑] into ax-2 | |
| 13045 | →→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Modus ponens 13043, 13044 | |
| 13046 | →𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑 | Modus ponens 12926, 13045 | |
| 13047 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜎] into ax-1 | |
| 13048 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Subs [𝜑↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13049 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Modus ponens 13047, 13048 | |
| 13050 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-2 | |
| 13051 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Modus ponens 13049, 13050 | |
| 13052 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂 | Modus ponens 13019, 13051 | |
| 13053 | →→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑 | Subs [𝜑↗𝜎, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗𝜑] into ax-2 | |
| 13054 | →→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑 | Modus ponens 13046, 13053 | |
| 13055 | →→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑 | Subs [𝜑↗→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13056 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑 | Modus ponens 13054, 13055 | |
| 13057 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→𝜎𝜑] into ax-2 | |
| 13058 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑 | Modus ponens 13056, 13057 | |
| 13059 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑 | Modus ponens 13052, 13058 | |
| 13060 | →𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Subs [𝜑↗𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13061 | →→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Subs [𝜑↗→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜎] into ax-1 | |
| 13062 | →𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Modus ponens 13060, 13061 | |
| 13063 | →→𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜎𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Subs [𝜑↗𝜎, 𝜓↗𝜎, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-2 | |
| 13064 | →→𝜎𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Modus ponens 13062, 13063 | |
| 13065 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜎, 𝜒↗𝜑] into ax-2 | |
| 13066 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Modus ponens 13059, 13065 | |
| 13067 | →→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑, 𝜓↗𝜎] into ax-1 | |
| 13068 | →𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Modus ponens 13066, 13067 | |
| 13069 | →→𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Subs [𝜑↗𝜎, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑] into ax-2 | |
| 13070 | →→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Modus ponens 13068, 13069 | |
| 13071 | →𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Modus ponens 13060, 13070 | |
| 13072 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into id | |
| 13073 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜎] into ax-1 | |
| 13074 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13075 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Modus ponens 13073, 13074 | |
| 13076 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-2 | |
| 13077 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Modus ponens 13075, 13076 | |
| 13078 | →→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑 | Subs [𝜑↗𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗𝜑] into ax-2 | |
| 13079 | →→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑 | Modus ponens 13071, 13078 | |
| 13080 | →→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑 | Subs [𝜑↗→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13081 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑 | Modus ponens 13079, 13080 | |
| 13082 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→𝜎𝜑] into ax-2 | |
| 13083 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑 | Modus ponens 13081, 13082 | |
| 13084 | ↔⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜎] into df-an | |
| 13085 | →→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Subs [𝜑↗→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬¬𝜎] into ax-1 | |
| 13086 | →¬¬𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Modus ponens 13060, 13085 | |
| 13087 | →→¬¬𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜎𝜎→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Subs [𝜑↗¬¬𝜎, 𝜓↗𝜎, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-2 | |
| 13088 | →→¬¬𝜎𝜎→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Modus ponens 13086, 13087 | |
| 13089 | →¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Modus ponens 12925, 13088 | |
| 13090 | →→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→¬¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑, 𝜓↗¬¬𝜎] into ax-1 | |
| 13091 | →¬¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Modus ponens 13066, 13090 | |
| 13092 | →→¬¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Subs [𝜑↗¬¬𝜎, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑] into ax-2 | |
| 13093 | →→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Modus ponens 13091, 13092 | |
| 13094 | →¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Modus ponens 13089, 13093 | |
| 13095 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬¬𝜎] into ax-1 | |
| 13096 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13097 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Modus ponens 13095, 13096 | |
| 13098 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-2 | |
| 13099 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Modus ponens 13097, 13098 | |
| 13100 | →→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑 | Subs [𝜑↗¬¬𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗𝜑] into ax-2 | |
| 13101 | →→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑 | Modus ponens 13094, 13100 | |
| 13102 | →→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑 | Subs [𝜑↗→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13103 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑 | Modus ponens 13101, 13102 | |
| 13104 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→¬¬𝜎𝜑] into ax-2 | |
| 13105 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑 | Modus ponens 13103, 13104 | |
| 13106 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑 | Modus ponens 13095, 13105 | |
| 13107 | →→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑 | Subs [𝜑↗→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13108 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑 | Modus ponens 12954, 13107 | |
| 13109 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜎𝜑, 𝜒↗→¬¬𝜎¬¬𝜑] into ax-2 | |
| 13110 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜑 | Modus ponens 13108, 13109 | |
| 13111 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜑 | Modus ponens 13106, 13110 | |
| 13112 | →→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎 | Subs [𝜑↗→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13113 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎 | Modus ponens 12960, 13112 | |
| 13114 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜑¬𝜎 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜎¬¬𝜑, 𝜒↗→¬𝜑¬𝜎] into ax-2 | |
| 13115 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜑¬𝜎 | Modus ponens 13113, 13114 | |
| 13116 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜑¬𝜎 | Modus ponens 13111, 13115 | |
| 13117 | →¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13118 | →→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑 | Subs [𝜑↗→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 13119 | →¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑 | Modus ponens 13117, 13118 | |
| 13120 | →→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑] into ax-2 | |
| 13121 | →→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑 | Modus ponens 13119, 13120 | |
| 13122 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜑¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬𝜑, 𝜒↗¬𝜎] into ax-2 | |
| 13123 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13116, 13122 | |
| 13124 | →→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜑] into ax-1 | |
| 13125 | →¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13123, 13124 | |
| 13126 | →→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2 | |
| 13127 | →→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13125, 13126 | |
| 13128 | →¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13117, 13127 | |
| 13129 | →¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into id | |
| 13130 | →→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜑] into ax-1 | |
| 13131 | →¬𝜑→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13129, 13130 | |
| 13132 | →¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into notnotr | |
| 13133 | →¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜑] into ax-1 | |
| 13134 | →→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-1 | |
| 13135 | →¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13133, 13134 | |
| 13136 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2 | |
| 13137 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13135, 13136 | |
| 13138 | →¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13132, 13137 | |
| 13139 | →→¬𝜑→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2 | |
| 13140 | →→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13131, 13139 | |
| 13141 | →→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-1 | |
| 13142 | →¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13140, 13141 | |
| 13143 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2 | |
| 13144 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13142, 13143 | |
| 13145 | →¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-1 | |
| 13146 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 13147 | →¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑 | Modus ponens 13145, 13146 | |
| 13148 | →→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑] into ax-2 | |
| 13149 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑 | Modus ponens 13147, 13148 | |
| 13150 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2 | |
| 13151 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13138, 13150 | |
| 13152 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜑] into ax-1 | |
| 13153 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13151, 13152 | |
| 13154 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2 | |
| 13155 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13153, 13154 | |
| 13156 | →¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13145, 13155 | |
| 13157 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-3 | |
| 13158 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜑] into ax-1 | |
| 13159 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13157, 13158 | |
| 13160 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2 | |
| 13161 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13159, 13160 | |
| 13162 | →¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13156, 13161 | |
| 13163 | →→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2 | |
| 13164 | →→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13162, 13163 | |
| 13165 | →¬𝜑¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13128, 13164 | |
| 13166 | →→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜑 | Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-3 | |
| 13167 | →¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜑 | Modus ponens 13165, 13166 | |
| 13168 | →↔⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into biimp | |
| 13169 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13084, 13168 | |
| 13170 | →→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜑 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13171 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜑 | Modus ponens 13167, 13170 | |
| 13172 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗𝜑] into ax-2 | |
| 13173 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Modus ponens 13171, 13172 | |
| 13174 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Modus ponens 13169, 13173 | simp-7l |
| 13175 | →→𝜓→𝜂𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜓→𝜂𝜓 | Subs [𝜑↗→𝜓→𝜂𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1 | |
| 13176 | →⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜓→𝜂𝜓 | Modus ponens 12259, 13175 | |
| 13177 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜓→𝜂𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓 | Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→𝜂𝜓] into ax-2 | |
| 13178 | →→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓 | Modus ponens 13176, 13177 | |
| 13179 | →𝜓→𝜎𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜎] into ax-1 | |
| 13180 | →→𝜓→𝜎𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜓→𝜎𝜓 | Subs [𝜑↗→𝜓→𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 13181 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜓→𝜎𝜓 | Modus ponens 13179, 13180 | |
| 13182 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜓→𝜎𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→𝜎𝜓] into ax-2 | |
| 13183 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓 | Modus ponens 13181, 13182 | |
| 13184 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓 | Modus ponens simp-5r, 13183 | |
| 13185 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜎, 𝜒↗𝜓] into ax-2 | |
| 13186 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Modus ponens 13184, 13185 | |
| 13187 | →→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→¬¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓, 𝜓↗¬¬𝜎] into ax-1 | |
| 13188 | →¬¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Modus ponens 13186, 13187 | |
| 13189 | →→¬¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Subs [𝜑↗¬¬𝜎, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓] into ax-2 | |
| 13190 | →→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Modus ponens 13188, 13189 | |
| 13191 | →¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Modus ponens 12931, 13190 | |
| 13192 | →→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓 | Subs [𝜑↗¬¬𝜎, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗𝜓] into ax-2 | |
| 13193 | →→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓 | Modus ponens 13191, 13192 | |
| 13194 | →→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓 | Subs [𝜑↗→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 13195 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓 | Modus ponens 13193, 13194 | |
| 13196 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→¬¬𝜎𝜓] into ax-2 | |
| 13197 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓 | Modus ponens 13195, 13196 | |
| 13198 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓 | Modus ponens 12939, 13197 | |
| 13199 | →→𝜓¬¬𝜓→¬¬𝜎→𝜓¬¬𝜓 | Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜎] into ax-1 | |
| 13200 | →¬¬𝜎→𝜓¬¬𝜓 | Modus ponens 448, 13199 | |
| 13201 | →→¬¬𝜎→𝜓¬¬𝜓→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓 | Subs [𝜑↗¬¬𝜎, 𝜒↗¬¬𝜓] into ax-2 | |
| 13202 | →→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓 | Modus ponens 13200, 13201 | |
| 13203 | →→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓 | Subs [𝜑↗→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 13204 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓 | Modus ponens 13202, 13203 | |
| 13205 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜎𝜓, 𝜒↗→¬¬𝜎¬¬𝜓] into ax-2 | |
| 13206 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜓 | Modus ponens 13204, 13205 | |
| 13207 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜓 | Modus ponens 13198, 13206 | |
| 13208 | →→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎 | Subs [𝜑↗¬𝜎, 𝜓↗¬𝜓] into ax-3 | |
| 13209 | →→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎 | Subs [𝜑↗→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 13210 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎 | Modus ponens 13208, 13209 | |
| 13211 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜓¬𝜎 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜎¬¬𝜓, 𝜒↗→¬𝜓¬𝜎] into ax-2 | |
| 13212 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜓¬𝜎 | Modus ponens 13210, 13211 | |
| 13213 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜓¬𝜎 | Modus ponens 13207, 13212 | |
| 13214 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜓¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬𝜓, 𝜒↗¬𝜎] into ax-2 | |
| 13215 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 13213, 13214 | |
| 13216 | →→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜓] into ax-1 | |
| 13217 | →¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 13215, 13216 | |
| 13218 | →→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2 | |
| 13219 | →→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 13217, 13218 | |
| 13220 | →¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 12861, 13219 | |
| 13221 | →→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜓] into ax-1 | |
| 13222 | →¬𝜓→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 12973, 13221 | |
| 13223 | →¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜓] into ax-1 | |
| 13224 | →→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-1 | |
| 13225 | →¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 13223, 13224 | |
| 13226 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2 | |
| 13227 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 13225, 13226 | |
| 13228 | →¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 12976, 13227 | |
| 13229 | →→¬𝜓→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2 | |
| 13230 | →→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 13222, 13229 | |
| 13231 | →→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-1 | |
| 13232 | →¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 13230, 13231 | |
| 13233 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2 | |
| 13234 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 13232, 13233 | |
| 13235 | →¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-1 | |
| 13236 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 13237 | →¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓 | Modus ponens 13235, 13236 | |
| 13238 | →→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓] into ax-2 | |
| 13239 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓 | Modus ponens 13237, 13238 | |
| 13240 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2 | |
| 13241 | →→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 13228, 13240 | |
| 13242 | →→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜓] into ax-1 | |
| 13243 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 13241, 13242 | |
| 13244 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2 | |
| 13245 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 13243, 13244 | |
| 13246 | →¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 13235, 13245 | |
| 13247 | →→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜓] into ax-1 | |
| 13248 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 13001, 13247 | |
| 13249 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2 | |
| 13250 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 13248, 13249 | |
| 13251 | →¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 13246, 13250 | |
| 13252 | →→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2 | |
| 13253 | →→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 13251, 13252 | |
| 13254 | →¬𝜓¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎 | Modus ponens 13220, 13253 | |
| 13255 | →→¬𝜓¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-3 | |
| 13256 | →¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓 | Modus ponens 13254, 13255 | |
| 13257 | →→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎] into ax-1 | |
| 13258 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓 | Modus ponens 13256, 13257 | |
| 13259 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗𝜓] into ax-2 | |
| 13260 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜓 | Modus ponens 13258, 13259 | |
| 13261 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜓 | Modus ponens 13013, 13260 | |
| 13262 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜓→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜓 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-1 | |
| 13263 | →¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜓 | Modus ponens 13261, 13262 | |
| 13264 | →→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜓→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜒↗𝜓] into ax-2 | |
| 13265 | →→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓 | Modus ponens 13263, 13264 | |
| 13266 | →→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓→𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓, 𝜓↗𝜎] into ax-1 | |
| 13267 | →𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓 | Modus ponens 13256, 13266 | |
| 13268 | →→𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜓 | Subs [𝜑↗𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗𝜓] into ax-2 | |
| 13269 | →→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜓 | Modus ponens 13267, 13268 | |
| 13270 | →→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜓 | Subs [𝜑↗→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 13271 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜓 | Modus ponens 13269, 13270 | |
| 13272 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗→𝜎𝜓] into ax-2 | |
| 13273 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓 | Modus ponens 13271, 13272 | |
| 13274 | →→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓, 𝜓↗𝜎] into ax-1 | |
| 13275 | →𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Modus ponens 13186, 13274 | |
| 13276 | →→𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Subs [𝜑↗𝜎, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓] into ax-2 | |
| 13277 | →→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Modus ponens 13275, 13276 | |
| 13278 | →𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓 | Modus ponens 12926, 13277 | |
| 13279 | →→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓 | Subs [𝜑↗𝜎, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗𝜓] into ax-2 | |
| 13280 | →→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓 | Modus ponens 13278, 13279 | |
| 13281 | →→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓 | Subs [𝜑↗→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13282 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓 | Modus ponens 13280, 13281 | |
| 13283 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→𝜎𝜓] into ax-2 | |
| 13284 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓 | Modus ponens 13282, 13283 | |
| 13285 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓 | Modus ponens 13052, 13284 | |
| 13286 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜎, 𝜒↗𝜓] into ax-2 | |
| 13287 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Modus ponens 13285, 13286 | |
| 13288 | →→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓, 𝜓↗𝜎] into ax-1 | |
| 13289 | →𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Modus ponens 13287, 13288 | |
| 13290 | →→𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Subs [𝜑↗𝜎, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓] into ax-2 | |
| 13291 | →→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Modus ponens 13289, 13290 | |
| 13292 | →𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Modus ponens 13060, 13291 | |
| 13293 | →→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓 | Subs [𝜑↗𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗𝜓] into ax-2 | |
| 13294 | →→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓 | Modus ponens 13292, 13293 | |
| 13295 | →→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓 | Subs [𝜑↗→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13296 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓 | Modus ponens 13294, 13295 | |
| 13297 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→𝜎𝜓] into ax-2 | |
| 13298 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓 | Modus ponens 13296, 13297 | |
| 13299 | →→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→¬¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓, 𝜓↗¬¬𝜎] into ax-1 | |
| 13300 | →¬¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Modus ponens 13287, 13299 | |
| 13301 | →→¬¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Subs [𝜑↗¬¬𝜎, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓] into ax-2 | |
| 13302 | →→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Modus ponens 13300, 13301 | |
| 13303 | →¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Modus ponens 13089, 13302 | |
| 13304 | →→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓 | Subs [𝜑↗¬¬𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗𝜓] into ax-2 | |
| 13305 | →→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓 | Modus ponens 13303, 13304 | |
| 13306 | →→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓 | Subs [𝜑↗→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13307 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓 | Modus ponens 13305, 13306 | |
| 13308 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→¬¬𝜎𝜓] into ax-2 | |
| 13309 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓 | Modus ponens 13307, 13308 | |
| 13310 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓 | Modus ponens 13095, 13309 | |
| 13311 | →→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓 | Subs [𝜑↗→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13312 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓 | Modus ponens 13202, 13311 | |
| 13313 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜎𝜓, 𝜒↗→¬¬𝜎¬¬𝜓] into ax-2 | |
| 13314 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜓 | Modus ponens 13312, 13313 | |
| 13315 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜓 | Modus ponens 13310, 13314 | |
| 13316 | →→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎 | Subs [𝜑↗→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13317 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎 | Modus ponens 13208, 13316 | |
| 13318 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜓¬𝜎 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜎¬¬𝜓, 𝜒↗→¬𝜓¬𝜎] into ax-2 | |
| 13319 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜓¬𝜎 | Modus ponens 13317, 13318 | |
| 13320 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜓¬𝜎 | Modus ponens 13315, 13319 | |
| 13321 | →¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13322 | →→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓 | Subs [𝜑↗→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 13323 | →¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓 | Modus ponens 13321, 13322 | |
| 13324 | →→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓] into ax-2 | |
| 13325 | →→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓 | Modus ponens 13323, 13324 | |
| 13326 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜓¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬𝜓, 𝜒↗¬𝜎] into ax-2 | |
| 13327 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13320, 13326 | |
| 13328 | →→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜓] into ax-1 | |
| 13329 | →¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13327, 13328 | |
| 13330 | →→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2 | |
| 13331 | →→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13329, 13330 | |
| 13332 | →¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13321, 13331 | |
| 13333 | →→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜓] into ax-1 | |
| 13334 | →¬𝜓→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13129, 13333 | |
| 13335 | →¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜓] into ax-1 | |
| 13336 | →→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-1 | |
| 13337 | →¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13335, 13336 | |
| 13338 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2 | |
| 13339 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13337, 13338 | |
| 13340 | →¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13132, 13339 | |
| 13341 | →→¬𝜓→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2 | |
| 13342 | →→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13334, 13341 | |
| 13343 | →→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-1 | |
| 13344 | →¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13342, 13343 | |
| 13345 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2 | |
| 13346 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13344, 13345 | |
| 13347 | →¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-1 | |
| 13348 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 13349 | →¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓 | Modus ponens 13347, 13348 | |
| 13350 | →→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓] into ax-2 | |
| 13351 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓 | Modus ponens 13349, 13350 | |
| 13352 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2 | |
| 13353 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13340, 13352 | |
| 13354 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜓] into ax-1 | |
| 13355 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13353, 13354 | |
| 13356 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2 | |
| 13357 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13355, 13356 | |
| 13358 | →¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13347, 13357 | |
| 13359 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜓] into ax-1 | |
| 13360 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13157, 13359 | |
| 13361 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2 | |
| 13362 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13360, 13361 | |
| 13363 | →¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13358, 13362 | |
| 13364 | →→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2 | |
| 13365 | →→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13363, 13364 | |
| 13366 | →¬𝜓¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎 | Modus ponens 13332, 13365 | |
| 13367 | →→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-3 | |
| 13368 | →¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜓 | Modus ponens 13366, 13367 | |
| 13369 | →→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜓 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13370 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜓 | Modus ponens 13368, 13369 | |
| 13371 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗𝜓] into ax-2 | |
| 13372 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Modus ponens 13370, 13371 | |
| 13373 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Modus ponens 13169, 13372 | simp-7r |
| 13374 | →→𝜑→𝜁𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜑→𝜁𝜑 | Subs [𝜑↗→𝜑→𝜁𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 13375 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜑→𝜁𝜑 | Modus ponens 12458, 13374 | |
| 13376 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜑→𝜁𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜑, 𝜒↗→𝜁𝜑] into ax-2 | |
| 13377 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑 | Modus ponens 13375, 13376 | |
| 13378 | →𝜑→𝜌𝜑 | Subs [𝜓↗𝜌] into ax-1 | |
| 13379 | →→𝜑→𝜌𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜑→𝜌𝜑 | Subs [𝜑↗→𝜑→𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13380 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜑→𝜌𝜑 | Modus ponens 13378, 13379 | |
| 13381 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜑→𝜌𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜑, 𝜒↗→𝜌𝜑] into ax-2 | |
| 13382 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑 | Modus ponens 13380, 13381 | |
| 13383 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑 | Modus ponens simp-6l, 13382 | |
| 13384 | ↔⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜌] into df-an | |
| 13385 | →¬¬𝜌𝜌 | Subs [𝜑↗𝜌] into notnotr | |
| 13386 | →𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌 | Subs [𝜑↗𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13387 | →→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬¬𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌 | Subs [𝜑↗→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜓↗¬¬𝜌] into ax-1 | |
| 13388 | →¬¬𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌 | Modus ponens 13386, 13387 | |
| 13389 | →→¬¬𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→→¬¬𝜌𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌 | Subs [𝜑↗¬¬𝜌, 𝜓↗𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌] into ax-2 | |
| 13390 | →→¬¬𝜌𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌 | Modus ponens 13388, 13389 | |
| 13391 | →¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌 | Modus ponens 13385, 13390 | |
| 13392 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜌, 𝜒↗𝜑] into ax-2 | |
| 13393 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Modus ponens 13383, 13392 | |
| 13394 | →→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→¬¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑, 𝜓↗¬¬𝜌] into ax-1 | |
| 13395 | →¬¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Modus ponens 13393, 13394 | |
| 13396 | →→¬¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Subs [𝜑↗¬¬𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑] into ax-2 | |
| 13397 | →→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Modus ponens 13395, 13396 | |
| 13398 | →¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Modus ponens 13391, 13397 | |
| 13399 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬¬𝜌] into ax-1 | |
| 13400 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13401 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Modus ponens 13399, 13400 | |
| 13402 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-2 | |
| 13403 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Modus ponens 13401, 13402 | |
| 13404 | →→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑 | Subs [𝜑↗¬¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗𝜑] into ax-2 | |
| 13405 | →→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑 | Modus ponens 13398, 13404 | |
| 13406 | →→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑 | Subs [𝜑↗→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13407 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑 | Modus ponens 13405, 13406 | |
| 13408 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→¬¬𝜌𝜑] into ax-2 | |
| 13409 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑 | Modus ponens 13407, 13408 | |
| 13410 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑 | Modus ponens 13399, 13409 | |
| 13411 | →→𝜑¬¬𝜑→¬¬𝜌→𝜑¬¬𝜑 | Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜌] into ax-1 | |
| 13412 | →¬¬𝜌→𝜑¬¬𝜑 | Modus ponens notnot, 13411 | |
| 13413 | →→¬¬𝜌→𝜑¬¬𝜑→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑 | Subs [𝜑↗¬¬𝜌, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2 | |
| 13414 | →→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑 | Modus ponens 13412, 13413 | |
| 13415 | →→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑 | Subs [𝜑↗→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13416 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑 | Modus ponens 13414, 13415 | |
| 13417 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜌𝜑, 𝜒↗→¬¬𝜌¬¬𝜑] into ax-2 | |
| 13418 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜑 | Modus ponens 13416, 13417 | |
| 13419 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜑 | Modus ponens 13410, 13418 | |
| 13420 | →→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌 | Subs [𝜑↗¬𝜌, 𝜓↗¬𝜑] into ax-3 | |
| 13421 | →→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌 | Subs [𝜑↗→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13422 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌 | Modus ponens 13420, 13421 | |
| 13423 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜑¬𝜌 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜌¬¬𝜑, 𝜒↗→¬𝜑¬𝜌] into ax-2 | |
| 13424 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜑¬𝜌 | Modus ponens 13422, 13423 | |
| 13425 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜑¬𝜌 | Modus ponens 13419, 13424 | |
| 13426 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜑¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬𝜑, 𝜒↗¬𝜌] into ax-2 | |
| 13427 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13425, 13426 | |
| 13428 | →→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜑] into ax-1 | |
| 13429 | →¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13427, 13428 | |
| 13430 | →→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2 | |
| 13431 | →→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13429, 13430 | |
| 13432 | →¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13117, 13431 | |
| 13433 | →¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into id | |
| 13434 | →→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜑] into ax-1 | |
| 13435 | →¬𝜑→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13433, 13434 | |
| 13436 | →¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into notnotr | |
| 13437 | →¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜑] into ax-1 | |
| 13438 | →→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-1 | |
| 13439 | →¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13437, 13438 | |
| 13440 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2 | |
| 13441 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13439, 13440 | |
| 13442 | →¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13436, 13441 | |
| 13443 | →→¬𝜑→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2 | |
| 13444 | →→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13435, 13443 | |
| 13445 | →→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-1 | |
| 13446 | →¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13444, 13445 | |
| 13447 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2 | |
| 13448 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13446, 13447 | |
| 13449 | →¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-1 | |
| 13450 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 13451 | →¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑 | Modus ponens 13449, 13450 | |
| 13452 | →→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑] into ax-2 | |
| 13453 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑 | Modus ponens 13451, 13452 | |
| 13454 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2 | |
| 13455 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13442, 13454 | |
| 13456 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜑] into ax-1 | |
| 13457 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13455, 13456 | |
| 13458 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2 | |
| 13459 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13457, 13458 | |
| 13460 | →¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13449, 13459 | |
| 13461 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-3 | |
| 13462 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜑] into ax-1 | |
| 13463 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13461, 13462 | |
| 13464 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2 | |
| 13465 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13463, 13464 | |
| 13466 | →¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13460, 13465 | |
| 13467 | →→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2 | |
| 13468 | →→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13466, 13467 | |
| 13469 | →¬𝜑¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13432, 13468 | |
| 13470 | →→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑 | Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-3 | |
| 13471 | →¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑 | Modus ponens 13469, 13470 | |
| 13472 | →↔⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into biimp | |
| 13473 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13384, 13472 | |
| 13474 | →→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌] into ax-1 | |
| 13475 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑 | Modus ponens 13471, 13474 | |
| 13476 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗𝜑] into ax-2 | |
| 13477 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜑 | Modus ponens 13475, 13476 | |
| 13478 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜑 | Modus ponens 13473, 13477 | |
| 13479 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜎] into simpl | |
| 13480 | →↔⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌↔¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into bicom1 | |
| 13481 | ↔¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌 | Modus ponens 13384, 13480 | |
| 13482 | →↔¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌] into biimp | |
| 13483 | →¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌 | Modus ponens 13481, 13482 | |
| 13484 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜑→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜑 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-1 | |
| 13485 | →¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜑 | Modus ponens 13478, 13484 | |
| 13486 | →→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜑→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜒↗𝜑] into ax-2 | |
| 13487 | →→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑 | Modus ponens 13485, 13486 | |
| 13488 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜌] into pm3.2im | |
| 13489 | →→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑→𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑, 𝜓↗𝜌] into ax-1 | |
| 13490 | →𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑 | Modus ponens 13471, 13489 | |
| 13491 | →→𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜑 | Subs [𝜑↗𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗𝜑] into ax-2 | |
| 13492 | →→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜑 | Modus ponens 13490, 13491 | |
| 13493 | →→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜑 | Subs [𝜑↗→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13494 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜑 | Modus ponens 13492, 13493 | |
| 13495 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗→𝜌𝜑] into ax-2 | |
| 13496 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑 | Modus ponens 13494, 13495 | |
| 13497 | →𝜌𝜌 | Subs [𝜑↗𝜌] into id | |
| 13498 | →→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌 | Subs [𝜑↗→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜓↗𝜌] into ax-1 | |
| 13499 | →𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌 | Modus ponens 13386, 13498 | |
| 13500 | →→𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→→𝜌𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌 | Subs [𝜑↗𝜌, 𝜓↗𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌] into ax-2 | |
| 13501 | →→𝜌𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌 | Modus ponens 13499, 13500 | |
| 13502 | →→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑, 𝜓↗𝜌] into ax-1 | |
| 13503 | →𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Modus ponens 13393, 13502 | |
| 13504 | →→𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Subs [𝜑↗𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑] into ax-2 | |
| 13505 | →→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Modus ponens 13503, 13504 | |
| 13506 | →𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑 | Modus ponens 13386, 13505 | |
| 13507 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜌] into ax-1 | |
| 13508 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13509 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Modus ponens 13507, 13508 | |
| 13510 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-2 | |
| 13511 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Modus ponens 13509, 13510 | |
| 13512 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁 | Modus ponens 13479, 13511 | |
| 13513 | →→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑 | Subs [𝜑↗𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗𝜑] into ax-2 | |
| 13514 | →→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑 | Modus ponens 13506, 13513 | |
| 13515 | →→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑 | Subs [𝜑↗→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13516 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑 | Modus ponens 13514, 13515 | |
| 13517 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→𝜌𝜑] into ax-2 | |
| 13518 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑 | Modus ponens 13516, 13517 | |
| 13519 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑 | Modus ponens 13512, 13518 | |
| 13520 | →𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Subs [𝜑↗𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13521 | →→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Subs [𝜑↗→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜌] into ax-1 | |
| 13522 | →𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Modus ponens 13520, 13521 | |
| 13523 | →→𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜌𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Subs [𝜑↗𝜌, 𝜓↗𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-2 | |
| 13524 | →→𝜌𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Modus ponens 13522, 13523 | |
| 13525 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜌, 𝜒↗𝜑] into ax-2 | |
| 13526 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Modus ponens 13519, 13525 | |
| 13527 | →→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑, 𝜓↗𝜌] into ax-1 | |
| 13528 | →𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Modus ponens 13526, 13527 | |
| 13529 | →→𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Subs [𝜑↗𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑] into ax-2 | |
| 13530 | →→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Modus ponens 13528, 13529 | |
| 13531 | →𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Modus ponens 13520, 13530 | |
| 13532 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into id | |
| 13533 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜌] into ax-1 | |
| 13534 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13535 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Modus ponens 13533, 13534 | |
| 13536 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-2 | |
| 13537 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Modus ponens 13535, 13536 | |
| 13538 | →→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑 | Subs [𝜑↗𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗𝜑] into ax-2 | |
| 13539 | →→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑 | Modus ponens 13531, 13538 | |
| 13540 | →→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑 | Subs [𝜑↗→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13541 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑 | Modus ponens 13539, 13540 | |
| 13542 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→𝜌𝜑] into ax-2 | |
| 13543 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑 | Modus ponens 13541, 13542 | |
| 13544 | ↔⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜌] into df-an | |
| 13545 | →→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Subs [𝜑↗→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬¬𝜌] into ax-1 | |
| 13546 | →¬¬𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Modus ponens 13520, 13545 | |
| 13547 | →→¬¬𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜌𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Subs [𝜑↗¬¬𝜌, 𝜓↗𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-2 | |
| 13548 | →→¬¬𝜌𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Modus ponens 13546, 13547 | |
| 13549 | →¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Modus ponens 13385, 13548 | |
| 13550 | →→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→¬¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑, 𝜓↗¬¬𝜌] into ax-1 | |
| 13551 | →¬¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Modus ponens 13526, 13550 | |
| 13552 | →→¬¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Subs [𝜑↗¬¬𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑] into ax-2 | |
| 13553 | →→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Modus ponens 13551, 13552 | |
| 13554 | →¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Modus ponens 13549, 13553 | |
| 13555 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬¬𝜌] into ax-1 | |
| 13556 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13557 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Modus ponens 13555, 13556 | |
| 13558 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-2 | |
| 13559 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Modus ponens 13557, 13558 | |
| 13560 | →→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑 | Subs [𝜑↗¬¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗𝜑] into ax-2 | |
| 13561 | →→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑 | Modus ponens 13554, 13560 | |
| 13562 | →→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑 | Subs [𝜑↗→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13563 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑 | Modus ponens 13561, 13562 | |
| 13564 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→¬¬𝜌𝜑] into ax-2 | |
| 13565 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑 | Modus ponens 13563, 13564 | |
| 13566 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑 | Modus ponens 13555, 13565 | |
| 13567 | →→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑 | Subs [𝜑↗→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13568 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑 | Modus ponens 13414, 13567 | |
| 13569 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜌𝜑, 𝜒↗→¬¬𝜌¬¬𝜑] into ax-2 | |
| 13570 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜑 | Modus ponens 13568, 13569 | |
| 13571 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜑 | Modus ponens 13566, 13570 | |
| 13572 | →→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌 | Subs [𝜑↗→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13573 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌 | Modus ponens 13420, 13572 | |
| 13574 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜑¬𝜌 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜌¬¬𝜑, 𝜒↗→¬𝜑¬𝜌] into ax-2 | |
| 13575 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜑¬𝜌 | Modus ponens 13573, 13574 | |
| 13576 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜑¬𝜌 | Modus ponens 13571, 13575 | |
| 13577 | →¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13578 | →→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑 | Subs [𝜑↗→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 13579 | →¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑 | Modus ponens 13577, 13578 | |
| 13580 | →→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑] into ax-2 | |
| 13581 | →→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑 | Modus ponens 13579, 13580 | |
| 13582 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜑¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬𝜑, 𝜒↗¬𝜌] into ax-2 | |
| 13583 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13576, 13582 | |
| 13584 | →→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜑] into ax-1 | |
| 13585 | →¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13583, 13584 | |
| 13586 | →→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2 | |
| 13587 | →→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13585, 13586 | |
| 13588 | →¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13577, 13587 | |
| 13589 | →¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into id | |
| 13590 | →→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜑] into ax-1 | |
| 13591 | →¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13589, 13590 | |
| 13592 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into notnotr | |
| 13593 | →¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜑] into ax-1 | |
| 13594 | →→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-1 | |
| 13595 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13593, 13594 | |
| 13596 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2 | |
| 13597 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13595, 13596 | |
| 13598 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13592, 13597 | |
| 13599 | →→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2 | |
| 13600 | →→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13591, 13599 | |
| 13601 | →→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-1 | |
| 13602 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13600, 13601 | |
| 13603 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2 | |
| 13604 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13602, 13603 | |
| 13605 | →¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-1 | |
| 13606 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 13607 | →¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑 | Modus ponens 13605, 13606 | |
| 13608 | →→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑] into ax-2 | |
| 13609 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑 | Modus ponens 13607, 13608 | |
| 13610 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2 | |
| 13611 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13598, 13610 | |
| 13612 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜑] into ax-1 | |
| 13613 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13611, 13612 | |
| 13614 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2 | |
| 13615 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13613, 13614 | |
| 13616 | →¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13605, 13615 | |
| 13617 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-3 | |
| 13618 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜑] into ax-1 | |
| 13619 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13617, 13618 | |
| 13620 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2 | |
| 13621 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13619, 13620 | |
| 13622 | →¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13616, 13621 | |
| 13623 | →→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2 | |
| 13624 | →→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13622, 13623 | |
| 13625 | →¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13588, 13624 | |
| 13626 | →→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜑 | Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-3 | |
| 13627 | →¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜑 | Modus ponens 13625, 13626 | |
| 13628 | →↔⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into biimp | |
| 13629 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13544, 13628 | |
| 13630 | →→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜑 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 13631 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜑 | Modus ponens 13627, 13630 | |
| 13632 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗𝜑] into ax-2 | |
| 13633 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Modus ponens 13631, 13632 | |
| 13634 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Modus ponens 13629, 13633 | simp-8l |
| 13635 | →→𝜓→𝜁𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜓→𝜁𝜓 | Subs [𝜑↗→𝜓→𝜁𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1 | |
| 13636 | →⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜓→𝜁𝜓 | Modus ponens 12719, 13635 | |
| 13637 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜓→𝜁𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→𝜁𝜓] into ax-2 | |
| 13638 | →→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓 | Modus ponens 13636, 13637 | |
| 13639 | →𝜓→𝜌𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜌] into ax-1 | |
| 13640 | →→𝜓→𝜌𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜓→𝜌𝜓 | Subs [𝜑↗→𝜓→𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13641 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜓→𝜌𝜓 | Modus ponens 13639, 13640 | |
| 13642 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜓→𝜌𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→𝜌𝜓] into ax-2 | |
| 13643 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓 | Modus ponens 13641, 13642 | |
| 13644 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓 | Modus ponens simp-6r, 13643 | |
| 13645 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜌, 𝜒↗𝜓] into ax-2 | |
| 13646 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Modus ponens 13644, 13645 | |
| 13647 | →→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→¬¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓, 𝜓↗¬¬𝜌] into ax-1 | |
| 13648 | →¬¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Modus ponens 13646, 13647 | |
| 13649 | →→¬¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Subs [𝜑↗¬¬𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓] into ax-2 | |
| 13650 | →→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Modus ponens 13648, 13649 | |
| 13651 | →¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Modus ponens 13391, 13650 | |
| 13652 | →→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓 | Subs [𝜑↗¬¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗𝜓] into ax-2 | |
| 13653 | →→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓 | Modus ponens 13651, 13652 | |
| 13654 | →→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓 | Subs [𝜑↗→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13655 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓 | Modus ponens 13653, 13654 | |
| 13656 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→¬¬𝜌𝜓] into ax-2 | |
| 13657 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓 | Modus ponens 13655, 13656 | |
| 13658 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓 | Modus ponens 13399, 13657 | |
| 13659 | →→𝜓¬¬𝜓→¬¬𝜌→𝜓¬¬𝜓 | Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜌] into ax-1 | |
| 13660 | →¬¬𝜌→𝜓¬¬𝜓 | Modus ponens 448, 13659 | |
| 13661 | →→¬¬𝜌→𝜓¬¬𝜓→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓 | Subs [𝜑↗¬¬𝜌, 𝜒↗¬¬𝜓] into ax-2 | |
| 13662 | →→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓 | Modus ponens 13660, 13661 | |
| 13663 | →→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓 | Subs [𝜑↗→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13664 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓 | Modus ponens 13662, 13663 | |
| 13665 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜌𝜓, 𝜒↗→¬¬𝜌¬¬𝜓] into ax-2 | |
| 13666 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜓 | Modus ponens 13664, 13665 | |
| 13667 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜓 | Modus ponens 13658, 13666 | |
| 13668 | →→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌 | Subs [𝜑↗¬𝜌, 𝜓↗¬𝜓] into ax-3 | |
| 13669 | →→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌 | Subs [𝜑↗→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13670 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌 | Modus ponens 13668, 13669 | |
| 13671 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜓¬𝜌 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜌¬¬𝜓, 𝜒↗→¬𝜓¬𝜌] into ax-2 | |
| 13672 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜓¬𝜌 | Modus ponens 13670, 13671 | |
| 13673 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜓¬𝜌 | Modus ponens 13667, 13672 | |
| 13674 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜓¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬𝜓, 𝜒↗¬𝜌] into ax-2 | |
| 13675 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13673, 13674 | |
| 13676 | →→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜓] into ax-1 | |
| 13677 | →¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13675, 13676 | |
| 13678 | →→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2 | |
| 13679 | →→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13677, 13678 | |
| 13680 | →¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13321, 13679 | |
| 13681 | →→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜓] into ax-1 | |
| 13682 | →¬𝜓→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13433, 13681 | |
| 13683 | →¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜓] into ax-1 | |
| 13684 | →→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-1 | |
| 13685 | →¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13683, 13684 | |
| 13686 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2 | |
| 13687 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13685, 13686 | |
| 13688 | →¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13436, 13687 | |
| 13689 | →→¬𝜓→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2 | |
| 13690 | →→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13682, 13689 | |
| 13691 | →→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-1 | |
| 13692 | →¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13690, 13691 | |
| 13693 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2 | |
| 13694 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13692, 13693 | |
| 13695 | →¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-1 | |
| 13696 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 13697 | →¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓 | Modus ponens 13695, 13696 | |
| 13698 | →→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓] into ax-2 | |
| 13699 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓 | Modus ponens 13697, 13698 | |
| 13700 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2 | |
| 13701 | →→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13688, 13700 | |
| 13702 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜓] into ax-1 | |
| 13703 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13701, 13702 | |
| 13704 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2 | |
| 13705 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13703, 13704 | |
| 13706 | →¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13695, 13705 | |
| 13707 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜓] into ax-1 | |
| 13708 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13461, 13707 | |
| 13709 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2 | |
| 13710 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13708, 13709 | |
| 13711 | →¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13706, 13710 | |
| 13712 | →→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2 | |
| 13713 | →→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13711, 13712 | |
| 13714 | →¬𝜓¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌 | Modus ponens 13680, 13713 | |
| 13715 | →→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-3 | |
| 13716 | →¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓 | Modus ponens 13714, 13715 | |
| 13717 | →→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌] into ax-1 | |
| 13718 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓 | Modus ponens 13716, 13717 | |
| 13719 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗𝜓] into ax-2 | |
| 13720 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜓 | Modus ponens 13718, 13719 | |
| 13721 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜓 | Modus ponens 13473, 13720 | |
| 13722 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜓→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜓 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-1 | |
| 13723 | →¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜓 | Modus ponens 13721, 13722 | |
| 13724 | →→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜓→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜒↗𝜓] into ax-2 | |
| 13725 | →→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓 | Modus ponens 13723, 13724 | |
| 13726 | →→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓→𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓, 𝜓↗𝜌] into ax-1 | |
| 13727 | →𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓 | Modus ponens 13716, 13726 | |
| 13728 | →→𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜓 | Subs [𝜑↗𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗𝜓] into ax-2 | |
| 13729 | →→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜓 | Modus ponens 13727, 13728 | |
| 13730 | →→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜓 | Subs [𝜑↗→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13731 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜓 | Modus ponens 13729, 13730 | |
| 13732 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗→𝜌𝜓] into ax-2 | |
| 13733 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓 | Modus ponens 13731, 13732 | |
| 13734 | →→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓, 𝜓↗𝜌] into ax-1 | |
| 13735 | →𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Modus ponens 13646, 13734 | |
| 13736 | →→𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Subs [𝜑↗𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓] into ax-2 | |
| 13737 | →→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Modus ponens 13735, 13736 | |
| 13738 | →𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓 | Modus ponens 13386, 13737 | |
| 13739 | →→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓 | Subs [𝜑↗𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗𝜓] into ax-2 | |
| 13740 | →→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓 | Modus ponens 13738, 13739 | |
| 13741 | →→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓 | Subs [𝜑↗→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13742 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓 | Modus ponens 13740, 13741 | |
| 13743 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→𝜌𝜓] into ax-2 | |
| 13744 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓 | Modus ponens 13742, 13743 | |
| 13745 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓 | Modus ponens 13512, 13744 | |
| 13746 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜌, 𝜒↗𝜓] into ax-2 | |
| 13747 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Modus ponens 13745, 13746 | |
| 13748 | →→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓, 𝜓↗𝜌] into ax-1 | |
| 13749 | →𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Modus ponens 13747, 13748 | |
| 13750 | →→𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Subs [𝜑↗𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓] into ax-2 | |
| 13751 | →→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Modus ponens 13749, 13750 | |
| 13752 | →𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Modus ponens 13520, 13751 | |
| 13753 | →→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓 | Subs [𝜑↗𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗𝜓] into ax-2 | |
| 13754 | →→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓 | Modus ponens 13752, 13753 | |
| 13755 | →→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓 | Subs [𝜑↗→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13756 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓 | Modus ponens 13754, 13755 | |
| 13757 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→𝜌𝜓] into ax-2 | |
| 13758 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓 | Modus ponens 13756, 13757 | |
| 13759 | →→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→¬¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓, 𝜓↗¬¬𝜌] into ax-1 | |
| 13760 | →¬¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Modus ponens 13747, 13759 | |
| 13761 | →→¬¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Subs [𝜑↗¬¬𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓] into ax-2 | |
| 13762 | →→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Modus ponens 13760, 13761 | |
| 13763 | →¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Modus ponens 13549, 13762 | |
| 13764 | →→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓 | Subs [𝜑↗¬¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗𝜓] into ax-2 | |
| 13765 | →→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓 | Modus ponens 13763, 13764 | |
| 13766 | →→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓 | Subs [𝜑↗→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13767 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓 | Modus ponens 13765, 13766 | |
| 13768 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→¬¬𝜌𝜓] into ax-2 | |
| 13769 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓 | Modus ponens 13767, 13768 | |
| 13770 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓 | Modus ponens 13555, 13769 | |
| 13771 | →→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓 | Subs [𝜑↗→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13772 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓 | Modus ponens 13662, 13771 | |
| 13773 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜌𝜓, 𝜒↗→¬¬𝜌¬¬𝜓] into ax-2 | |
| 13774 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜓 | Modus ponens 13772, 13773 | |
| 13775 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜓 | Modus ponens 13770, 13774 | |
| 13776 | →→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌 | Subs [𝜑↗→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13777 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌 | Modus ponens 13668, 13776 | |
| 13778 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜓¬𝜌 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜌¬¬𝜓, 𝜒↗→¬𝜓¬𝜌] into ax-2 | |
| 13779 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜓¬𝜌 | Modus ponens 13777, 13778 | |
| 13780 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜓¬𝜌 | Modus ponens 13775, 13779 | |
| 13781 | →¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13782 | →→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓 | Subs [𝜑↗→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 13783 | →¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓 | Modus ponens 13781, 13782 | |
| 13784 | →→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓] into ax-2 | |
| 13785 | →→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓 | Modus ponens 13783, 13784 | |
| 13786 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜓¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬𝜓, 𝜒↗¬𝜌] into ax-2 | |
| 13787 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13780, 13786 | |
| 13788 | →→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜓] into ax-1 | |
| 13789 | →¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13787, 13788 | |
| 13790 | →→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2 | |
| 13791 | →→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13789, 13790 | |
| 13792 | →¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13781, 13791 | |
| 13793 | →→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜓] into ax-1 | |
| 13794 | →¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13589, 13793 | |
| 13795 | →¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜓] into ax-1 | |
| 13796 | →→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-1 | |
| 13797 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13795, 13796 | |
| 13798 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2 | |
| 13799 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13797, 13798 | |
| 13800 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13592, 13799 | |
| 13801 | →→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2 | |
| 13802 | →→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13794, 13801 | |
| 13803 | →→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-1 | |
| 13804 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13802, 13803 | |
| 13805 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2 | |
| 13806 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13804, 13805 | |
| 13807 | →¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-1 | |
| 13808 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 13809 | →¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓 | Modus ponens 13807, 13808 | |
| 13810 | →→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓] into ax-2 | |
| 13811 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓 | Modus ponens 13809, 13810 | |
| 13812 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2 | |
| 13813 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13800, 13812 | |
| 13814 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜓] into ax-1 | |
| 13815 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13813, 13814 | |
| 13816 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2 | |
| 13817 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13815, 13816 | |
| 13818 | →¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13807, 13817 | |
| 13819 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜓] into ax-1 | |
| 13820 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13617, 13819 | |
| 13821 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2 | |
| 13822 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13820, 13821 | |
| 13823 | →¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13818, 13822 | |
| 13824 | →→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2 | |
| 13825 | →→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13823, 13824 | |
| 13826 | →¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌 | Modus ponens 13792, 13825 | |
| 13827 | →→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-3 | |
| 13828 | →¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜓 | Modus ponens 13826, 13827 | |
| 13829 | →→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜓 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 13830 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜓 | Modus ponens 13828, 13829 | |
| 13831 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗𝜓] into ax-2 | |
| 13832 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Modus ponens 13830, 13831 | |
| 13833 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Modus ponens 13629, 13832 | simp-8r |
| 13834 | →→𝜑→𝜎𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜑→𝜎𝜑 | Subs [𝜑↗→𝜑→𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 13835 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜑→𝜎𝜑 | Modus ponens 12918, 13834 | |
| 13836 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜑→𝜎𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜑, 𝜒↗→𝜎𝜑] into ax-2 | |
| 13837 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑 | Modus ponens 13835, 13836 | |
| 13838 | →𝜑→𝜇𝜑 | Subs [𝜓↗𝜇] into ax-1 | |
| 13839 | →→𝜑→𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜑→𝜇𝜑 | Subs [𝜑↗→𝜑→𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13840 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜑→𝜇𝜑 | Modus ponens 13838, 13839 | |
| 13841 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜑→𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜑, 𝜒↗→𝜇𝜑] into ax-2 | |
| 13842 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑 | Modus ponens 13840, 13841 | |
| 13843 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑 | Modus ponens simp-7l, 13842 | |
| 13844 | ↔⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜇] into df-an | |
| 13845 | →¬¬𝜇𝜇 | Subs [𝜑↗𝜇] into notnotr | |
| 13846 | →𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇 | Subs [𝜑↗𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13847 | →→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬¬𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇 | Subs [𝜑↗→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜓↗¬¬𝜇] into ax-1 | |
| 13848 | →¬¬𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇 | Modus ponens 13846, 13847 | |
| 13849 | →→¬¬𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→→¬¬𝜇𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇 | Subs [𝜑↗¬¬𝜇, 𝜓↗𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇] into ax-2 | |
| 13850 | →→¬¬𝜇𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇 | Modus ponens 13848, 13849 | |
| 13851 | →¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇 | Modus ponens 13845, 13850 | |
| 13852 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜇, 𝜒↗𝜑] into ax-2 | |
| 13853 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Modus ponens 13843, 13852 | |
| 13854 | →→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑, 𝜓↗¬¬𝜇] into ax-1 | |
| 13855 | →¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Modus ponens 13853, 13854 | |
| 13856 | →→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Subs [𝜑↗¬¬𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑] into ax-2 | |
| 13857 | →→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Modus ponens 13855, 13856 | |
| 13858 | →¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Modus ponens 13851, 13857 | |
| 13859 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬¬𝜇] into ax-1 | |
| 13860 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13861 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Modus ponens 13859, 13860 | |
| 13862 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-2 | |
| 13863 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Modus ponens 13861, 13862 | |
| 13864 | →→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑 | Subs [𝜑↗¬¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗𝜑] into ax-2 | |
| 13865 | →→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑 | Modus ponens 13858, 13864 | |
| 13866 | →→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑 | Subs [𝜑↗→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13867 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑 | Modus ponens 13865, 13866 | |
| 13868 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→¬¬𝜇𝜑] into ax-2 | |
| 13869 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑 | Modus ponens 13867, 13868 | |
| 13870 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑 | Modus ponens 13859, 13869 | |
| 13871 | →→𝜑¬¬𝜑→¬¬𝜇→𝜑¬¬𝜑 | Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜇] into ax-1 | |
| 13872 | →¬¬𝜇→𝜑¬¬𝜑 | Modus ponens notnot, 13871 | |
| 13873 | →→¬¬𝜇→𝜑¬¬𝜑→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑 | Subs [𝜑↗¬¬𝜇, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2 | |
| 13874 | →→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑 | Modus ponens 13872, 13873 | |
| 13875 | →→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑 | Subs [𝜑↗→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13876 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑 | Modus ponens 13874, 13875 | |
| 13877 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜇𝜑, 𝜒↗→¬¬𝜇¬¬𝜑] into ax-2 | |
| 13878 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜑 | Modus ponens 13876, 13877 | |
| 13879 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜑 | Modus ponens 13870, 13878 | |
| 13880 | →→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇 | Subs [𝜑↗¬𝜇, 𝜓↗¬𝜑] into ax-3 | |
| 13881 | →→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇 | Subs [𝜑↗→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13882 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇 | Modus ponens 13880, 13881 | |
| 13883 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜑¬𝜇 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜇¬¬𝜑, 𝜒↗→¬𝜑¬𝜇] into ax-2 | |
| 13884 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜑¬𝜇 | Modus ponens 13882, 13883 | |
| 13885 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜑¬𝜇 | Modus ponens 13879, 13884 | |
| 13886 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜑¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬𝜑, 𝜒↗¬𝜇] into ax-2 | |
| 13887 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13885, 13886 | |
| 13888 | →→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜑] into ax-1 | |
| 13889 | →¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13887, 13888 | |
| 13890 | →→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2 | |
| 13891 | →→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13889, 13890 | |
| 13892 | →¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13577, 13891 | |
| 13893 | →¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into id | |
| 13894 | →→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜑] into ax-1 | |
| 13895 | →¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13893, 13894 | |
| 13896 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into notnotr | |
| 13897 | →¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜑] into ax-1 | |
| 13898 | →→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-1 | |
| 13899 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13897, 13898 | |
| 13900 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2 | |
| 13901 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13899, 13900 | |
| 13902 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13896, 13901 | |
| 13903 | →→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2 | |
| 13904 | →→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13895, 13903 | |
| 13905 | →→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-1 | |
| 13906 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13904, 13905 | |
| 13907 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2 | |
| 13908 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13906, 13907 | |
| 13909 | →¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-1 | |
| 13910 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 13911 | →¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑 | Modus ponens 13909, 13910 | |
| 13912 | →→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑] into ax-2 | |
| 13913 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑 | Modus ponens 13911, 13912 | |
| 13914 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2 | |
| 13915 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13902, 13914 | |
| 13916 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜑] into ax-1 | |
| 13917 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13915, 13916 | |
| 13918 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2 | |
| 13919 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13917, 13918 | |
| 13920 | →¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13909, 13919 | |
| 13921 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-3 | |
| 13922 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜑] into ax-1 | |
| 13923 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13921, 13922 | |
| 13924 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2 | |
| 13925 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13923, 13924 | |
| 13926 | →¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13920, 13925 | |
| 13927 | →→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2 | |
| 13928 | →→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13926, 13927 | |
| 13929 | →¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13892, 13928 | |
| 13930 | →→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑 | Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-3 | |
| 13931 | →¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑 | Modus ponens 13929, 13930 | |
| 13932 | →↔⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into biimp | |
| 13933 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13844, 13932 | |
| 13934 | →→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇] into ax-1 | |
| 13935 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑 | Modus ponens 13931, 13934 | |
| 13936 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗𝜑] into ax-2 | |
| 13937 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜑 | Modus ponens 13935, 13936 | |
| 13938 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜑 | Modus ponens 13933, 13937 | |
| 13939 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜌] into simpl | |
| 13940 | →↔⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇↔¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into bicom1 | |
| 13941 | ↔¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇 | Modus ponens 13844, 13940 | |
| 13942 | →↔¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇] into biimp | |
| 13943 | →¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇 | Modus ponens 13941, 13942 | |
| 13944 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜑→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜑 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-1 | |
| 13945 | →¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜑 | Modus ponens 13938, 13944 | |
| 13946 | →→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜑→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜒↗𝜑] into ax-2 | |
| 13947 | →→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑 | Modus ponens 13945, 13946 | |
| 13948 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜇] into pm3.2im | |
| 13949 | →→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑→𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑, 𝜓↗𝜇] into ax-1 | |
| 13950 | →𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑 | Modus ponens 13931, 13949 | |
| 13951 | →→𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜑 | Subs [𝜑↗𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗𝜑] into ax-2 | |
| 13952 | →→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜑 | Modus ponens 13950, 13951 | |
| 13953 | →→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜑 | Subs [𝜑↗→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 13954 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜑 | Modus ponens 13952, 13953 | |
| 13955 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗→𝜇𝜑] into ax-2 | |
| 13956 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑 | Modus ponens 13954, 13955 | |
| 13957 | →𝜇𝜇 | Subs [𝜑↗𝜇] into id | |
| 13958 | →→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇 | Subs [𝜑↗→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜓↗𝜇] into ax-1 | |
| 13959 | →𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇 | Modus ponens 13846, 13958 | |
| 13960 | →→𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→→𝜇𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇 | Subs [𝜑↗𝜇, 𝜓↗𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇] into ax-2 | |
| 13961 | →→𝜇𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇 | Modus ponens 13959, 13960 | |
| 13962 | →→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑, 𝜓↗𝜇] into ax-1 | |
| 13963 | →𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Modus ponens 13853, 13962 | |
| 13964 | →→𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Subs [𝜑↗𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑] into ax-2 | |
| 13965 | →→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Modus ponens 13963, 13964 | |
| 13966 | →𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑 | Modus ponens 13846, 13965 | |
| 13967 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜇] into ax-1 | |
| 13968 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 13969 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Modus ponens 13967, 13968 | |
| 13970 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-2 | |
| 13971 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Modus ponens 13969, 13970 | |
| 13972 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎 | Modus ponens 13939, 13971 | |
| 13973 | →→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑 | Subs [𝜑↗𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗𝜑] into ax-2 | |
| 13974 | →→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑 | Modus ponens 13966, 13973 | |
| 13975 | →→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑 | Subs [𝜑↗→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 13976 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑 | Modus ponens 13974, 13975 | |
| 13977 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→𝜇𝜑] into ax-2 | |
| 13978 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑 | Modus ponens 13976, 13977 | |
| 13979 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑 | Modus ponens 13972, 13978 | |
| 13980 | →𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Subs [𝜑↗𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 13981 | →→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Subs [𝜑↗→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜇] into ax-1 | |
| 13982 | →𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Modus ponens 13980, 13981 | |
| 13983 | →→𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜇𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Subs [𝜑↗𝜇, 𝜓↗𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-2 | |
| 13984 | →→𝜇𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Modus ponens 13982, 13983 | |
| 13985 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜇, 𝜒↗𝜑] into ax-2 | |
| 13986 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Modus ponens 13979, 13985 | |
| 13987 | →→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑, 𝜓↗𝜇] into ax-1 | |
| 13988 | →𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Modus ponens 13986, 13987 | |
| 13989 | →→𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Subs [𝜑↗𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑] into ax-2 | |
| 13990 | →→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Modus ponens 13988, 13989 | |
| 13991 | →𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Modus ponens 13980, 13990 | |
| 13992 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into id | |
| 13993 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜇] into ax-1 | |
| 13994 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 13995 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Modus ponens 13993, 13994 | |
| 13996 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-2 | |
| 13997 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Modus ponens 13995, 13996 | |
| 13998 | →→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑 | Subs [𝜑↗𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗𝜑] into ax-2 | |
| 13999 | →→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑 | Modus ponens 13991, 13998 | |
| 14000 | →→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑 | Subs [𝜑↗→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14001 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑 | Modus ponens 13999, 14000 | |
| 14002 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→𝜇𝜑] into ax-2 | |
| 14003 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑 | Modus ponens 14001, 14002 | |
| 14004 | ↔⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜇] into df-an | |
| 14005 | →→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Subs [𝜑↗→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬¬𝜇] into ax-1 | |
| 14006 | →¬¬𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Modus ponens 13980, 14005 | |
| 14007 | →→¬¬𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜇𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Subs [𝜑↗¬¬𝜇, 𝜓↗𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-2 | |
| 14008 | →→¬¬𝜇𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Modus ponens 14006, 14007 | |
| 14009 | →¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Modus ponens 13845, 14008 | |
| 14010 | →→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑, 𝜓↗¬¬𝜇] into ax-1 | |
| 14011 | →¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Modus ponens 13986, 14010 | |
| 14012 | →→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Subs [𝜑↗¬¬𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑] into ax-2 | |
| 14013 | →→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Modus ponens 14011, 14012 | |
| 14014 | →¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Modus ponens 14009, 14013 | |
| 14015 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬¬𝜇] into ax-1 | |
| 14016 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14017 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Modus ponens 14015, 14016 | |
| 14018 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-2 | |
| 14019 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Modus ponens 14017, 14018 | |
| 14020 | →→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑 | Subs [𝜑↗¬¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗𝜑] into ax-2 | |
| 14021 | →→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑 | Modus ponens 14014, 14020 | |
| 14022 | →→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑 | Subs [𝜑↗→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14023 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑 | Modus ponens 14021, 14022 | |
| 14024 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→¬¬𝜇𝜑] into ax-2 | |
| 14025 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑 | Modus ponens 14023, 14024 | |
| 14026 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑 | Modus ponens 14015, 14025 | |
| 14027 | →→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑 | Subs [𝜑↗→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14028 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑 | Modus ponens 13874, 14027 | |
| 14029 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜇𝜑, 𝜒↗→¬¬𝜇¬¬𝜑] into ax-2 | |
| 14030 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜑 | Modus ponens 14028, 14029 | |
| 14031 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜑 | Modus ponens 14026, 14030 | |
| 14032 | →→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇 | Subs [𝜑↗→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14033 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇 | Modus ponens 13880, 14032 | |
| 14034 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜑¬𝜇 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜇¬¬𝜑, 𝜒↗→¬𝜑¬𝜇] into ax-2 | |
| 14035 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜑¬𝜇 | Modus ponens 14033, 14034 | |
| 14036 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜑¬𝜇 | Modus ponens 14031, 14035 | |
| 14037 | →¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14038 | →→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑 | Subs [𝜑↗→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 14039 | →¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑 | Modus ponens 14037, 14038 | |
| 14040 | →→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑] into ax-2 | |
| 14041 | →→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑 | Modus ponens 14039, 14040 | |
| 14042 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜑¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬𝜑, 𝜒↗¬𝜇] into ax-2 | |
| 14043 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14036, 14042 | |
| 14044 | →→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜑] into ax-1 | |
| 14045 | →¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14043, 14044 | |
| 14046 | →→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2 | |
| 14047 | →→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14045, 14046 | |
| 14048 | →¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14037, 14047 | |
| 14049 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into id | |
| 14050 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜑] into ax-1 | |
| 14051 | →¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14049, 14050 | |
| 14052 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into notnotr | |
| 14053 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜑] into ax-1 | |
| 14054 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-1 | |
| 14055 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14053, 14054 | |
| 14056 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2 | |
| 14057 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14055, 14056 | |
| 14058 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14052, 14057 | |
| 14059 | →→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2 | |
| 14060 | →→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14051, 14059 | |
| 14061 | →→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-1 | |
| 14062 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14060, 14061 | |
| 14063 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2 | |
| 14064 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14062, 14063 | |
| 14065 | →¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-1 | |
| 14066 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 14067 | →¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑 | Modus ponens 14065, 14066 | |
| 14068 | →→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑] into ax-2 | |
| 14069 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑 | Modus ponens 14067, 14068 | |
| 14070 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2 | |
| 14071 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14058, 14070 | |
| 14072 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜑] into ax-1 | |
| 14073 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14071, 14072 | |
| 14074 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2 | |
| 14075 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14073, 14074 | |
| 14076 | →¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14065, 14075 | |
| 14077 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-3 | |
| 14078 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜑] into ax-1 | |
| 14079 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14077, 14078 | |
| 14080 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2 | |
| 14081 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14079, 14080 | |
| 14082 | →¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14076, 14081 | |
| 14083 | →→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2 | |
| 14084 | →→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14082, 14083 | |
| 14085 | →¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14048, 14084 | |
| 14086 | →→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜑 | Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-3 | |
| 14087 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜑 | Modus ponens 14085, 14086 | |
| 14088 | →↔⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into biimp | |
| 14089 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14004, 14088 | |
| 14090 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜑 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14091 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜑 | Modus ponens 14087, 14090 | |
| 14092 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗𝜑] into ax-2 | |
| 14093 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Modus ponens 14091, 14092 | |
| 14094 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Modus ponens 14089, 14093 | simp-9l |
| 14095 | →→𝜓→𝜎𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜓→𝜎𝜓 | Subs [𝜑↗→𝜓→𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1 | |
| 14096 | →⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜓→𝜎𝜓 | Modus ponens 13179, 14095 | |
| 14097 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜓→𝜎𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→𝜎𝜓] into ax-2 | |
| 14098 | →→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓 | Modus ponens 14096, 14097 | |
| 14099 | →𝜓→𝜇𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜇] into ax-1 | |
| 14100 | →→𝜓→𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜓→𝜇𝜓 | Subs [𝜑↗→𝜓→𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 14101 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜓→𝜇𝜓 | Modus ponens 14099, 14100 | |
| 14102 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜓→𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→𝜇𝜓] into ax-2 | |
| 14103 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓 | Modus ponens 14101, 14102 | |
| 14104 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓 | Modus ponens simp-7r, 14103 | |
| 14105 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜇, 𝜒↗𝜓] into ax-2 | |
| 14106 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Modus ponens 14104, 14105 | |
| 14107 | →→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓, 𝜓↗¬¬𝜇] into ax-1 | |
| 14108 | →¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Modus ponens 14106, 14107 | |
| 14109 | →→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Subs [𝜑↗¬¬𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓] into ax-2 | |
| 14110 | →→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Modus ponens 14108, 14109 | |
| 14111 | →¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Modus ponens 13851, 14110 | |
| 14112 | →→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓 | Subs [𝜑↗¬¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗𝜓] into ax-2 | |
| 14113 | →→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓 | Modus ponens 14111, 14112 | |
| 14114 | →→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓 | Subs [𝜑↗→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 14115 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓 | Modus ponens 14113, 14114 | |
| 14116 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→¬¬𝜇𝜓] into ax-2 | |
| 14117 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓 | Modus ponens 14115, 14116 | |
| 14118 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓 | Modus ponens 13859, 14117 | |
| 14119 | →→𝜓¬¬𝜓→¬¬𝜇→𝜓¬¬𝜓 | Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜇] into ax-1 | |
| 14120 | →¬¬𝜇→𝜓¬¬𝜓 | Modus ponens 448, 14119 | |
| 14121 | →→¬¬𝜇→𝜓¬¬𝜓→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓 | Subs [𝜑↗¬¬𝜇, 𝜒↗¬¬𝜓] into ax-2 | |
| 14122 | →→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓 | Modus ponens 14120, 14121 | |
| 14123 | →→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓 | Subs [𝜑↗→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 14124 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓 | Modus ponens 14122, 14123 | |
| 14125 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜇𝜓, 𝜒↗→¬¬𝜇¬¬𝜓] into ax-2 | |
| 14126 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜓 | Modus ponens 14124, 14125 | |
| 14127 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜓 | Modus ponens 14118, 14126 | |
| 14128 | →→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇 | Subs [𝜑↗¬𝜇, 𝜓↗¬𝜓] into ax-3 | |
| 14129 | →→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇 | Subs [𝜑↗→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 14130 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇 | Modus ponens 14128, 14129 | |
| 14131 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜓¬𝜇 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜇¬¬𝜓, 𝜒↗→¬𝜓¬𝜇] into ax-2 | |
| 14132 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜓¬𝜇 | Modus ponens 14130, 14131 | |
| 14133 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜓¬𝜇 | Modus ponens 14127, 14132 | |
| 14134 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜓¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬𝜓, 𝜒↗¬𝜇] into ax-2 | |
| 14135 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 14133, 14134 | |
| 14136 | →→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜓] into ax-1 | |
| 14137 | →¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 14135, 14136 | |
| 14138 | →→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2 | |
| 14139 | →→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 14137, 14138 | |
| 14140 | →¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13781, 14139 | |
| 14141 | →→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜓] into ax-1 | |
| 14142 | →¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13893, 14141 | |
| 14143 | →¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜓] into ax-1 | |
| 14144 | →→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-1 | |
| 14145 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 14143, 14144 | |
| 14146 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2 | |
| 14147 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 14145, 14146 | |
| 14148 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13896, 14147 | |
| 14149 | →→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2 | |
| 14150 | →→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 14142, 14149 | |
| 14151 | →→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-1 | |
| 14152 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 14150, 14151 | |
| 14153 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2 | |
| 14154 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 14152, 14153 | |
| 14155 | →¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-1 | |
| 14156 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 14157 | →¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓 | Modus ponens 14155, 14156 | |
| 14158 | →→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓] into ax-2 | |
| 14159 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓 | Modus ponens 14157, 14158 | |
| 14160 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2 | |
| 14161 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 14148, 14160 | |
| 14162 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜓] into ax-1 | |
| 14163 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 14161, 14162 | |
| 14164 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2 | |
| 14165 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 14163, 14164 | |
| 14166 | →¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 14155, 14165 | |
| 14167 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜓] into ax-1 | |
| 14168 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 13921, 14167 | |
| 14169 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2 | |
| 14170 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 14168, 14169 | |
| 14171 | →¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 14166, 14170 | |
| 14172 | →→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2 | |
| 14173 | →→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 14171, 14172 | |
| 14174 | →¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇 | Modus ponens 14140, 14173 | |
| 14175 | →→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-3 | |
| 14176 | →¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓 | Modus ponens 14174, 14175 | |
| 14177 | →→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇] into ax-1 | |
| 14178 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓 | Modus ponens 14176, 14177 | |
| 14179 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗𝜓] into ax-2 | |
| 14180 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜓 | Modus ponens 14178, 14179 | |
| 14181 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜓 | Modus ponens 13933, 14180 | |
| 14182 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜓→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜓 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-1 | |
| 14183 | →¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜓 | Modus ponens 14181, 14182 | |
| 14184 | →→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜓→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜒↗𝜓] into ax-2 | |
| 14185 | →→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓 | Modus ponens 14183, 14184 | |
| 14186 | →→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓→𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓, 𝜓↗𝜇] into ax-1 | |
| 14187 | →𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓 | Modus ponens 14176, 14186 | |
| 14188 | →→𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜓 | Subs [𝜑↗𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗𝜓] into ax-2 | |
| 14189 | →→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜓 | Modus ponens 14187, 14188 | |
| 14190 | →→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜓 | Subs [𝜑↗→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 14191 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜓 | Modus ponens 14189, 14190 | |
| 14192 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗→𝜇𝜓] into ax-2 | |
| 14193 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓 | Modus ponens 14191, 14192 | |
| 14194 | →→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓, 𝜓↗𝜇] into ax-1 | |
| 14195 | →𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Modus ponens 14106, 14194 | |
| 14196 | →→𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Subs [𝜑↗𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓] into ax-2 | |
| 14197 | →→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Modus ponens 14195, 14196 | |
| 14198 | →𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓 | Modus ponens 13846, 14197 | |
| 14199 | →→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓 | Subs [𝜑↗𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗𝜓] into ax-2 | |
| 14200 | →→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓 | Modus ponens 14198, 14199 | |
| 14201 | →→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓 | Subs [𝜑↗→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14202 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓 | Modus ponens 14200, 14201 | |
| 14203 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→𝜇𝜓] into ax-2 | |
| 14204 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓 | Modus ponens 14202, 14203 | |
| 14205 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓 | Modus ponens 13972, 14204 | |
| 14206 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜇, 𝜒↗𝜓] into ax-2 | |
| 14207 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Modus ponens 14205, 14206 | |
| 14208 | →→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓, 𝜓↗𝜇] into ax-1 | |
| 14209 | →𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Modus ponens 14207, 14208 | |
| 14210 | →→𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Subs [𝜑↗𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓] into ax-2 | |
| 14211 | →→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Modus ponens 14209, 14210 | |
| 14212 | →𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Modus ponens 13980, 14211 | |
| 14213 | →→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓 | Subs [𝜑↗𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗𝜓] into ax-2 | |
| 14214 | →→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓 | Modus ponens 14212, 14213 | |
| 14215 | →→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓 | Subs [𝜑↗→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14216 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓 | Modus ponens 14214, 14215 | |
| 14217 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→𝜇𝜓] into ax-2 | |
| 14218 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓 | Modus ponens 14216, 14217 | |
| 14219 | →→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓, 𝜓↗¬¬𝜇] into ax-1 | |
| 14220 | →¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Modus ponens 14207, 14219 | |
| 14221 | →→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Subs [𝜑↗¬¬𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓] into ax-2 | |
| 14222 | →→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Modus ponens 14220, 14221 | |
| 14223 | →¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Modus ponens 14009, 14222 | |
| 14224 | →→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓 | Subs [𝜑↗¬¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗𝜓] into ax-2 | |
| 14225 | →→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓 | Modus ponens 14223, 14224 | |
| 14226 | →→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓 | Subs [𝜑↗→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14227 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓 | Modus ponens 14225, 14226 | |
| 14228 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→¬¬𝜇𝜓] into ax-2 | |
| 14229 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓 | Modus ponens 14227, 14228 | |
| 14230 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓 | Modus ponens 14015, 14229 | |
| 14231 | →→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓 | Subs [𝜑↗→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14232 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓 | Modus ponens 14122, 14231 | |
| 14233 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜇𝜓, 𝜒↗→¬¬𝜇¬¬𝜓] into ax-2 | |
| 14234 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜓 | Modus ponens 14232, 14233 | |
| 14235 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜓 | Modus ponens 14230, 14234 | |
| 14236 | →→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇 | Subs [𝜑↗→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14237 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇 | Modus ponens 14128, 14236 | |
| 14238 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜓¬𝜇 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜇¬¬𝜓, 𝜒↗→¬𝜓¬𝜇] into ax-2 | |
| 14239 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜓¬𝜇 | Modus ponens 14237, 14238 | |
| 14240 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜓¬𝜇 | Modus ponens 14235, 14239 | |
| 14241 | →¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14242 | →→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓 | Subs [𝜑↗→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 14243 | →¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓 | Modus ponens 14241, 14242 | |
| 14244 | →→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓] into ax-2 | |
| 14245 | →→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓 | Modus ponens 14243, 14244 | |
| 14246 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜓¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬𝜓, 𝜒↗¬𝜇] into ax-2 | |
| 14247 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14240, 14246 | |
| 14248 | →→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜓] into ax-1 | |
| 14249 | →¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14247, 14248 | |
| 14250 | →→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2 | |
| 14251 | →→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14249, 14250 | |
| 14252 | →¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14241, 14251 | |
| 14253 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜓] into ax-1 | |
| 14254 | →¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14049, 14253 | |
| 14255 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜓] into ax-1 | |
| 14256 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-1 | |
| 14257 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14255, 14256 | |
| 14258 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2 | |
| 14259 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14257, 14258 | |
| 14260 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14052, 14259 | |
| 14261 | →→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2 | |
| 14262 | →→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14254, 14261 | |
| 14263 | →→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-1 | |
| 14264 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14262, 14263 | |
| 14265 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2 | |
| 14266 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14264, 14265 | |
| 14267 | →¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-1 | |
| 14268 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 14269 | →¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓 | Modus ponens 14267, 14268 | |
| 14270 | →→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓] into ax-2 | |
| 14271 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓 | Modus ponens 14269, 14270 | |
| 14272 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2 | |
| 14273 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14260, 14272 | |
| 14274 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜓] into ax-1 | |
| 14275 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14273, 14274 | |
| 14276 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2 | |
| 14277 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14275, 14276 | |
| 14278 | →¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14267, 14277 | |
| 14279 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜓] into ax-1 | |
| 14280 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14077, 14279 | |
| 14281 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2 | |
| 14282 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14280, 14281 | |
| 14283 | →¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14278, 14282 | |
| 14284 | →→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2 | |
| 14285 | →→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14283, 14284 | |
| 14286 | →¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇 | Modus ponens 14252, 14285 | |
| 14287 | →→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-3 | |
| 14288 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜓 | Modus ponens 14286, 14287 | |
| 14289 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜓 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14290 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜓 | Modus ponens 14288, 14289 | |
| 14291 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗𝜓] into ax-2 | |
| 14292 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Modus ponens 14290, 14291 | |
| 14293 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Modus ponens 14089, 14292 | simp-9r |
| 14294 | →→𝜑→𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜑→𝜌𝜑 | Subs [𝜑↗→𝜑→𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 14295 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜑→𝜌𝜑 | Modus ponens 13378, 14294 | |
| 14296 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜑→𝜌𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜑, 𝜒↗→𝜌𝜑] into ax-2 | |
| 14297 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑 | Modus ponens 14295, 14296 | |
| 14298 | →𝜑→𝜆𝜑 | Subs [𝜓↗𝜆] into ax-1 | |
| 14299 | →→𝜑→𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜑→𝜆𝜑 | Subs [𝜑↗→𝜑→𝜆𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14300 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜑→𝜆𝜑 | Modus ponens 14298, 14299 | |
| 14301 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜑→𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜑, 𝜒↗→𝜆𝜑] into ax-2 | |
| 14302 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑 | Modus ponens 14300, 14301 | |
| 14303 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑 | Modus ponens simp-8l, 14302 | |
| 14304 | ↔⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜆] into df-an | |
| 14305 | →¬¬𝜆𝜆 | Subs [𝜑↗𝜆] into notnotr | |
| 14306 | →𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆 | Subs [𝜑↗𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14307 | →→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬¬𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆 | Subs [𝜑↗→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜓↗¬¬𝜆] into ax-1 | |
| 14308 | →¬¬𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆 | Modus ponens 14306, 14307 | |
| 14309 | →→¬¬𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→→¬¬𝜆𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆 | Subs [𝜑↗¬¬𝜆, 𝜓↗𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆] into ax-2 | |
| 14310 | →→¬¬𝜆𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆 | Modus ponens 14308, 14309 | |
| 14311 | →¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆 | Modus ponens 14305, 14310 | |
| 14312 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜆, 𝜒↗𝜑] into ax-2 | |
| 14313 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Modus ponens 14303, 14312 | |
| 14314 | →→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑, 𝜓↗¬¬𝜆] into ax-1 | |
| 14315 | →¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Modus ponens 14313, 14314 | |
| 14316 | →→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Subs [𝜑↗¬¬𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑] into ax-2 | |
| 14317 | →→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Modus ponens 14315, 14316 | |
| 14318 | →¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Modus ponens 14311, 14317 | |
| 14319 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬¬𝜆] into ax-1 | |
| 14320 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14321 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Modus ponens 14319, 14320 | |
| 14322 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-2 | |
| 14323 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Modus ponens 14321, 14322 | |
| 14324 | →→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑 | Subs [𝜑↗¬¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗𝜑] into ax-2 | |
| 14325 | →→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑 | Modus ponens 14318, 14324 | |
| 14326 | →→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑 | Subs [𝜑↗→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14327 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑 | Modus ponens 14325, 14326 | |
| 14328 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→¬¬𝜆𝜑] into ax-2 | |
| 14329 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑 | Modus ponens 14327, 14328 | |
| 14330 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑 | Modus ponens 14319, 14329 | |
| 14331 | →→𝜑¬¬𝜑→¬¬𝜆→𝜑¬¬𝜑 | Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜆] into ax-1 | |
| 14332 | →¬¬𝜆→𝜑¬¬𝜑 | Modus ponens notnot, 14331 | |
| 14333 | →→¬¬𝜆→𝜑¬¬𝜑→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑 | Subs [𝜑↗¬¬𝜆, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2 | |
| 14334 | →→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑 | Modus ponens 14332, 14333 | |
| 14335 | →→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑 | Subs [𝜑↗→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14336 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑 | Modus ponens 14334, 14335 | |
| 14337 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜆𝜑, 𝜒↗→¬¬𝜆¬¬𝜑] into ax-2 | |
| 14338 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜑 | Modus ponens 14336, 14337 | |
| 14339 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜑 | Modus ponens 14330, 14338 | |
| 14340 | →→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆 | Subs [𝜑↗¬𝜆, 𝜓↗¬𝜑] into ax-3 | |
| 14341 | →→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆 | Subs [𝜑↗→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14342 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆 | Modus ponens 14340, 14341 | |
| 14343 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜑¬𝜆 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜆¬¬𝜑, 𝜒↗→¬𝜑¬𝜆] into ax-2 | |
| 14344 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜑¬𝜆 | Modus ponens 14342, 14343 | |
| 14345 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜑¬𝜆 | Modus ponens 14339, 14344 | |
| 14346 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜑¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬𝜑, 𝜒↗¬𝜆] into ax-2 | |
| 14347 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14345, 14346 | |
| 14348 | →→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜑] into ax-1 | |
| 14349 | →¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14347, 14348 | |
| 14350 | →→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2 | |
| 14351 | →→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14349, 14350 | |
| 14352 | →¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14037, 14351 | |
| 14353 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into id | |
| 14354 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜑] into ax-1 | |
| 14355 | →¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14353, 14354 | |
| 14356 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into notnotr | |
| 14357 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜑] into ax-1 | |
| 14358 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-1 | |
| 14359 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14357, 14358 | |
| 14360 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2 | |
| 14361 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14359, 14360 | |
| 14362 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14356, 14361 | |
| 14363 | →→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2 | |
| 14364 | →→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14355, 14363 | |
| 14365 | →→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-1 | |
| 14366 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14364, 14365 | |
| 14367 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2 | |
| 14368 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14366, 14367 | |
| 14369 | →¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-1 | |
| 14370 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 14371 | →¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑 | Modus ponens 14369, 14370 | |
| 14372 | →→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑] into ax-2 | |
| 14373 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑 | Modus ponens 14371, 14372 | |
| 14374 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2 | |
| 14375 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14362, 14374 | |
| 14376 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜑] into ax-1 | |
| 14377 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14375, 14376 | |
| 14378 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2 | |
| 14379 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14377, 14378 | |
| 14380 | →¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14369, 14379 | |
| 14381 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-3 | |
| 14382 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜑] into ax-1 | |
| 14383 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14381, 14382 | |
| 14384 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2 | |
| 14385 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14383, 14384 | |
| 14386 | →¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14380, 14385 | |
| 14387 | →→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2 | |
| 14388 | →→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14386, 14387 | |
| 14389 | →¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14352, 14388 | |
| 14390 | →→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑 | Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-3 | |
| 14391 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑 | Modus ponens 14389, 14390 | |
| 14392 | →↔⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into biimp | |
| 14393 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14304, 14392 | |
| 14394 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆] into ax-1 | |
| 14395 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑 | Modus ponens 14391, 14394 | |
| 14396 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗𝜑] into ax-2 | |
| 14397 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜑 | Modus ponens 14395, 14396 | |
| 14398 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜑 | Modus ponens 14393, 14397 | |
| 14399 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜇] into simpl | |
| 14400 | →↔⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆↔¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into bicom1 | |
| 14401 | ↔¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆 | Modus ponens 14304, 14400 | |
| 14402 | →↔¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆] into biimp | |
| 14403 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆 | Modus ponens 14401, 14402 | |
| 14404 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜑 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-1 | |
| 14405 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜑 | Modus ponens 14398, 14404 | |
| 14406 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜑→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜒↗𝜑] into ax-2 | |
| 14407 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑 | Modus ponens 14405, 14406 | |
| 14408 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜆] into pm3.2im | |
| 14409 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑→𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑, 𝜓↗𝜆] into ax-1 | |
| 14410 | →𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑 | Modus ponens 14391, 14409 | |
| 14411 | →→𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜑 | Subs [𝜑↗𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗𝜑] into ax-2 | |
| 14412 | →→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜑 | Modus ponens 14410, 14411 | |
| 14413 | →→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜑 | Subs [𝜑↗→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14414 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜑 | Modus ponens 14412, 14413 | |
| 14415 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗→𝜆𝜑] into ax-2 | |
| 14416 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑 | Modus ponens 14414, 14415 | |
| 14417 | →𝜆𝜆 | Subs [𝜑↗𝜆] into id | |
| 14418 | →→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆 | Subs [𝜑↗→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜓↗𝜆] into ax-1 | |
| 14419 | →𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆 | Modus ponens 14306, 14418 | |
| 14420 | →→𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→→𝜆𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆 | Subs [𝜑↗𝜆, 𝜓↗𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆] into ax-2 | |
| 14421 | →→𝜆𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆 | Modus ponens 14419, 14420 | |
| 14422 | →→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑, 𝜓↗𝜆] into ax-1 | |
| 14423 | →𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Modus ponens 14313, 14422 | |
| 14424 | →→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Subs [𝜑↗𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑] into ax-2 | |
| 14425 | →→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Modus ponens 14423, 14424 | |
| 14426 | →𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑 | Modus ponens 14306, 14425 | |
| 14427 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜆] into ax-1 | |
| 14428 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14429 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Modus ponens 14427, 14428 | |
| 14430 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-2 | |
| 14431 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Modus ponens 14429, 14430 | |
| 14432 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌 | Modus ponens 14399, 14431 | |
| 14433 | →→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑 | Subs [𝜑↗𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗𝜑] into ax-2 | |
| 14434 | →→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑 | Modus ponens 14426, 14433 | |
| 14435 | →→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑 | Subs [𝜑↗→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14436 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑 | Modus ponens 14434, 14435 | |
| 14437 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→𝜆𝜑] into ax-2 | |
| 14438 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑 | Modus ponens 14436, 14437 | |
| 14439 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑 | Modus ponens 14432, 14438 | |
| 14440 | →𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆 | Subs [𝜑↗𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14441 | →→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆 | Subs [𝜑↗→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗𝜆] into ax-1 | |
| 14442 | →𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆 | Modus ponens 14440, 14441 | |
| 14443 | →→𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜆𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆 | Subs [𝜑↗𝜆, 𝜓↗𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-2 | |
| 14444 | →→𝜆𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆 | Modus ponens 14442, 14443 | |
| 14445 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜆, 𝜒↗𝜑] into ax-2 | |
| 14446 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Modus ponens 14439, 14445 | |
| 14447 | →→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑, 𝜓↗𝜆] into ax-1 | |
| 14448 | →𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Modus ponens 14446, 14447 | |
| 14449 | →→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Subs [𝜑↗𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑] into ax-2 | |
| 14450 | →→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Modus ponens 14448, 14449 | |
| 14451 | →𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Modus ponens 14440, 14450 | |
| 14452 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into id | |
| 14453 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜆] into ax-1 | |
| 14454 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14455 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Modus ponens 14453, 14454 | |
| 14456 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-2 | |
| 14457 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Modus ponens 14455, 14456 | |
| 14458 | →→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑 | Subs [𝜑↗𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗𝜑] into ax-2 | |
| 14459 | →→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑 | Modus ponens 14451, 14458 | |
| 14460 | →→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑 | Subs [𝜑↗→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14461 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑 | Modus ponens 14459, 14460 | |
| 14462 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→𝜆𝜑] into ax-2 | |
| 14463 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑 | Modus ponens 14461, 14462 | |
| 14464 | ↔⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜆] into df-an | |
| 14465 | →→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆 | Subs [𝜑↗→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗¬¬𝜆] into ax-1 | |
| 14466 | →¬¬𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆 | Modus ponens 14440, 14465 | |
| 14467 | →→¬¬𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜆𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆 | Subs [𝜑↗¬¬𝜆, 𝜓↗𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-2 | |
| 14468 | →→¬¬𝜆𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆 | Modus ponens 14466, 14467 | |
| 14469 | →¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆 | Modus ponens 14305, 14468 | |
| 14470 | →→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑, 𝜓↗¬¬𝜆] into ax-1 | |
| 14471 | →¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Modus ponens 14446, 14470 | |
| 14472 | →→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Subs [𝜑↗¬¬𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑] into ax-2 | |
| 14473 | →→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Modus ponens 14471, 14472 | |
| 14474 | →¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Modus ponens 14469, 14473 | |
| 14475 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬¬𝜆] into ax-1 | |
| 14476 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14477 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Modus ponens 14475, 14476 | |
| 14478 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-2 | |
| 14479 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Modus ponens 14477, 14478 | |
| 14480 | →→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑 | Subs [𝜑↗¬¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗𝜑] into ax-2 | |
| 14481 | →→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑 | Modus ponens 14474, 14480 | |
| 14482 | →→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑 | Subs [𝜑↗→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14483 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑 | Modus ponens 14481, 14482 | |
| 14484 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→¬¬𝜆𝜑] into ax-2 | |
| 14485 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑 | Modus ponens 14483, 14484 | |
| 14486 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑 | Modus ponens 14475, 14485 | |
| 14487 | →→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑 | Subs [𝜑↗→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14488 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑 | Modus ponens 14334, 14487 | |
| 14489 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜆𝜑, 𝜒↗→¬¬𝜆¬¬𝜑] into ax-2 | |
| 14490 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜑 | Modus ponens 14488, 14489 | |
| 14491 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜑 | Modus ponens 14486, 14490 | |
| 14492 | →→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆 | Subs [𝜑↗→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14493 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆 | Modus ponens 14340, 14492 | |
| 14494 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜑¬𝜆 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜆¬¬𝜑, 𝜒↗→¬𝜑¬𝜆] into ax-2 | |
| 14495 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜑¬𝜆 | Modus ponens 14493, 14494 | |
| 14496 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜑¬𝜆 | Modus ponens 14491, 14495 | |
| 14497 | →¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14498 | →→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑 | Subs [𝜑↗→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 14499 | →¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑 | Modus ponens 14497, 14498 | |
| 14500 | →→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑] into ax-2 | |
| 14501 | →→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑 | Modus ponens 14499, 14500 | |
| 14502 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜑¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬𝜑, 𝜒↗¬𝜆] into ax-2 | |
| 14503 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14496, 14502 | |
| 14504 | →→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜑] into ax-1 | |
| 14505 | →¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14503, 14504 | |
| 14506 | →→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2 | |
| 14507 | →→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14505, 14506 | |
| 14508 | →¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14497, 14507 | |
| 14509 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into id | |
| 14510 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜑] into ax-1 | |
| 14511 | →¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14509, 14510 | |
| 14512 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into notnotr | |
| 14513 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜑] into ax-1 | |
| 14514 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-1 | |
| 14515 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14513, 14514 | |
| 14516 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2 | |
| 14517 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14515, 14516 | |
| 14518 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14512, 14517 | |
| 14519 | →→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2 | |
| 14520 | →→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14511, 14519 | |
| 14521 | →→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-1 | |
| 14522 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14520, 14521 | |
| 14523 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2 | |
| 14524 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14522, 14523 | |
| 14525 | →¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-1 | |
| 14526 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 14527 | →¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑 | Modus ponens 14525, 14526 | |
| 14528 | →→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑] into ax-2 | |
| 14529 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑 | Modus ponens 14527, 14528 | |
| 14530 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2 | |
| 14531 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14518, 14530 | |
| 14532 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜑] into ax-1 | |
| 14533 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14531, 14532 | |
| 14534 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2 | |
| 14535 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14533, 14534 | |
| 14536 | →¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14525, 14535 | |
| 14537 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-3 | |
| 14538 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜑] into ax-1 | |
| 14539 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14537, 14538 | |
| 14540 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2 | |
| 14541 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14539, 14540 | |
| 14542 | →¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14536, 14541 | |
| 14543 | →→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2 | |
| 14544 | →→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14542, 14543 | |
| 14545 | →¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14508, 14544 | |
| 14546 | →→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜑 | Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-3 | |
| 14547 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜑 | Modus ponens 14545, 14546 | |
| 14548 | →↔⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into biimp | |
| 14549 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14464, 14548 | |
| 14550 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜑 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1 | |
| 14551 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜑 | Modus ponens 14547, 14550 | |
| 14552 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗𝜑] into ax-2 | |
| 14553 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑 | Modus ponens 14551, 14552 | |
| 14554 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑 | Modus ponens 14549, 14553 | simp-10l |
| 14555 | →→𝜓→𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜓→𝜌𝜓 | Subs [𝜑↗→𝜓→𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1 | |
| 14556 | →⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜓→𝜌𝜓 | Modus ponens 13639, 14555 | |
| 14557 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜓→𝜌𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→𝜌𝜓] into ax-2 | |
| 14558 | →→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓 | Modus ponens 14556, 14557 | |
| 14559 | →𝜓→𝜆𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜆] into ax-1 | |
| 14560 | →→𝜓→𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜓→𝜆𝜓 | Subs [𝜑↗→𝜓→𝜆𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14561 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜓→𝜆𝜓 | Modus ponens 14559, 14560 | |
| 14562 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜓→𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→𝜆𝜓] into ax-2 | |
| 14563 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓 | Modus ponens 14561, 14562 | |
| 14564 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓 | Modus ponens simp-8r, 14563 | |
| 14565 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜆, 𝜒↗𝜓] into ax-2 | |
| 14566 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Modus ponens 14564, 14565 | |
| 14567 | →→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓, 𝜓↗¬¬𝜆] into ax-1 | |
| 14568 | →¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Modus ponens 14566, 14567 | |
| 14569 | →→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Subs [𝜑↗¬¬𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓] into ax-2 | |
| 14570 | →→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Modus ponens 14568, 14569 | |
| 14571 | →¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Modus ponens 14311, 14570 | |
| 14572 | →→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓 | Subs [𝜑↗¬¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗𝜓] into ax-2 | |
| 14573 | →→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓 | Modus ponens 14571, 14572 | |
| 14574 | →→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓 | Subs [𝜑↗→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14575 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓 | Modus ponens 14573, 14574 | |
| 14576 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→¬¬𝜆𝜓] into ax-2 | |
| 14577 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓 | Modus ponens 14575, 14576 | |
| 14578 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓 | Modus ponens 14319, 14577 | |
| 14579 | →→𝜓¬¬𝜓→¬¬𝜆→𝜓¬¬𝜓 | Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜆] into ax-1 | |
| 14580 | →¬¬𝜆→𝜓¬¬𝜓 | Modus ponens 448, 14579 | |
| 14581 | →→¬¬𝜆→𝜓¬¬𝜓→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓 | Subs [𝜑↗¬¬𝜆, 𝜒↗¬¬𝜓] into ax-2 | |
| 14582 | →→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓 | Modus ponens 14580, 14581 | |
| 14583 | →→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓 | Subs [𝜑↗→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14584 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓 | Modus ponens 14582, 14583 | |
| 14585 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜆𝜓, 𝜒↗→¬¬𝜆¬¬𝜓] into ax-2 | |
| 14586 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜓 | Modus ponens 14584, 14585 | |
| 14587 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜓 | Modus ponens 14578, 14586 | |
| 14588 | →→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆 | Subs [𝜑↗¬𝜆, 𝜓↗¬𝜓] into ax-3 | |
| 14589 | →→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆 | Subs [𝜑↗→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14590 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆 | Modus ponens 14588, 14589 | |
| 14591 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜓¬𝜆 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜆¬¬𝜓, 𝜒↗→¬𝜓¬𝜆] into ax-2 | |
| 14592 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜓¬𝜆 | Modus ponens 14590, 14591 | |
| 14593 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜓¬𝜆 | Modus ponens 14587, 14592 | |
| 14594 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜓¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬𝜓, 𝜒↗¬𝜆] into ax-2 | |
| 14595 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14593, 14594 | |
| 14596 | →→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜓] into ax-1 | |
| 14597 | →¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14595, 14596 | |
| 14598 | →→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2 | |
| 14599 | →→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14597, 14598 | |
| 14600 | →¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14241, 14599 | |
| 14601 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜓] into ax-1 | |
| 14602 | →¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14353, 14601 | |
| 14603 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜓] into ax-1 | |
| 14604 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-1 | |
| 14605 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14603, 14604 | |
| 14606 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2 | |
| 14607 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14605, 14606 | |
| 14608 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14356, 14607 | |
| 14609 | →→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2 | |
| 14610 | →→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14602, 14609 | |
| 14611 | →→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-1 | |
| 14612 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14610, 14611 | |
| 14613 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2 | |
| 14614 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14612, 14613 | |
| 14615 | →¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-1 | |
| 14616 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 14617 | →¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓 | Modus ponens 14615, 14616 | |
| 14618 | →→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓] into ax-2 | |
| 14619 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓 | Modus ponens 14617, 14618 | |
| 14620 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2 | |
| 14621 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14608, 14620 | |
| 14622 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜓] into ax-1 | |
| 14623 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14621, 14622 | |
| 14624 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2 | |
| 14625 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14623, 14624 | |
| 14626 | →¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14615, 14625 | |
| 14627 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜓] into ax-1 | |
| 14628 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14381, 14627 | |
| 14629 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2 | |
| 14630 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14628, 14629 | |
| 14631 | →¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14626, 14630 | |
| 14632 | →→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2 | |
| 14633 | →→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14631, 14632 | |
| 14634 | →¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆 | Modus ponens 14600, 14633 | |
| 14635 | →→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-3 | |
| 14636 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓 | Modus ponens 14634, 14635 | |
| 14637 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆] into ax-1 | |
| 14638 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓 | Modus ponens 14636, 14637 | |
| 14639 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗𝜓] into ax-2 | |
| 14640 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜓 | Modus ponens 14638, 14639 | |
| 14641 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜓 | Modus ponens 14393, 14640 | |
| 14642 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜓 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-1 | |
| 14643 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜓 | Modus ponens 14641, 14642 | |
| 14644 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜓→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜒↗𝜓] into ax-2 | |
| 14645 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓 | Modus ponens 14643, 14644 | |
| 14646 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓→𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓, 𝜓↗𝜆] into ax-1 | |
| 14647 | →𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓 | Modus ponens 14636, 14646 | |
| 14648 | →→𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜓 | Subs [𝜑↗𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗𝜓] into ax-2 | |
| 14649 | →→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜓 | Modus ponens 14647, 14648 | |
| 14650 | →→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜓 | Subs [𝜑↗→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14651 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜓 | Modus ponens 14649, 14650 | |
| 14652 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗→𝜆𝜓] into ax-2 | |
| 14653 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓 | Modus ponens 14651, 14652 | |
| 14654 | →→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓, 𝜓↗𝜆] into ax-1 | |
| 14655 | →𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Modus ponens 14566, 14654 | |
| 14656 | →→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Subs [𝜑↗𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓] into ax-2 | |
| 14657 | →→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Modus ponens 14655, 14656 | |
| 14658 | →𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓 | Modus ponens 14306, 14657 | |
| 14659 | →→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓 | Subs [𝜑↗𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗𝜓] into ax-2 | |
| 14660 | →→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓 | Modus ponens 14658, 14659 | |
| 14661 | →→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓 | Subs [𝜑↗→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14662 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓 | Modus ponens 14660, 14661 | |
| 14663 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→𝜆𝜓] into ax-2 | |
| 14664 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓 | Modus ponens 14662, 14663 | |
| 14665 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓 | Modus ponens 14432, 14664 | |
| 14666 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜆, 𝜒↗𝜓] into ax-2 | |
| 14667 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Modus ponens 14665, 14666 | |
| 14668 | →→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓, 𝜓↗𝜆] into ax-1 | |
| 14669 | →𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Modus ponens 14667, 14668 | |
| 14670 | →→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Subs [𝜑↗𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓] into ax-2 | |
| 14671 | →→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Modus ponens 14669, 14670 | |
| 14672 | →𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Modus ponens 14440, 14671 | |
| 14673 | →→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓 | Subs [𝜑↗𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗𝜓] into ax-2 | |
| 14674 | →→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓 | Modus ponens 14672, 14673 | |
| 14675 | →→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓 | Subs [𝜑↗→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14676 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓 | Modus ponens 14674, 14675 | |
| 14677 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→𝜆𝜓] into ax-2 | |
| 14678 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓 | Modus ponens 14676, 14677 | |
| 14679 | →→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓, 𝜓↗¬¬𝜆] into ax-1 | |
| 14680 | →¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Modus ponens 14667, 14679 | |
| 14681 | →→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Subs [𝜑↗¬¬𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓] into ax-2 | |
| 14682 | →→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Modus ponens 14680, 14681 | |
| 14683 | →¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Modus ponens 14469, 14682 | |
| 14684 | →→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓 | Subs [𝜑↗¬¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗𝜓] into ax-2 | |
| 14685 | →→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓 | Modus ponens 14683, 14684 | |
| 14686 | →→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓 | Subs [𝜑↗→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14687 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓 | Modus ponens 14685, 14686 | |
| 14688 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→¬¬𝜆𝜓] into ax-2 | |
| 14689 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓 | Modus ponens 14687, 14688 | |
| 14690 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓 | Modus ponens 14475, 14689 | |
| 14691 | →→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓 | Subs [𝜑↗→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14692 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓 | Modus ponens 14582, 14691 | |
| 14693 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜆𝜓, 𝜒↗→¬¬𝜆¬¬𝜓] into ax-2 | |
| 14694 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜓 | Modus ponens 14692, 14693 | |
| 14695 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜓 | Modus ponens 14690, 14694 | |
| 14696 | →→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆 | Subs [𝜑↗→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14697 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆 | Modus ponens 14588, 14696 | |
| 14698 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜓¬𝜆 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜆¬¬𝜓, 𝜒↗→¬𝜓¬𝜆] into ax-2 | |
| 14699 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜓¬𝜆 | Modus ponens 14697, 14698 | |
| 14700 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜓¬𝜆 | Modus ponens 14695, 14699 | |
| 14701 | →¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14702 | →→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓 | Subs [𝜑↗→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 14703 | →¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓 | Modus ponens 14701, 14702 | |
| 14704 | →→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓] into ax-2 | |
| 14705 | →→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓 | Modus ponens 14703, 14704 | |
| 14706 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜓¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬𝜓, 𝜒↗¬𝜆] into ax-2 | |
| 14707 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14700, 14706 | |
| 14708 | →→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜓] into ax-1 | |
| 14709 | →¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14707, 14708 | |
| 14710 | →→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2 | |
| 14711 | →→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14709, 14710 | |
| 14712 | →¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14701, 14711 | |
| 14713 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜓] into ax-1 | |
| 14714 | →¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14509, 14713 | |
| 14715 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜓] into ax-1 | |
| 14716 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-1 | |
| 14717 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14715, 14716 | |
| 14718 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2 | |
| 14719 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14717, 14718 | |
| 14720 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14512, 14719 | |
| 14721 | →→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2 | |
| 14722 | →→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14714, 14721 | |
| 14723 | →→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-1 | |
| 14724 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14722, 14723 | |
| 14725 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2 | |
| 14726 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14724, 14725 | |
| 14727 | →¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-1 | |
| 14728 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 14729 | →¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓 | Modus ponens 14727, 14728 | |
| 14730 | →→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓] into ax-2 | |
| 14731 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓 | Modus ponens 14729, 14730 | |
| 14732 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2 | |
| 14733 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14720, 14732 | |
| 14734 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜓] into ax-1 | |
| 14735 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14733, 14734 | |
| 14736 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2 | |
| 14737 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14735, 14736 | |
| 14738 | →¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14727, 14737 | |
| 14739 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜓] into ax-1 | |
| 14740 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14537, 14739 | |
| 14741 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2 | |
| 14742 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14740, 14741 | |
| 14743 | →¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14738, 14742 | |
| 14744 | →→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2 | |
| 14745 | →→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14743, 14744 | |
| 14746 | →¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆 | Modus ponens 14712, 14745 | |
| 14747 | →→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-3 | |
| 14748 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜓 | Modus ponens 14746, 14747 | |
| 14749 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜓 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1 | |
| 14750 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜓 | Modus ponens 14748, 14749 | |
| 14751 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗𝜓] into ax-2 | |
| 14752 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓 | Modus ponens 14750, 14751 | |
| 14753 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓 | Modus ponens 14549, 14752 | simp-10r |
| 14754 | →→𝜑→𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜑→𝜇𝜑 | Subs [𝜑↗→𝜑→𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 14755 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜑→𝜇𝜑 | Modus ponens 13838, 14754 | |
| 14756 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜑→𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜑, 𝜒↗→𝜇𝜑] into ax-2 | |
| 14757 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑 | Modus ponens 14755, 14756 | |
| 14758 | →𝜑→𝜅𝜑 | Subs [𝜓↗𝜅] into ax-1 | |
| 14759 | →→𝜑→𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜑→𝜅𝜑 | Subs [𝜑↗→𝜑→𝜅𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14760 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜑→𝜅𝜑 | Modus ponens 14758, 14759 | |
| 14761 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜑→𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜑, 𝜒↗→𝜅𝜑] into ax-2 | |
| 14762 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑 | Modus ponens 14760, 14761 | |
| 14763 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑 | Modus ponens simp-9l, 14762 | |
| 14764 | ↔⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜅] into df-an | |
| 14765 | →¬¬𝜅𝜅 | Subs [𝜑↗𝜅] into notnotr | |
| 14766 | →𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅 | Subs [𝜑↗𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14767 | →→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬¬𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅 | Subs [𝜑↗→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜓↗¬¬𝜅] into ax-1 | |
| 14768 | →¬¬𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅 | Modus ponens 14766, 14767 | |
| 14769 | →→¬¬𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→→¬¬𝜅𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅 | Subs [𝜑↗¬¬𝜅, 𝜓↗𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅] into ax-2 | |
| 14770 | →→¬¬𝜅𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅 | Modus ponens 14768, 14769 | |
| 14771 | →¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅 | Modus ponens 14765, 14770 | |
| 14772 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜅, 𝜒↗𝜑] into ax-2 | |
| 14773 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Modus ponens 14763, 14772 | |
| 14774 | →→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑, 𝜓↗¬¬𝜅] into ax-1 | |
| 14775 | →¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Modus ponens 14773, 14774 | |
| 14776 | →→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Subs [𝜑↗¬¬𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑] into ax-2 | |
| 14777 | →→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Modus ponens 14775, 14776 | |
| 14778 | →¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Modus ponens 14771, 14777 | |
| 14779 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬¬𝜅] into ax-1 | |
| 14780 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14781 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Modus ponens 14779, 14780 | |
| 14782 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-2 | |
| 14783 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Modus ponens 14781, 14782 | |
| 14784 | →→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑 | Subs [𝜑↗¬¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗𝜑] into ax-2 | |
| 14785 | →→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑 | Modus ponens 14778, 14784 | |
| 14786 | →→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑 | Subs [𝜑↗→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14787 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑 | Modus ponens 14785, 14786 | |
| 14788 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→¬¬𝜅𝜑] into ax-2 | |
| 14789 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑 | Modus ponens 14787, 14788 | |
| 14790 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑 | Modus ponens 14779, 14789 | |
| 14791 | →→𝜑¬¬𝜑→¬¬𝜅→𝜑¬¬𝜑 | Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜅] into ax-1 | |
| 14792 | →¬¬𝜅→𝜑¬¬𝜑 | Modus ponens notnot, 14791 | |
| 14793 | →→¬¬𝜅→𝜑¬¬𝜑→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑 | Subs [𝜑↗¬¬𝜅, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2 | |
| 14794 | →→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑 | Modus ponens 14792, 14793 | |
| 14795 | →→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑 | Subs [𝜑↗→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14796 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑 | Modus ponens 14794, 14795 | |
| 14797 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜅𝜑, 𝜒↗→¬¬𝜅¬¬𝜑] into ax-2 | |
| 14798 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜑 | Modus ponens 14796, 14797 | |
| 14799 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜑 | Modus ponens 14790, 14798 | |
| 14800 | →→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅 | Subs [𝜑↗¬𝜅, 𝜓↗¬𝜑] into ax-3 | |
| 14801 | →→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅 | Subs [𝜑↗→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14802 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅 | Modus ponens 14800, 14801 | |
| 14803 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜑¬𝜅 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜅¬¬𝜑, 𝜒↗→¬𝜑¬𝜅] into ax-2 | |
| 14804 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜑¬𝜅 | Modus ponens 14802, 14803 | |
| 14805 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜑¬𝜅 | Modus ponens 14799, 14804 | |
| 14806 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜑¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬𝜑, 𝜒↗¬𝜅] into ax-2 | |
| 14807 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14805, 14806 | |
| 14808 | →→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜑] into ax-1 | |
| 14809 | →¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14807, 14808 | |
| 14810 | →→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2 | |
| 14811 | →→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14809, 14810 | |
| 14812 | →¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14497, 14811 | |
| 14813 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into id | |
| 14814 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜑] into ax-1 | |
| 14815 | →¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14813, 14814 | |
| 14816 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into notnotr | |
| 14817 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜑] into ax-1 | |
| 14818 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-1 | |
| 14819 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14817, 14818 | |
| 14820 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2 | |
| 14821 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14819, 14820 | |
| 14822 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14816, 14821 | |
| 14823 | →→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2 | |
| 14824 | →→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14815, 14823 | |
| 14825 | →→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-1 | |
| 14826 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14824, 14825 | |
| 14827 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2 | |
| 14828 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14826, 14827 | |
| 14829 | →¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-1 | |
| 14830 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 14831 | →¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑 | Modus ponens 14829, 14830 | |
| 14832 | →→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑] into ax-2 | |
| 14833 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑 | Modus ponens 14831, 14832 | |
| 14834 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2 | |
| 14835 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14822, 14834 | |
| 14836 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜑] into ax-1 | |
| 14837 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14835, 14836 | |
| 14838 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2 | |
| 14839 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14837, 14838 | |
| 14840 | →¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14829, 14839 | |
| 14841 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-3 | |
| 14842 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜑] into ax-1 | |
| 14843 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14841, 14842 | |
| 14844 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2 | |
| 14845 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14843, 14844 | |
| 14846 | →¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14840, 14845 | |
| 14847 | →→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2 | |
| 14848 | →→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14846, 14847 | |
| 14849 | →¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14812, 14848 | |
| 14850 | →→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑 | Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-3 | |
| 14851 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑 | Modus ponens 14849, 14850 | |
| 14852 | →↔⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into biimp | |
| 14853 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14764, 14852 | |
| 14854 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅] into ax-1 | |
| 14855 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑 | Modus ponens 14851, 14854 | |
| 14856 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗𝜑] into ax-2 | |
| 14857 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜑 | Modus ponens 14855, 14856 | |
| 14858 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜑 | Modus ponens 14853, 14857 | |
| 14859 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜆] into simpl | |
| 14860 | →↔⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅↔¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into bicom1 | |
| 14861 | ↔¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅 | Modus ponens 14764, 14860 | |
| 14862 | →↔¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅] into biimp | |
| 14863 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅 | Modus ponens 14861, 14862 | |
| 14864 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜑 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-1 | |
| 14865 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜑 | Modus ponens 14858, 14864 | |
| 14866 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜑→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜒↗𝜑] into ax-2 | |
| 14867 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑 | Modus ponens 14865, 14866 | |
| 14868 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜅] into pm3.2im | |
| 14869 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑→𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑, 𝜓↗𝜅] into ax-1 | |
| 14870 | →𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑 | Modus ponens 14851, 14869 | |
| 14871 | →→𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜑 | Subs [𝜑↗𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗𝜑] into ax-2 | |
| 14872 | →→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜑 | Modus ponens 14870, 14871 | |
| 14873 | →→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜑 | Subs [𝜑↗→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 14874 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜑 | Modus ponens 14872, 14873 | |
| 14875 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗→𝜅𝜑] into ax-2 | |
| 14876 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑 | Modus ponens 14874, 14875 | |
| 14877 | →𝜅𝜅 | Subs [𝜑↗𝜅] into id | |
| 14878 | →→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅 | Subs [𝜑↗→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜓↗𝜅] into ax-1 | |
| 14879 | →𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅 | Modus ponens 14766, 14878 | |
| 14880 | →→𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→→𝜅𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅 | Subs [𝜑↗𝜅, 𝜓↗𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅] into ax-2 | |
| 14881 | →→𝜅𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅 | Modus ponens 14879, 14880 | |
| 14882 | →→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑, 𝜓↗𝜅] into ax-1 | |
| 14883 | →𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Modus ponens 14773, 14882 | |
| 14884 | →→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Subs [𝜑↗𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑] into ax-2 | |
| 14885 | →→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Modus ponens 14883, 14884 | |
| 14886 | →𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑 | Modus ponens 14766, 14885 | |
| 14887 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜅] into ax-1 | |
| 14888 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1 | |
| 14889 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Modus ponens 14887, 14888 | |
| 14890 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-2 | |
| 14891 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Modus ponens 14889, 14890 | |
| 14892 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇 | Modus ponens 14859, 14891 | |
| 14893 | →→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑 | Subs [𝜑↗𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗𝜑] into ax-2 | |
| 14894 | →→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑 | Modus ponens 14886, 14893 | |
| 14895 | →→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑 | Subs [𝜑↗→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1 | |
| 14896 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑 | Modus ponens 14894, 14895 | |
| 14897 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→𝜅𝜑] into ax-2 | |
| 14898 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑 | Modus ponens 14896, 14897 | |
| 14899 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑 | Modus ponens 14892, 14898 | |
| 14900 | →𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅 | Subs [𝜑↗𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1 | |
| 14901 | →→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅 | Subs [𝜑↗→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜓↗𝜅] into ax-1 | |
| 14902 | →𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅 | Modus ponens 14900, 14901 | |
| 14903 | →→𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→→𝜅𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅 | Subs [𝜑↗𝜅, 𝜓↗𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅] into ax-2 | |
| 14904 | →→𝜅𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅 | Modus ponens 14902, 14903 | |
| 14905 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗𝜅, 𝜒↗𝜑] into ax-2 | |
| 14906 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑 | Modus ponens 14899, 14905 | |
| 14907 | →→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑, 𝜓↗𝜅] into ax-1 | |
| 14908 | →𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑 | Modus ponens 14906, 14907 | |
| 14909 | →→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑 | Subs [𝜑↗𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑] into ax-2 | |
| 14910 | →→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑 | Modus ponens 14908, 14909 | |
| 14911 | →𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑 | Modus ponens 14900, 14910 | |
| 14912 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into id | |
| 14913 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗𝜅] into ax-1 | |
| 14914 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1 | |
| 14915 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆 | Modus ponens 14913, 14914 | |
| 14916 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-2 | |
| 14917 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆 | Modus ponens 14915, 14916 | |
| 14918 | →→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑 | Subs [𝜑↗𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗𝜑] into ax-2 | |
| 14919 | →→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑 | Modus ponens 14911, 14918 | |
| 14920 | →→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑 | Subs [𝜑↗→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1 | |
| 14921 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑 | Modus ponens 14919, 14920 | |
| 14922 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→𝜅𝜑] into ax-2 | |
| 14923 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑 | Modus ponens 14921, 14922 | |
| 14924 | ↔⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗𝜅] into df-an | |
| 14925 | →→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬¬𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅 | Subs [𝜑↗→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜓↗¬¬𝜅] into ax-1 | |
| 14926 | →¬¬𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅 | Modus ponens 14900, 14925 | |
| 14927 | →→¬¬𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→→¬¬𝜅𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅 | Subs [𝜑↗¬¬𝜅, 𝜓↗𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅] into ax-2 | |
| 14928 | →→¬¬𝜅𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅 | Modus ponens 14926, 14927 | |
| 14929 | →¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅 | Modus ponens 14765, 14928 | |
| 14930 | →→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑, 𝜓↗¬¬𝜅] into ax-1 | |
| 14931 | →¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑 | Modus ponens 14906, 14930 | |
| 14932 | →→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑 | Subs [𝜑↗¬¬𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑] into ax-2 | |
| 14933 | →→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑 | Modus ponens 14931, 14932 | |
| 14934 | →¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑 | Modus ponens 14929, 14933 | |
| 14935 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗¬¬𝜅] into ax-1 | |
| 14936 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1 | |
| 14937 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆 | Modus ponens 14935, 14936 | |
| 14938 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-2 | |
| 14939 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆 | Modus ponens 14937, 14938 | |
| 14940 | →→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑 | Subs [𝜑↗¬¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗𝜑] into ax-2 | |
| 14941 | →→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑 | Modus ponens 14934, 14940 | |
| 14942 | →→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑 | Subs [𝜑↗→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1 | |
| 14943 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑 | Modus ponens 14941, 14942 | |
| 14944 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→¬¬𝜅𝜑] into ax-2 | |
| 14945 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑 | Modus ponens 14943, 14944 | |
| 14946 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑 | Modus ponens 14935, 14945 | |
| 14947 | →→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑 | Subs [𝜑↗→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1 | |
| 14948 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑 | Modus ponens 14794, 14947 | |
| 14949 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→¬¬𝜅𝜑, 𝜒↗→¬¬𝜅¬¬𝜑] into ax-2 | |
| 14950 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜑 | Modus ponens 14948, 14949 | |
| 14951 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜑 | Modus ponens 14946, 14950 | |
| 14952 | →→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅 | Subs [𝜑↗→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1 | |
| 14953 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅 | Modus ponens 14800, 14952 | |
| 14954 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬𝜑¬𝜅 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→¬¬𝜅¬¬𝜑, 𝜒↗→¬𝜑¬𝜅] into ax-2 | |
| 14955 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬𝜑¬𝜅 | Modus ponens 14953, 14954 | |
| 14956 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬𝜑¬𝜅 | Modus ponens 14951, 14955 | |
| 14957 | →¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1 | |
| 14958 | →→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑 | Subs [𝜑↗→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 14959 | →¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑 | Modus ponens 14957, 14958 | |
| 14960 | →→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑] into ax-2 | |
| 14961 | →→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑 | Modus ponens 14959, 14960 | |
| 14962 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬𝜑¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗¬𝜑, 𝜒↗¬𝜅] into ax-2 | |
| 14963 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 14956, 14962 | |
| 14964 | →→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜑] into ax-1 | |
| 14965 | →¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 14963, 14964 | |
| 14966 | →→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2 | |
| 14967 | →→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 14965, 14966 | |
| 14968 | →¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 14957, 14967 | |
| 14969 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into id | |
| 14970 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜑] into ax-1 | |
| 14971 | →¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 14969, 14970 | |
| 14972 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into notnotr | |
| 14973 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜑] into ax-1 | |
| 14974 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-1 | |
| 14975 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 14973, 14974 | |
| 14976 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2 | |
| 14977 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 14975, 14976 | |
| 14978 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 14972, 14977 | |
| 14979 | →→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2 | |
| 14980 | →→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 14971, 14979 | |
| 14981 | →→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-1 | |
| 14982 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 14980, 14981 | |
| 14983 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2 | |
| 14984 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 14982, 14983 | |
| 14985 | →¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-1 | |
| 14986 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 14987 | →¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑 | Modus ponens 14985, 14986 | |
| 14988 | →→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑] into ax-2 | |
| 14989 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑 | Modus ponens 14987, 14988 | |
| 14990 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2 | |
| 14991 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 14978, 14990 | |
| 14992 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜑] into ax-1 | |
| 14993 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 14991, 14992 | |
| 14994 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2 | |
| 14995 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 14993, 14994 | |
| 14996 | →¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 14985, 14995 | |
| 14997 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-3 | |
| 14998 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜑] into ax-1 | |
| 14999 | →¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 14997, 14998 | |
| 15000 | →→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2 | |
| 15001 | →→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 14999, 15000 | |
| 15002 | →¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 14996, 15001 | |
| 15003 | →→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2 | |
| 15004 | →→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 15002, 15003 | |
| 15005 | →¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 14968, 15004 | |
| 15006 | →→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜑 | Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-3 | |
| 15007 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜑 | Modus ponens 15005, 15006 | |
| 15008 | →↔⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into biimp | |
| 15009 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 14924, 15008 | |
| 15010 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜑 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅] into ax-1 | |
| 15011 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜑 | Modus ponens 15007, 15010 | |
| 15012 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅𝜑 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗𝜑] into ax-2 | |
| 15013 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅𝜑 | Modus ponens 15011, 15012 | |
| 15014 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅𝜑 | Modus ponens 15009, 15013 | simp-11l |
| 15015 | →→𝜓→𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜓→𝜇𝜓 | Subs [𝜑↗→𝜓→𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1 | |
| 15016 | →⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜓→𝜇𝜓 | Modus ponens 14099, 15015 | |
| 15017 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜓→𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→𝜇𝜓] into ax-2 | |
| 15018 | →→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓 | Modus ponens 15016, 15017 | |
| 15019 | →𝜓→𝜅𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜅] into ax-1 | |
| 15020 | →→𝜓→𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜓→𝜅𝜓 | Subs [𝜑↗→𝜓→𝜅𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 15021 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜓→𝜅𝜓 | Modus ponens 15019, 15020 | |
| 15022 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜓→𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→𝜅𝜓] into ax-2 | |
| 15023 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓 | Modus ponens 15021, 15022 | |
| 15024 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓 | Modus ponens simp-9r, 15023 | |
| 15025 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜅, 𝜒↗𝜓] into ax-2 | |
| 15026 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Modus ponens 15024, 15025 | |
| 15027 | →→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓, 𝜓↗¬¬𝜅] into ax-1 | |
| 15028 | →¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Modus ponens 15026, 15027 | |
| 15029 | →→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Subs [𝜑↗¬¬𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓] into ax-2 | |
| 15030 | →→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Modus ponens 15028, 15029 | |
| 15031 | →¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Modus ponens 14771, 15030 | |
| 15032 | →→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓 | Subs [𝜑↗¬¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗𝜓] into ax-2 | |
| 15033 | →→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓 | Modus ponens 15031, 15032 | |
| 15034 | →→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓 | Subs [𝜑↗→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 15035 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓 | Modus ponens 15033, 15034 | |
| 15036 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→¬¬𝜅𝜓] into ax-2 | |
| 15037 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓 | Modus ponens 15035, 15036 | |
| 15038 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓 | Modus ponens 14779, 15037 | |
| 15039 | →→𝜓¬¬𝜓→¬¬𝜅→𝜓¬¬𝜓 | Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜅] into ax-1 | |
| 15040 | →¬¬𝜅→𝜓¬¬𝜓 | Modus ponens 448, 15039 | |
| 15041 | →→¬¬𝜅→𝜓¬¬𝜓→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓 | Subs [𝜑↗¬¬𝜅, 𝜒↗¬¬𝜓] into ax-2 | |
| 15042 | →→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓 | Modus ponens 15040, 15041 | |
| 15043 | →→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓 | Subs [𝜑↗→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 15044 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓 | Modus ponens 15042, 15043 | |
| 15045 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜅𝜓, 𝜒↗→¬¬𝜅¬¬𝜓] into ax-2 | |
| 15046 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜓 | Modus ponens 15044, 15045 | |
| 15047 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜓 | Modus ponens 15038, 15046 | |
| 15048 | →→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅 | Subs [𝜑↗¬𝜅, 𝜓↗¬𝜓] into ax-3 | |
| 15049 | →→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅 | Subs [𝜑↗→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 15050 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅 | Modus ponens 15048, 15049 | |
| 15051 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜓¬𝜅 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜅¬¬𝜓, 𝜒↗→¬𝜓¬𝜅] into ax-2 | |
| 15052 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜓¬𝜅 | Modus ponens 15050, 15051 | |
| 15053 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜓¬𝜅 | Modus ponens 15047, 15052 | |
| 15054 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜓¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬𝜓, 𝜒↗¬𝜅] into ax-2 | |
| 15055 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 15053, 15054 | |
| 15056 | →→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜓] into ax-1 | |
| 15057 | →¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 15055, 15056 | |
| 15058 | →→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2 | |
| 15059 | →→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 15057, 15058 | |
| 15060 | →¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14701, 15059 | |
| 15061 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜓] into ax-1 | |
| 15062 | →¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14813, 15061 | |
| 15063 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜓] into ax-1 | |
| 15064 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-1 | |
| 15065 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 15063, 15064 | |
| 15066 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2 | |
| 15067 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 15065, 15066 | |
| 15068 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14816, 15067 | |
| 15069 | →→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2 | |
| 15070 | →→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 15062, 15069 | |
| 15071 | →→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-1 | |
| 15072 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 15070, 15071 | |
| 15073 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2 | |
| 15074 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 15072, 15073 | |
| 15075 | →¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-1 | |
| 15076 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 15077 | →¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓 | Modus ponens 15075, 15076 | |
| 15078 | →→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓] into ax-2 | |
| 15079 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓 | Modus ponens 15077, 15078 | |
| 15080 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2 | |
| 15081 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 15068, 15080 | |
| 15082 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜓] into ax-1 | |
| 15083 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 15081, 15082 | |
| 15084 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2 | |
| 15085 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 15083, 15084 | |
| 15086 | →¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 15075, 15085 | |
| 15087 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜓] into ax-1 | |
| 15088 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 14841, 15087 | |
| 15089 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2 | |
| 15090 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 15088, 15089 | |
| 15091 | →¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 15086, 15090 | |
| 15092 | →→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2 | |
| 15093 | →→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 15091, 15092 | |
| 15094 | →¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅 | Modus ponens 15060, 15093 | |
| 15095 | →→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-3 | |
| 15096 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓 | Modus ponens 15094, 15095 | |
| 15097 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅] into ax-1 | |
| 15098 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓 | Modus ponens 15096, 15097 | |
| 15099 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗𝜓] into ax-2 | |
| 15100 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜓 | Modus ponens 15098, 15099 | |
| 15101 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜓 | Modus ponens 14853, 15100 | |
| 15102 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜓 | Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-1 | |
| 15103 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜓 | Modus ponens 15101, 15102 | |
| 15104 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜓→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜒↗𝜓] into ax-2 | |
| 15105 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓 | Modus ponens 15103, 15104 | |
| 15106 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓→𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓, 𝜓↗𝜅] into ax-1 | |
| 15107 | →𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓 | Modus ponens 15096, 15106 | |
| 15108 | →→𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜓 | Subs [𝜑↗𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗𝜓] into ax-2 | |
| 15109 | →→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜓 | Modus ponens 15107, 15108 | |
| 15110 | →→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜓 | Subs [𝜑↗→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1 | |
| 15111 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜓 | Modus ponens 15109, 15110 | |
| 15112 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗→𝜅𝜓] into ax-2 | |
| 15113 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓 | Modus ponens 15111, 15112 | |
| 15114 | →→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓, 𝜓↗𝜅] into ax-1 | |
| 15115 | →𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Modus ponens 15026, 15114 | |
| 15116 | →→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Subs [𝜑↗𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓] into ax-2 | |
| 15117 | →→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Modus ponens 15115, 15116 | |
| 15118 | →𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓 | Modus ponens 14766, 15117 | |
| 15119 | →→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓 | Subs [𝜑↗𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗𝜓] into ax-2 | |
| 15120 | →→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓 | Modus ponens 15118, 15119 | |
| 15121 | →→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓 | Subs [𝜑↗→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1 | |
| 15122 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓 | Modus ponens 15120, 15121 | |
| 15123 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→𝜅𝜓] into ax-2 | |
| 15124 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓 | Modus ponens 15122, 15123 | |
| 15125 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓 | Modus ponens 14892, 15124 | |
| 15126 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗𝜅, 𝜒↗𝜓] into ax-2 | |
| 15127 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓 | Modus ponens 15125, 15126 | |
| 15128 | →→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓, 𝜓↗𝜅] into ax-1 | |
| 15129 | →𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓 | Modus ponens 15127, 15128 | |
| 15130 | →→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓 | Subs [𝜑↗𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓] into ax-2 | |
| 15131 | →→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓 | Modus ponens 15129, 15130 | |
| 15132 | →𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓 | Modus ponens 14900, 15131 | |
| 15133 | →→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓 | Subs [𝜑↗𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗𝜓] into ax-2 | |
| 15134 | →→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓 | Modus ponens 15132, 15133 | |
| 15135 | →→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓 | Subs [𝜑↗→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1 | |
| 15136 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓 | Modus ponens 15134, 15135 | |
| 15137 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→𝜅𝜓] into ax-2 | |
| 15138 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓 | Modus ponens 15136, 15137 | |
| 15139 | →→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓, 𝜓↗¬¬𝜅] into ax-1 | |
| 15140 | →¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓 | Modus ponens 15127, 15139 | |
| 15141 | →→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓 | Subs [𝜑↗¬¬𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓] into ax-2 | |
| 15142 | →→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓 | Modus ponens 15140, 15141 | |
| 15143 | →¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓 | Modus ponens 14929, 15142 | |
| 15144 | →→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓 | Subs [𝜑↗¬¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗𝜓] into ax-2 | |
| 15145 | →→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓 | Modus ponens 15143, 15144 | |
| 15146 | →→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓 | Subs [𝜑↗→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1 | |
| 15147 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓 | Modus ponens 15145, 15146 | |
| 15148 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→¬¬𝜅𝜓] into ax-2 | |
| 15149 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓 | Modus ponens 15147, 15148 | |
| 15150 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓 | Modus ponens 14935, 15149 | |
| 15151 | →→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓 | Subs [𝜑↗→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1 | |
| 15152 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓 | Modus ponens 15042, 15151 | |
| 15153 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→¬¬𝜅𝜓, 𝜒↗→¬¬𝜅¬¬𝜓] into ax-2 | |
| 15154 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜓 | Modus ponens 15152, 15153 | |
| 15155 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜓 | Modus ponens 15150, 15154 | |
| 15156 | →→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅 | Subs [𝜑↗→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1 | |
| 15157 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅 | Modus ponens 15048, 15156 | |
| 15158 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬𝜓¬𝜅 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→¬¬𝜅¬¬𝜓, 𝜒↗→¬𝜓¬𝜅] into ax-2 | |
| 15159 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬𝜓¬𝜅 | Modus ponens 15157, 15158 | |
| 15160 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬𝜓¬𝜅 | Modus ponens 15155, 15159 | |
| 15161 | →¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1 | |
| 15162 | →→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓 | Subs [𝜑↗→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 15163 | →¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓 | Modus ponens 15161, 15162 | |
| 15164 | →→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓] into ax-2 | |
| 15165 | →→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓 | Modus ponens 15163, 15164 | |
| 15166 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬𝜓¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗¬𝜓, 𝜒↗¬𝜅] into ax-2 | |
| 15167 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 15160, 15166 | |
| 15168 | →→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜓] into ax-1 | |
| 15169 | →¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 15167, 15168 | |
| 15170 | →→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2 | |
| 15171 | →→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 15169, 15170 | |
| 15172 | →¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 15161, 15171 | |
| 15173 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜓] into ax-1 | |
| 15174 | →¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 14969, 15173 | |
| 15175 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜓] into ax-1 | |
| 15176 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-1 | |
| 15177 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 15175, 15176 | |
| 15178 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2 | |
| 15179 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 15177, 15178 | |
| 15180 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 14972, 15179 | |
| 15181 | →→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2 | |
| 15182 | →→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 15174, 15181 | |
| 15183 | →→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-1 | |
| 15184 | →¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 15182, 15183 | |
| 15185 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2 | |
| 15186 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 15184, 15185 | |
| 15187 | →¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-1 | |
| 15188 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 15189 | →¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓 | Modus ponens 15187, 15188 | |
| 15190 | →→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓] into ax-2 | |
| 15191 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓 | Modus ponens 15189, 15190 | |
| 15192 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2 | |
| 15193 | →→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 15180, 15192 | |
| 15194 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜓] into ax-1 | |
| 15195 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 15193, 15194 | |
| 15196 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2 | |
| 15197 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 15195, 15196 | |
| 15198 | →¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 15187, 15197 | |
| 15199 | →→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜓] into ax-1 | |
| 15200 | →¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 14997, 15199 | |
| 15201 | →→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2 | |
| 15202 | →→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 15200, 15201 | |
| 15203 | →¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 15198, 15202 | |
| 15204 | →→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2 | |
| 15205 | →→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 15203, 15204 | |
| 15206 | →¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅 | Modus ponens 15172, 15205 | |
| 15207 | →→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-3 | |
| 15208 | →¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜓 | Modus ponens 15206, 15207 | |
| 15209 | →→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜓 | Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅] into ax-1 | |
| 15210 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜓 | Modus ponens 15208, 15209 | |
| 15211 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅𝜓 | Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗𝜓] into ax-2 | |
| 15212 | →→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅𝜓 | Modus ponens 15210, 15211 | |
| 15213 | →⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅𝜓 | Modus ponens 15009, 15212 | simp-11r |
| 15214 | ↔⋀𝜑→𝜑𝜓¬→𝜑¬→𝜑𝜓 | Subs [𝜓↗→𝜑𝜓] into df-an | |
| 15215 | →→𝜑→¬𝜓¬→𝜑𝜓→→𝜑¬𝜓→𝜑¬→𝜑𝜓 | Subs [𝜓↗¬𝜓, 𝜒↗¬→𝜑𝜓] into ax-2 | |
| 15216 | →→𝜑¬𝜓→𝜑¬→𝜑𝜓 | Modus ponens jcn, 15215 | |
| 15217 | →→→𝜑¬𝜓→𝜑¬→𝜑𝜓→¬𝜓→→𝜑¬𝜓→𝜑¬→𝜑𝜓 | Subs [𝜑↗→→𝜑¬𝜓→𝜑¬→𝜑𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 15218 | →¬𝜓→→𝜑¬𝜓→𝜑¬→𝜑𝜓 | Modus ponens 15216, 15217 | |
| 15219 | →→¬𝜓→→𝜑¬𝜓→𝜑¬→𝜑𝜓→→¬𝜓→𝜑¬𝜓→¬𝜓→𝜑¬→𝜑𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗→𝜑¬𝜓, 𝜒↗→𝜑¬→𝜑𝜓] into ax-2 | |
| 15220 | →→¬𝜓→𝜑¬𝜓→¬𝜓→𝜑¬→𝜑𝜓 | Modus ponens 15218, 15219 | |
| 15221 | →¬𝜓→𝜑¬→𝜑𝜓 | Modus ponens 609, 15220 | |
| 15222 | →¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑¬→𝜑𝜓] into id | |
| 15223 | →→¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→¬𝜓→¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓 | Subs [𝜑↗→¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 15224 | →¬𝜓→¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓 | Modus ponens 15222, 15223 | |
| 15225 | →¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑¬→𝜑𝜓] into notnotr | |
| 15226 | →¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑¬→𝜑𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 15227 | →→¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓→¬¬¬→𝜑¬→𝜑𝜓→¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓 | Subs [𝜑↗→¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓, 𝜓↗¬¬¬→𝜑¬→𝜑𝜓] into ax-1 | |
| 15228 | →¬¬¬→𝜑¬→𝜑𝜓→¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓 | Modus ponens 15226, 15227 | |
| 15229 | →→¬¬¬→𝜑¬→𝜑𝜓→¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓→→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→¬¬¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓 | Subs [𝜑↗¬¬¬→𝜑¬→𝜑𝜓, 𝜓↗¬→𝜑¬→𝜑𝜓, 𝜒↗→¬𝜓¬→𝜑¬→𝜑𝜓] into ax-2 | |
| 15230 | →→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→¬¬¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓 | Modus ponens 15228, 15229 | |
| 15231 | →¬¬¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓 | Modus ponens 15225, 15230 | |
| 15232 | →→¬𝜓→¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→→¬𝜓¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬→𝜑¬→𝜑𝜓, 𝜒↗¬→𝜑¬→𝜑𝜓] into ax-2 | |
| 15233 | →→¬𝜓¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓 | Modus ponens 15224, 15232 | |
| 15234 | →→→¬𝜓¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓→¬¬¬→𝜑¬→𝜑𝜓→→¬𝜓¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓 | Subs [𝜑↗→→¬𝜓¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓, 𝜓↗¬¬¬→𝜑¬→𝜑𝜓] into ax-1 | |
| 15235 | →¬¬¬→𝜑¬→𝜑𝜓→→¬𝜓¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓 | Modus ponens 15233, 15234 | |
| 15236 | →→¬¬¬→𝜑¬→𝜑𝜓→→¬𝜓¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓→→¬¬¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓→¬¬¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓 | Subs [𝜑↗¬¬¬→𝜑¬→𝜑𝜓, 𝜓↗→¬𝜓¬→𝜑¬→𝜑𝜓, 𝜒↗→¬𝜓¬→𝜑¬→𝜑𝜓] into ax-2 | |
| 15237 | →→¬¬¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓→¬¬¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓 | Modus ponens 15235, 15236 | |
| 15238 | →¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→𝜑¬→𝜑𝜓] into ax-1 | |
| 15239 | →→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬𝜓→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓 | Subs [𝜑↗→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 15240 | →¬𝜓→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓 | Modus ponens 15238, 15239 | |
| 15241 | →→¬𝜓→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→𝜑¬→𝜑𝜓¬𝜓] into ax-2 | |
| 15242 | →→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓 | Modus ponens 15240, 15241 | |
| 15243 | →→¬¬¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓→→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓 | Subs [𝜑↗¬¬¬→𝜑¬→𝜑𝜓, 𝜓↗¬𝜓, 𝜒↗¬→𝜑¬→𝜑𝜓] into ax-2 | |
| 15244 | →→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓 | Modus ponens 15231, 15243 | |
| 15245 | →→→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→¬𝜓→→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓 | Subs [𝜑↗→→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 15246 | →¬𝜓→→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓 | Modus ponens 15244, 15245 | |
| 15247 | →→¬𝜓→→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜑¬→𝜑𝜓¬𝜓, 𝜒↗→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓] into ax-2 | |
| 15248 | →→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓 | Modus ponens 15246, 15247 | |
| 15249 | →¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓 | Modus ponens 15238, 15248 | |
| 15250 | →→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓 | Subs [𝜑↗¬¬→𝜑¬→𝜑𝜓, 𝜓↗→𝜑¬→𝜑𝜓] into ax-3 | |
| 15251 | →→→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓→¬𝜓→→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓 | Subs [𝜑↗→→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓, 𝜓↗¬𝜓] into ax-1 | |
| 15252 | →¬𝜓→→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓 | Modus ponens 15250, 15251 | |
| 15253 | →→¬𝜓→→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓→→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→¬𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓, 𝜒↗→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓] into ax-2 | |
| 15254 | →→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→¬𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓 | Modus ponens 15252, 15253 | |
| 15255 | →¬𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓 | Modus ponens 15249, 15254 | |
| 15256 | →→¬𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓→→¬𝜓→𝜑¬→𝜑𝜓→¬𝜓¬¬→𝜑¬→𝜑𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗→𝜑¬→𝜑𝜓, 𝜒↗¬¬→𝜑¬→𝜑𝜓] into ax-2 | |
| 15257 | →→¬𝜓→𝜑¬→𝜑𝜓→¬𝜓¬¬→𝜑¬→𝜑𝜓 | Modus ponens 15255, 15256 | |
| 15258 | →¬𝜓¬¬→𝜑¬→𝜑𝜓 | Modus ponens 15221, 15257 | |
| 15259 | →→¬𝜓¬¬→𝜑¬→𝜑𝜓→¬→𝜑¬→𝜑𝜓𝜓 | Subs [𝜑↗𝜓, 𝜓↗¬→𝜑¬→𝜑𝜓] into ax-3 | |
| 15260 | →¬→𝜑¬→𝜑𝜓𝜓 | Modus ponens 15258, 15259 | |
| 15261 | →↔⋀𝜑→𝜑𝜓¬→𝜑¬→𝜑𝜓→⋀𝜑→𝜑𝜓¬→𝜑¬→𝜑𝜓 | Subs [𝜑↗⋀𝜑→𝜑𝜓, 𝜓↗¬→𝜑¬→𝜑𝜓] into biimp | |
| 15262 | →⋀𝜑→𝜑𝜓¬→𝜑¬→𝜑𝜓 | Modus ponens 15214, 15261 | |
| 15263 | →→¬→𝜑¬→𝜑𝜓𝜓→⋀𝜑→𝜑𝜓→¬→𝜑¬→𝜑𝜓𝜓 | Subs [𝜑↗→¬→𝜑¬→𝜑𝜓𝜓, 𝜓↗⋀𝜑→𝜑𝜓] into ax-1 | |
| 15264 | →⋀𝜑→𝜑𝜓→¬→𝜑¬→𝜑𝜓𝜓 | Modus ponens 15260, 15263 | |
| 15265 | →→⋀𝜑→𝜑𝜓→¬→𝜑¬→𝜑𝜓𝜓→→⋀𝜑→𝜑𝜓¬→𝜑¬→𝜑𝜓→⋀𝜑→𝜑𝜓𝜓 | Subs [𝜑↗⋀𝜑→𝜑𝜓, 𝜓↗¬→𝜑¬→𝜑𝜓, 𝜒↗𝜓] into ax-2 | |
| 15266 | →→⋀𝜑→𝜑𝜓¬→𝜑¬→𝜑𝜓→⋀𝜑→𝜑𝜓𝜓 | Modus ponens 15264, 15265 | |
| 15267 | →⋀𝜑→𝜑𝜓𝜓 | Modus ponens 15262, 15266 | pm3.35 |
| 15268 | →↔𝜓𝜒↔𝜓𝜒 | Subs [𝜑↗↔𝜓𝜒] into id | |
| 15269 | ↔↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒 | Subs [𝜑↗↔𝜑𝜒, 𝜓↗↔𝜓𝜒] into bicom | |
| 15270 | →↔↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒→↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒 | Subs [𝜑↗↔↔𝜑𝜒↔𝜓𝜒, 𝜓↗↔↔𝜓𝜒↔𝜑𝜒] into biimp | |
| 15271 | →↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒 | Modus ponens 15269, 15270 | |
| 15272 | →→↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒→↔𝜑𝜓→↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒 | Subs [𝜑↗→↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 15273 | →↔𝜑𝜓→↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒 | Modus ponens 15271, 15272 | |
| 15274 | →→↔𝜑𝜓→↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒→→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜓↔↔𝜓𝜒↔𝜑𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔↔𝜑𝜒↔𝜓𝜒, 𝜒↗↔↔𝜓𝜒↔𝜑𝜒] into ax-2 | |
| 15275 | →→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜓↔↔𝜓𝜒↔𝜑𝜒 | Modus ponens 15273, 15274 | |
| 15276 | →↔𝜑𝜓↔↔𝜓𝜒↔𝜑𝜒 | Modus ponens bibi1, 15275 | |
| 15277 | →↔↔𝜓𝜒↔𝜑𝜒→↔𝜓𝜒↔𝜑𝜒 | Subs [𝜑↗↔𝜓𝜒, 𝜓↗↔𝜑𝜒] into biimp | |
| 15278 | →→↔↔𝜓𝜒↔𝜑𝜒→↔𝜓𝜒↔𝜑𝜒→↔𝜑𝜓→↔↔𝜓𝜒↔𝜑𝜒→↔𝜓𝜒↔𝜑𝜒 | Subs [𝜑↗→↔↔𝜓𝜒↔𝜑𝜒→↔𝜓𝜒↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 15279 | →↔𝜑𝜓→↔↔𝜓𝜒↔𝜑𝜒→↔𝜓𝜒↔𝜑𝜒 | Modus ponens 15277, 15278 | |
| 15280 | →→↔𝜑𝜓→↔↔𝜓𝜒↔𝜑𝜒→↔𝜓𝜒↔𝜑𝜒→→↔𝜑𝜓↔↔𝜓𝜒↔𝜑𝜒→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔↔𝜓𝜒↔𝜑𝜒, 𝜒↗→↔𝜓𝜒↔𝜑𝜒] into ax-2 | |
| 15281 | →→↔𝜑𝜓↔↔𝜓𝜒↔𝜑𝜒→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒 | Modus ponens 15279, 15280 | |
| 15282 | →↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒 | Modus ponens 15276, 15281 | |
| 15283 | →↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒 | Subs [𝜑↗↔𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 15284 | →→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒→↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒 | Subs [𝜑↗→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒, 𝜓↗↔𝜓𝜒] into ax-1 | |
| 15285 | →↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒 | Modus ponens 15283, 15284 | |
| 15286 | →→↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒→→↔𝜓𝜒↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒 | Subs [𝜑↗↔𝜓𝜒, 𝜓↗↔𝜓𝜒, 𝜒↗→↔𝜑𝜓↔𝜓𝜒] into ax-2 | |
| 15287 | →→↔𝜓𝜒↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒 | Modus ponens 15285, 15286 | |
| 15288 | →→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜓𝜒, 𝜒↗↔𝜑𝜒] into ax-2 | |
| 15289 | →→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒→↔𝜓𝜒→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒, 𝜓↗↔𝜓𝜒] into ax-1 | |
| 15290 | →↔𝜓𝜒→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒 | Modus ponens 2744, 15289 | |
| 15291 | →→↔𝜓𝜒→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒→→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗↔𝜓𝜒, 𝜓↗→↔𝜑𝜓↔𝜓𝜒, 𝜒↗→↔𝜑𝜓↔𝜑𝜒] into ax-2 | |
| 15292 | →→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒 | Modus ponens 15290, 15291 | |
| 15293 | →↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒 | Modus ponens 15283, 15292 | |
| 15294 | →↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜓𝜒] into ax-1 | |
| 15295 | →→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓 | Subs [𝜑↗→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 15296 | →↔𝜑𝜓→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓 | Modus ponens 15294, 15295 | |
| 15297 | →→↔𝜑𝜓→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→↔𝜓𝜒↔𝜑𝜓] into ax-2 | |
| 15298 | →→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓 | Modus ponens 15296, 15297 | |
| 15299 | →→↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒→→↔𝜓𝜒↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒 | Subs [𝜑↗↔𝜓𝜒, 𝜓↗↔𝜑𝜓, 𝜒↗↔𝜑𝜒] into ax-2 | |
| 15300 | →→↔𝜓𝜒↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒 | Modus ponens 15293, 15299 | |
| 15301 | →→→↔𝜓𝜒↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒→↔𝜑𝜓→→↔𝜓𝜒↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒 | Subs [𝜑↗→→↔𝜓𝜒↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 15302 | →↔𝜑𝜓→→↔𝜓𝜒↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒 | Modus ponens 15300, 15301 | |
| 15303 | →→↔𝜑𝜓→→↔𝜓𝜒↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒→→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→↔𝜓𝜒↔𝜑𝜓, 𝜒↗→↔𝜓𝜒↔𝜑𝜒] into ax-2 | |
| 15304 | →→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒 | Modus ponens 15302, 15303 | |
| 15305 | ↔⋀↔𝜑𝜓↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜓𝜒] into df-an | |
| 15306 | →¬¬↔𝜓𝜒↔𝜓𝜒 | Subs [𝜑↗↔𝜓𝜒] into notnotr | |
| 15307 | →→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒→¬¬↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒 | Subs [𝜑↗→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒, 𝜓↗¬¬↔𝜓𝜒] into ax-1 | |
| 15308 | →¬¬↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒 | Modus ponens 15283, 15307 | |
| 15309 | →→¬¬↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒→→¬¬↔𝜓𝜒↔𝜓𝜒→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒 | Subs [𝜑↗¬¬↔𝜓𝜒, 𝜓↗↔𝜓𝜒, 𝜒↗→↔𝜑𝜓↔𝜓𝜒] into ax-2 | |
| 15310 | →→¬¬↔𝜓𝜒↔𝜓𝜒→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒 | Modus ponens 15308, 15309 | |
| 15311 | →¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒 | Modus ponens 15306, 15310 | |
| 15312 | →→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒→¬¬↔𝜓𝜒→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒, 𝜓↗¬¬↔𝜓𝜒] into ax-1 | |
| 15313 | →¬¬↔𝜓𝜒→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒 | Modus ponens 2744, 15312 | |
| 15314 | →→¬¬↔𝜓𝜒→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒→→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗¬¬↔𝜓𝜒, 𝜓↗→↔𝜑𝜓↔𝜓𝜒, 𝜒↗→↔𝜑𝜓↔𝜑𝜒] into ax-2 | |
| 15315 | →→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒 | Modus ponens 15313, 15314 | |
| 15316 | →¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒 | Modus ponens 15311, 15315 | |
| 15317 | →↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬¬↔𝜓𝜒] into ax-1 | |
| 15318 | →→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓 | Subs [𝜑↗→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 15319 | →↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓 | Modus ponens 15317, 15318 | |
| 15320 | →→↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→¬¬↔𝜓𝜒↔𝜑𝜓] into ax-2 | |
| 15321 | →→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓 | Modus ponens 15319, 15320 | |
| 15322 | →→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒→→¬¬↔𝜓𝜒↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒 | Subs [𝜑↗¬¬↔𝜓𝜒, 𝜓↗↔𝜑𝜓, 𝜒↗↔𝜑𝜒] into ax-2 | |
| 15323 | →→¬¬↔𝜓𝜒↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒 | Modus ponens 15316, 15322 | |
| 15324 | →→→¬¬↔𝜓𝜒↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒→↔𝜑𝜓→→¬¬↔𝜓𝜒↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒 | Subs [𝜑↗→→¬¬↔𝜓𝜒↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 15325 | →↔𝜑𝜓→→¬¬↔𝜓𝜒↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒 | Modus ponens 15323, 15324 | |
| 15326 | →→↔𝜑𝜓→→¬¬↔𝜓𝜒↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒→→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬↔𝜓𝜒↔𝜑𝜓, 𝜒↗→¬¬↔𝜓𝜒↔𝜑𝜒] into ax-2 | |
| 15327 | →→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒 | Modus ponens 15325, 15326 | |
| 15328 | →↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒 | Modus ponens 15317, 15327 | |
| 15329 | →↔𝜑𝜒¬¬↔𝜑𝜒 | Subs [𝜑↗↔𝜑𝜒] into notnot | |
| 15330 | →→↔𝜑𝜒¬¬↔𝜑𝜒→¬¬↔𝜓𝜒→↔𝜑𝜒¬¬↔𝜑𝜒 | Subs [𝜑↗→↔𝜑𝜒¬¬↔𝜑𝜒, 𝜓↗¬¬↔𝜓𝜒] into ax-1 | |
| 15331 | →¬¬↔𝜓𝜒→↔𝜑𝜒¬¬↔𝜑𝜒 | Modus ponens 15329, 15330 | |
| 15332 | →→¬¬↔𝜓𝜒→↔𝜑𝜒¬¬↔𝜑𝜒→→¬¬↔𝜓𝜒↔𝜑𝜒→¬¬↔𝜓𝜒¬¬↔𝜑𝜒 | Subs [𝜑↗¬¬↔𝜓𝜒, 𝜓↗↔𝜑𝜒, 𝜒↗¬¬↔𝜑𝜒] into ax-2 | |
| 15333 | →→¬¬↔𝜓𝜒↔𝜑𝜒→¬¬↔𝜓𝜒¬¬↔𝜑𝜒 | Modus ponens 15331, 15332 | |
| 15334 | →→→¬¬↔𝜓𝜒↔𝜑𝜒→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→↔𝜑𝜓→→¬¬↔𝜓𝜒↔𝜑𝜒→¬¬↔𝜓𝜒¬¬↔𝜑𝜒 | Subs [𝜑↗→→¬¬↔𝜓𝜒↔𝜑𝜒→¬¬↔𝜓𝜒¬¬↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 15335 | →↔𝜑𝜓→→¬¬↔𝜓𝜒↔𝜑𝜒→¬¬↔𝜓𝜒¬¬↔𝜑𝜒 | Modus ponens 15333, 15334 | |
| 15336 | →→↔𝜑𝜓→→¬¬↔𝜓𝜒↔𝜑𝜒→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒→↔𝜑𝜓→¬¬↔𝜓𝜒¬¬↔𝜑𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬↔𝜓𝜒↔𝜑𝜒, 𝜒↗→¬¬↔𝜓𝜒¬¬↔𝜑𝜒] into ax-2 | |
| 15337 | →→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒→↔𝜑𝜓→¬¬↔𝜓𝜒¬¬↔𝜑𝜒 | Modus ponens 15335, 15336 | |
| 15338 | →↔𝜑𝜓→¬¬↔𝜓𝜒¬¬↔𝜑𝜒 | Modus ponens 15328, 15337 | |
| 15339 | →→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜓𝜒 | Subs [𝜑↗¬↔𝜓𝜒, 𝜓↗¬↔𝜑𝜒] into ax-3 | |
| 15340 | →→→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜓𝜒→↔𝜑𝜓→→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜓𝜒 | Subs [𝜑↗→→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 15341 | →↔𝜑𝜓→→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜓𝜒 | Modus ponens 15339, 15340 | |
| 15342 | →→↔𝜑𝜓→→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜓𝜒→→↔𝜑𝜓→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→↔𝜑𝜓→¬↔𝜑𝜒¬↔𝜓𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬↔𝜓𝜒¬¬↔𝜑𝜒, 𝜒↗→¬↔𝜑𝜒¬↔𝜓𝜒] into ax-2 | |
| 15343 | →→↔𝜑𝜓→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→↔𝜑𝜓→¬↔𝜑𝜒¬↔𝜓𝜒 | Modus ponens 15341, 15342 | |
| 15344 | →↔𝜑𝜓→¬↔𝜑𝜒¬↔𝜓𝜒 | Modus ponens 15338, 15343 | |
| 15345 | →¬↔𝜑𝜒¬↔𝜑𝜒 | Subs [𝜑↗¬↔𝜑𝜒] into id | |
| 15346 | →¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒 | Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 15347 | →→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒→¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒 | Subs [𝜑↗→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒, 𝜓↗¬↔𝜑𝜒] into ax-1 | |
| 15348 | →¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒 | Modus ponens 15346, 15347 | |
| 15349 | →→¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒→→¬↔𝜑𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒 | Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗¬↔𝜑𝜒, 𝜒↗→↔𝜑𝜓¬↔𝜑𝜒] into ax-2 | |
| 15350 | →→¬↔𝜑𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒 | Modus ponens 15348, 15349 | |
| 15351 | →→↔𝜑𝜓→¬↔𝜑𝜒¬↔𝜓𝜒→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬↔𝜑𝜒, 𝜒↗¬↔𝜓𝜒] into ax-2 | |
| 15352 | →→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒 | Modus ponens 15344, 15351 | |
| 15353 | →→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒 | Subs [𝜑↗→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬↔𝜑𝜒] into ax-1 | |
| 15354 | →¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒 | Modus ponens 15352, 15353 | |
| 15355 | →→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒→→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒 | Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗→↔𝜑𝜓¬↔𝜑𝜒, 𝜒↗→↔𝜑𝜓¬↔𝜓𝜒] into ax-2 | |
| 15356 | →→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒 | Modus ponens 15354, 15355 | |
| 15357 | →¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒 | Modus ponens 15346, 15356 | |
| 15358 | →¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜓𝜒] into id | |
| 15359 | →→¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬↔𝜑𝜒] into ax-1 | |
| 15360 | →¬↔𝜑𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Modus ponens 15358, 15359 | |
| 15361 | →¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜓𝜒] into notnotr | |
| 15362 | →¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬↔𝜑𝜒] into ax-1 | |
| 15363 | →→¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬¬¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-1 | |
| 15364 | →¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Modus ponens 15362, 15363 | |
| 15365 | →→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Subs [𝜑↗¬¬¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜒↗→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-2 | |
| 15366 | →→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Modus ponens 15364, 15365 | |
| 15367 | →¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Modus ponens 15361, 15366 | |
| 15368 | →→¬↔𝜑𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜒↗¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-2 | |
| 15369 | →→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Modus ponens 15360, 15368 | |
| 15370 | →→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Subs [𝜑↗→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬¬¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-1 | |
| 15371 | →¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Modus ponens 15369, 15370 | |
| 15372 | →→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Subs [𝜑↗¬¬¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜒↗→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-2 | |
| 15373 | →→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Modus ponens 15371, 15372 | |
| 15374 | →¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒 | Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗¬¬¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-1 | |
| 15375 | →→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒 | Subs [𝜑↗→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒, 𝜓↗¬↔𝜑𝜒] into ax-1 | |
| 15376 | →¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒 | Modus ponens 15374, 15375 | |
| 15377 | →→¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→→¬↔𝜑𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒 | Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗¬↔𝜑𝜒, 𝜒↗→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒] into ax-2 | |
| 15378 | →→¬↔𝜑𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒 | Modus ponens 15376, 15377 | |
| 15379 | →→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Subs [𝜑↗¬¬¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬↔𝜑𝜒, 𝜒↗¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-2 | |
| 15380 | →→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Modus ponens 15367, 15379 | |
| 15381 | →→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Subs [𝜑↗→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬↔𝜑𝜒] into ax-1 | |
| 15382 | →¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Modus ponens 15380, 15381 | |
| 15383 | →→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒, 𝜒↗→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-2 | |
| 15384 | →→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Modus ponens 15382, 15383 | |
| 15385 | →¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Modus ponens 15374, 15384 | |
| 15386 | →→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒 | Subs [𝜑↗¬¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗→↔𝜑𝜓¬↔𝜓𝜒] into ax-3 | |
| 15387 | →→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒 | Subs [𝜑↗→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬↔𝜑𝜒] into ax-1 | |
| 15388 | →¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒 | Modus ponens 15386, 15387 | |
| 15389 | →→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒→→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒 | Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜒↗→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-2 | |
| 15390 | →→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒 | Modus ponens 15388, 15389 | |
| 15391 | →¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒 | Modus ponens 15385, 15390 | |
| 15392 | →→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒→→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒 | Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗→↔𝜑𝜓¬↔𝜓𝜒, 𝜒↗¬¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-2 | |
| 15393 | →→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒 | Modus ponens 15391, 15392 | |
| 15394 | →¬↔𝜑𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒 | Modus ponens 15357, 15393 | |
| 15395 | →→¬↔𝜑𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒↔𝜑𝜒 | Subs [𝜑↗↔𝜑𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-3 | |
| 15396 | →¬→↔𝜑𝜓¬↔𝜓𝜒↔𝜑𝜒 | Modus ponens 15394, 15395 | |
| 15397 | →↔⋀↔𝜑𝜓↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→⋀↔𝜑𝜓↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Subs [𝜑↗⋀↔𝜑𝜓↔𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜓𝜒] into biimp | |
| 15398 | →⋀↔𝜑𝜓↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒 | Modus ponens 15305, 15397 | |
| 15399 | →→¬→↔𝜑𝜓¬↔𝜓𝜒↔𝜑𝜒→⋀↔𝜑𝜓↔𝜓𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒↔𝜑𝜒 | Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜓𝜒↔𝜑𝜒, 𝜓↗⋀↔𝜑𝜓↔𝜓𝜒] into ax-1 | |
| 15400 | →⋀↔𝜑𝜓↔𝜓𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒↔𝜑𝜒 | Modus ponens 15396, 15399 | |
| 15401 | →→⋀↔𝜑𝜓↔𝜓𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒↔𝜑𝜒→→⋀↔𝜑𝜓↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→⋀↔𝜑𝜓↔𝜓𝜒↔𝜑𝜒 | Subs [𝜑↗⋀↔𝜑𝜓↔𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜒↗↔𝜑𝜒] into ax-2 | |
| 15402 | →→⋀↔𝜑𝜓↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→⋀↔𝜑𝜓↔𝜓𝜒↔𝜑𝜒 | Modus ponens 15400, 15401 | |
| 15403 | →⋀↔𝜑𝜓↔𝜓𝜒↔𝜑𝜒 | Modus ponens 15398, 15402 | bitr |
| 15404 | →↔𝜒𝜓↔𝜒𝜓 | Subs [𝜑↗↔𝜒𝜓] into id | |
| 15405 | ↔→↔𝜒𝜓↔𝜒𝜓↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓 | Subs [𝜑↗↔𝜒𝜓, 𝜓↗𝜒, 𝜒↗𝜓] into pm5.74 | |
| 15406 | →↔→↔𝜒𝜓↔𝜒𝜓↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→↔𝜒𝜓↔𝜒𝜓↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓 | Subs [𝜑↗→↔𝜒𝜓↔𝜒𝜓, 𝜓↗↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓] into biimp | |
| 15407 | →→↔𝜒𝜓↔𝜒𝜓↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓 | Modus ponens 15405, 15406 | |
| 15408 | ↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓 | Modus ponens 15404, 15407 | |
| 15409 | →↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒 | Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into id | |
| 15410 | →↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓 | Subs [𝜑↗↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into ax-1 | |
| 15411 | →↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓 | Modus ponens 15408, 15410 | |
| 15412 | ↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒 | Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓𝜑, 𝜒↗→↔𝜒𝜓𝜒] into pm5.74 | |
| 15413 | →↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒] into biimp | |
| 15414 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒 | Modus ponens 15412, 15413 | |
| 15415 | ↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒 | Modus ponens 15409, 15414 | |
| 15416 | ↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓 | Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓𝜒, 𝜒↗→↔𝜒𝜓𝜓] into pm5.74 | |
| 15417 | →↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓, 𝜓↗↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓] into biimp | |
| 15418 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓 | Modus ponens 15416, 15417 | |
| 15419 | ↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓 | Modus ponens 15411, 15418 | |
| 15420 | →↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓] into biimp | |
| 15421 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓 | Modus ponens 15419, 15420 | |
| 15422 | →↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒] into biimp | |
| 15423 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒 | Modus ponens 15415, 15422 | |
| 15424 | →→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓 | Subs [𝜑↗→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑] into ax-1 | |
| 15425 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓 | Modus ponens 15421, 15424 | |
| 15426 | →→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒, 𝜒↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓] into ax-2 | |
| 15427 | →→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓 | Modus ponens 15425, 15426 | |
| 15428 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓 | Modus ponens 15423, 15427 | |
| 15429 | →↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓] into bicom1 | |
| 15430 | ↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒 | Modus ponens 15419, 15429 | |
| 15431 | →↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒] into biimp | |
| 15432 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒 | Modus ponens 15430, 15431 | |
| 15433 | →↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒] into bicom1 | |
| 15434 | ↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑 | Modus ponens 15415, 15433 | |
| 15435 | →↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑] into biimp | |
| 15436 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑 | Modus ponens 15434, 15435 | |
| 15437 | →→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑 | Subs [𝜑↗→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓] into ax-1 | |
| 15438 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑 | Modus ponens 15436, 15437 | |
| 15439 | →→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒, 𝜒↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑] into ax-2 | |
| 15440 | →→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑 | Modus ponens 15438, 15439 | |
| 15441 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑 | Modus ponens 15432, 15440 | |
| 15442 | →→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓] into impbi | |
| 15443 | →→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓 | Modus ponens 15428, 15442 | |
| 15444 | ↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓 | Modus ponens 15441, 15443 | |
| 15445 | ↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓 | Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓𝜑, 𝜒↗→↔𝜒𝜓𝜓] into pm5.74 | |
| 15446 | →↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓↔↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜓↗↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓] into bicom1 | |
| 15447 | ↔↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓 | Modus ponens 15445, 15446 | |
| 15448 | →↔↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓 | Subs [𝜑↗↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓] into biimp | |
| 15449 | →↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓 | Modus ponens 15447, 15448 | |
| 15450 | →↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓 | Modus ponens 15444, 15449 | |
| 15451 | →↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓 | Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓] into id | |
| 15452 | →↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒 | Subs [𝜑↗→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓𝜓] into bicom1 | |
| 15453 | ↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒 | Modus ponens 15408, 15452 | |
| 15454 | →↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒 | Subs [𝜑↗↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓] into ax-1 | |
| 15455 | →↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒 | Modus ponens 15453, 15454 | |
| 15456 | ↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓 | Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜓↗→↔𝜒𝜓𝜑, 𝜒↗→↔𝜒𝜓𝜓] into pm5.74 | |
| 15457 | →↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜓↗↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓] into biimp | |
| 15458 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓 | Modus ponens 15456, 15457 | |
| 15459 | ↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓 | Modus ponens 15451, 15458 | |
| 15460 | ↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒 | Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜓↗→↔𝜒𝜓𝜓, 𝜒↗→↔𝜒𝜓𝜒] into pm5.74 | |
| 15461 | →↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒, 𝜓↗↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒] into biimp | |
| 15462 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒 | Modus ponens 15460, 15461 | |
| 15463 | ↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒 | Modus ponens 15455, 15462 | |
| 15464 | →↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒] into biimp | |
| 15465 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒 | Modus ponens 15463, 15464 | |
| 15466 | →↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓] into biimp | |
| 15467 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓 | Modus ponens 15459, 15466 | |
| 15468 | →→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒 | Subs [𝜑↗→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑] into ax-1 | |
| 15469 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒 | Modus ponens 15465, 15468 | |
| 15470 | →→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓, 𝜒↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒] into ax-2 | |
| 15471 | →→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒 | Modus ponens 15469, 15470 | |
| 15472 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒 | Modus ponens 15467, 15471 | |
| 15473 | →↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒] into bicom1 | |
| 15474 | ↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓 | Modus ponens 15463, 15473 | |
| 15475 | →↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓] into biimp | |
| 15476 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓 | Modus ponens 15474, 15475 | |
| 15477 | →↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓] into bicom1 | |
| 15478 | ↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑 | Modus ponens 15459, 15477 | |
| 15479 | →↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑] into biimp | |
| 15480 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑 | Modus ponens 15478, 15479 | |
| 15481 | →→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑 | Subs [𝜑↗→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒] into ax-1 | |
| 15482 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑 | Modus ponens 15480, 15481 | |
| 15483 | →→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓, 𝜒↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑] into ax-2 | |
| 15484 | →→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑 | Modus ponens 15482, 15483 | |
| 15485 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑 | Modus ponens 15476, 15484 | |
| 15486 | →→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒] into impbi | |
| 15487 | →→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒 | Modus ponens 15472, 15486 | |
| 15488 | ↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒 | Modus ponens 15485, 15487 | |
| 15489 | ↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒 | Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜓↗→↔𝜒𝜓𝜑, 𝜒↗→↔𝜒𝜓𝜒] into pm5.74 | |
| 15490 | →↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒↔↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒] into bicom1 | |
| 15491 | ↔↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒 | Modus ponens 15489, 15490 | |
| 15492 | →↔↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒 | Subs [𝜑↗↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into biimp | |
| 15493 | →↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒 | Modus ponens 15491, 15492 | |
| 15494 | →↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒 | Modus ponens 15488, 15493 | |
| 15495 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓 | Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓] into impbi | |
| 15496 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓 | Modus ponens 15450, 15495 | |
| 15497 | ↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓 | Modus ponens 15494, 15496 | |
| 15498 | ↔→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒 | Subs [𝜑↗↔𝜒𝜓, 𝜓↗𝜑] into pm5.74 | |
| 15499 | ↔→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓 | Subs [𝜑↗↔𝜒𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into pm5.74 | |
| 15500 | →↔→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓 | Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜓, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓] into bicom1 | |
| 15501 | ↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓 | Modus ponens 15499, 15500 | |
| 15502 | →↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓 | Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜓↗→↔𝜒𝜓↔𝜑𝜓] into biimp | |
| 15503 | →↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓 | Modus ponens 15501, 15502 | |
| 15504 | →↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓 | Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓] into biimp | |
| 15505 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into ax-1 | |
| 15506 | →↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓 | Modus ponens 15503, 15505 | |
| 15507 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓 | Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜒↗→↔𝜒𝜓↔𝜑𝜓] into ax-2 | |
| 15508 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓 | Modus ponens 15506, 15507 | |
| 15509 | →↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓 | Modus ponens 15450, 15508 | |
| 15510 | →↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓 | Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜓↗→↔𝜒𝜓↔𝜑𝜓] into bicom1 | |
| 15511 | →↔→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓 | Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜓, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓] into biimp | |
| 15512 | →→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓 | Modus ponens 15499, 15511 | |
| 15513 | →↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒 | Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓] into bicom1 | |
| 15514 | ↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒 | Modus ponens 15497, 15513 | |
| 15515 | →↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒 | Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into biimp | |
| 15516 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓↔𝜑𝜓] into ax-1 | |
| 15517 | →→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒 | Modus ponens 15494, 15516 | |
| 15518 | →→→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒 | Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜓, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜒↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into ax-2 | |
| 15519 | →→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒 | Modus ponens 15517, 15518 | |
| 15520 | →→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒 | Modus ponens 15512, 15519 | |
| 15521 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓→→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓 | Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓↔𝜑𝜓] into impbi | |
| 15522 | →→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓 | Modus ponens 15509, 15521 | |
| 15523 | ↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓 | Modus ponens 15520, 15522 | |
| 15524 | →↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓 | Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓↔𝜑𝜓] into biimp | |
| 15525 | →↔→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒 | Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into biimp | |
| 15526 | →→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒 | Modus ponens 15498, 15525 | |
| 15527 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓→→↔𝜒𝜓↔𝜑𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓, 𝜓↗→↔𝜒𝜓↔𝜑𝜒] into ax-1 | |
| 15528 | →→↔𝜒𝜓↔𝜑𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓 | Modus ponens 15509, 15527 | |
| 15529 | →→→↔𝜒𝜓↔𝜑𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓→→→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓 | Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜒↗→↔𝜒𝜓↔𝜑𝜓] into ax-2 | |
| 15530 | →→→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓 | Modus ponens 15528, 15529 | |
| 15531 | →→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓 | Modus ponens 15526, 15530 | |
| 15532 | →↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒 | Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓↔𝜑𝜓] into bicom1 | |
| 15533 | ↔→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒 | Modus ponens 15523, 15532 | |
| 15534 | →↔→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒 | Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜓, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into biimp | |
| 15535 | →↔→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒 | Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into bicom1 | |
| 15536 | ↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒 | Modus ponens 15498, 15535 | |
| 15537 | →↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒 | Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓↔𝜑𝜒] into biimp | |
| 15538 | →↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒 | Modus ponens 15536, 15537 | |
| 15539 | →→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒→→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒 | Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒, 𝜓↗→↔𝜒𝜓↔𝜑𝜓] into ax-1 | |
| 15540 | →→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒 | Modus ponens 15538, 15539 | |
| 15541 | →→→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒→→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒 | Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜓, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜒↗→↔𝜒𝜓↔𝜑𝜒] into ax-2 | |
| 15542 | →→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒 | Modus ponens 15540, 15541 | |
| 15543 | →→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒 | Modus ponens 15520, 15542 | |
| 15544 | →→→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓→→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓 | Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜒, 𝜓↗→↔𝜒𝜓↔𝜑𝜓] into impbi | |
| 15545 | →→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓 | Modus ponens 15531, 15544 | |
| 15546 | ↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓 | Modus ponens 15543, 15545 | |
| 15547 | ↔→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓 | Subs [𝜑↗↔𝜒𝜓, 𝜓↗↔𝜑𝜒, 𝜒↗↔𝜑𝜓] into pm5.74 | |
| 15548 | →↔→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓↔↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓 | Subs [𝜑↗→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓, 𝜓↗↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓] into bicom1 | |
| 15549 | ↔↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓 | Modus ponens 15547, 15548 | |
| 15550 | →↔↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓→↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓 | Subs [𝜑↗↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓, 𝜓↗→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓] into biimp | |
| 15551 | →↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓 | Modus ponens 15549, 15550 | |
| 15552 | →↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓 | Modus ponens 15546, 15551 | |
| 15553 | ↔↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into bicom | |
| 15554 | →↔↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒→↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗↔↔𝜑𝜒↔𝜑𝜓, 𝜓↗↔↔𝜑𝜓↔𝜑𝜒] into biimp | |
| 15555 | →↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒 | Modus ponens 15553, 15554 | |
| 15556 | →→↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒→↔𝜒𝜓→↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗→↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒, 𝜓↗↔𝜒𝜓] into ax-1 | |
| 15557 | →↔𝜒𝜓→↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒 | Modus ponens 15555, 15556 | |
| 15558 | →→↔𝜒𝜓→↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒→→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓→↔𝜒𝜓↔↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗↔𝜒𝜓, 𝜓↗↔↔𝜑𝜒↔𝜑𝜓, 𝜒↗↔↔𝜑𝜓↔𝜑𝜒] into ax-2 | |
| 15559 | →→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓→↔𝜒𝜓↔↔𝜑𝜓↔𝜑𝜒 | Modus ponens 15557, 15558 | |
| 15560 | →↔𝜒𝜓↔↔𝜑𝜓↔𝜑𝜒 | Modus ponens 15552, 15559 | |
| 15561 | →↔↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜒] into biimp | |
| 15562 | →→↔↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜑𝜒→↔𝜒𝜓→↔↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗→↔↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜑𝜒, 𝜓↗↔𝜒𝜓] into ax-1 | |
| 15563 | →↔𝜒𝜓→↔↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜑𝜒 | Modus ponens 15561, 15562 | |
| 15564 | →→↔𝜒𝜓→↔↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜑𝜒→→↔𝜒𝜓↔↔𝜑𝜓↔𝜑𝜒→↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗↔𝜒𝜓, 𝜓↗↔↔𝜑𝜓↔𝜑𝜒, 𝜒↗→↔𝜑𝜓↔𝜑𝜒] into ax-2 | |
| 15565 | →→↔𝜒𝜓↔↔𝜑𝜓↔𝜑𝜒→↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒 | Modus ponens 15563, 15564 | |
| 15566 | →↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒 | Modus ponens 15560, 15565 | |
| 15567 | →↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒𝜓] into ax-1 | |
| 15568 | →→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓 | Subs [𝜑↗→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 15569 | →↔𝜑𝜓→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓 | Modus ponens 15567, 15568 | |
| 15570 | →→↔𝜑𝜓→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→↔𝜒𝜓↔𝜑𝜓] into ax-2 | |
| 15571 | →→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓 | Modus ponens 15569, 15570 | |
| 15572 | →→↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒 | Subs [𝜑↗↔𝜒𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗↔𝜑𝜒] into ax-2 | |
| 15573 | →→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒→↔𝜑𝜓→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒 | Subs [𝜑↗→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 15574 | →↔𝜑𝜓→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒 | Modus ponens 15543, 15573 | |
| 15575 | →→↔𝜑𝜓→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒→→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→↔𝜒𝜓↔𝜑𝜓, 𝜒↗→↔𝜒𝜓↔𝜑𝜒] into ax-2 | |
| 15576 | →→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒 | Modus ponens 15574, 15575 | |
| 15577 | →↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒 | Modus ponens 15567, 15576 | |
| 15578 | →↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗↔𝜒𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 15579 | →→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓→↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓, 𝜓↗↔𝜒𝜓] into ax-1 | |
| 15580 | →↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 15578, 15579 | |
| 15581 | →→↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓→→↔𝜒𝜓↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗↔𝜒𝜓, 𝜓↗↔𝜒𝜓, 𝜒↗→↔𝜑𝜓↔𝜒𝜓] into ax-2 | |
| 15582 | →→↔𝜒𝜓↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 15580, 15581 | |
| 15583 | →→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒𝜓, 𝜒↗↔𝜑𝜒] into ax-2 | |
| 15584 | →→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒, 𝜓↗↔𝜒𝜓] into ax-1 | |
| 15585 | →↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒 | Modus ponens 2705, 15584 | |
| 15586 | →→↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜒𝜓, 𝜒↗→↔𝜑𝜓↔𝜑𝜒] into ax-2 | |
| 15587 | →→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒 | Modus ponens 15585, 15586 | |
| 15588 | ↔⋀↔𝜑𝜓↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒𝜓] into df-an | |
| 15589 | →¬¬↔𝜒𝜓↔𝜒𝜓 | Subs [𝜑↗↔𝜒𝜓] into notnotr | |
| 15590 | →→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓→¬¬↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓, 𝜓↗¬¬↔𝜒𝜓] into ax-1 | |
| 15591 | →¬¬↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 15578, 15590 | |
| 15592 | →→¬¬↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓→→¬¬↔𝜒𝜓↔𝜒𝜓→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓 | Subs [𝜑↗¬¬↔𝜒𝜓, 𝜓↗↔𝜒𝜓, 𝜒↗→↔𝜑𝜓↔𝜒𝜓] into ax-2 | |
| 15593 | →→¬¬↔𝜒𝜓↔𝜒𝜓→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 15591, 15592 | |
| 15594 | →¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓 | Modus ponens 15589, 15593 | |
| 15595 | →→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→¬¬↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒, 𝜓↗¬¬↔𝜒𝜓] into ax-1 | |
| 15596 | →¬¬↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒 | Modus ponens 2705, 15595 | |
| 15597 | →→¬¬↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒 | Subs [𝜑↗¬¬↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜒𝜓, 𝜒↗→↔𝜑𝜓↔𝜑𝜒] into ax-2 | |
| 15598 | →→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒 | Modus ponens 15596, 15597 | |
| 15599 | →¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒 | Modus ponens 15594, 15598 | |
| 15600 | →↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬¬↔𝜒𝜓] into ax-1 | |
| 15601 | →→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓 | Subs [𝜑↗→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 15602 | →↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓 | Modus ponens 15600, 15601 | |
| 15603 | →→↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→¬¬↔𝜒𝜓↔𝜑𝜓] into ax-2 | |
| 15604 | →→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓 | Modus ponens 15602, 15603 | |
| 15605 | →→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→→¬¬↔𝜒𝜓↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒 | Subs [𝜑↗¬¬↔𝜒𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗↔𝜑𝜒] into ax-2 | |
| 15606 | →→¬¬↔𝜒𝜓↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒 | Modus ponens 15599, 15605 | |
| 15607 | →→→¬¬↔𝜒𝜓↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒→↔𝜑𝜓→→¬¬↔𝜒𝜓↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒 | Subs [𝜑↗→→¬¬↔𝜒𝜓↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 15608 | →↔𝜑𝜓→→¬¬↔𝜒𝜓↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒 | Modus ponens 15606, 15607 | |
| 15609 | →→↔𝜑𝜓→→¬¬↔𝜒𝜓↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒→→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬↔𝜒𝜓↔𝜑𝜓, 𝜒↗→¬¬↔𝜒𝜓↔𝜑𝜒] into ax-2 | |
| 15610 | →→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒 | Modus ponens 15608, 15609 | |
| 15611 | →↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒 | Modus ponens 15600, 15610 | |
| 15612 | →→↔𝜑𝜒¬¬↔𝜑𝜒→¬¬↔𝜒𝜓→↔𝜑𝜒¬¬↔𝜑𝜒 | Subs [𝜑↗→↔𝜑𝜒¬¬↔𝜑𝜒, 𝜓↗¬¬↔𝜒𝜓] into ax-1 | |
| 15613 | →¬¬↔𝜒𝜓→↔𝜑𝜒¬¬↔𝜑𝜒 | Modus ponens 15329, 15612 | |
| 15614 | →→¬¬↔𝜒𝜓→↔𝜑𝜒¬¬↔𝜑𝜒→→¬¬↔𝜒𝜓↔𝜑𝜒→¬¬↔𝜒𝜓¬¬↔𝜑𝜒 | Subs [𝜑↗¬¬↔𝜒𝜓, 𝜓↗↔𝜑𝜒, 𝜒↗¬¬↔𝜑𝜒] into ax-2 | |
| 15615 | →→¬¬↔𝜒𝜓↔𝜑𝜒→¬¬↔𝜒𝜓¬¬↔𝜑𝜒 | Modus ponens 15613, 15614 | |
| 15616 | →→→¬¬↔𝜒𝜓↔𝜑𝜒→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→↔𝜑𝜓→→¬¬↔𝜒𝜓↔𝜑𝜒→¬¬↔𝜒𝜓¬¬↔𝜑𝜒 | Subs [𝜑↗→→¬¬↔𝜒𝜓↔𝜑𝜒→¬¬↔𝜒𝜓¬¬↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 15617 | →↔𝜑𝜓→→¬¬↔𝜒𝜓↔𝜑𝜒→¬¬↔𝜒𝜓¬¬↔𝜑𝜒 | Modus ponens 15615, 15616 | |
| 15618 | →→↔𝜑𝜓→→¬¬↔𝜒𝜓↔𝜑𝜒→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒→↔𝜑𝜓→¬¬↔𝜒𝜓¬¬↔𝜑𝜒 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬↔𝜒𝜓↔𝜑𝜒, 𝜒↗→¬¬↔𝜒𝜓¬¬↔𝜑𝜒] into ax-2 | |
| 15619 | →→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒→↔𝜑𝜓→¬¬↔𝜒𝜓¬¬↔𝜑𝜒 | Modus ponens 15617, 15618 | |
| 15620 | →↔𝜑𝜓→¬¬↔𝜒𝜓¬¬↔𝜑𝜒 | Modus ponens 15611, 15619 | |
| 15621 | →→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜒𝜓 | Subs [𝜑↗¬↔𝜒𝜓, 𝜓↗¬↔𝜑𝜒] into ax-3 | |
| 15622 | →→→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜒𝜓→↔𝜑𝜓→→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜒𝜓 | Subs [𝜑↗→→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜒𝜓, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 15623 | →↔𝜑𝜓→→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜒𝜓 | Modus ponens 15621, 15622 | |
| 15624 | →→↔𝜑𝜓→→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜒𝜓→→↔𝜑𝜓→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→↔𝜑𝜓→¬↔𝜑𝜒¬↔𝜒𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬↔𝜒𝜓¬¬↔𝜑𝜒, 𝜒↗→¬↔𝜑𝜒¬↔𝜒𝜓] into ax-2 | |
| 15625 | →→↔𝜑𝜓→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→↔𝜑𝜓→¬↔𝜑𝜒¬↔𝜒𝜓 | Modus ponens 15623, 15624 | |
| 15626 | →↔𝜑𝜓→¬↔𝜑𝜒¬↔𝜒𝜓 | Modus ponens 15620, 15625 | |
| 15627 | →→↔𝜑𝜓→¬↔𝜑𝜒¬↔𝜒𝜓→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬↔𝜑𝜒, 𝜒↗¬↔𝜒𝜓] into ax-2 | |
| 15628 | →→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓 | Modus ponens 15626, 15627 | |
| 15629 | →→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓 | Subs [𝜑↗→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬↔𝜑𝜒] into ax-1 | |
| 15630 | →¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓 | Modus ponens 15628, 15629 | |
| 15631 | →→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓→→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓 | Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗→↔𝜑𝜓¬↔𝜑𝜒, 𝜒↗→↔𝜑𝜓¬↔𝜒𝜓] into ax-2 | |
| 15632 | →→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓 | Modus ponens 15630, 15631 | |
| 15633 | →¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓 | Modus ponens 15346, 15632 | |
| 15634 | →¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜓] into id | |
| 15635 | →→¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓 | Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬↔𝜑𝜒] into ax-1 | |
| 15636 | →¬↔𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓 | Modus ponens 15634, 15635 | |
| 15637 | →¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜓] into notnotr | |
| 15638 | →¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓 | Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬↔𝜑𝜒] into ax-1 | |
| 15639 | →→¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓 | Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬¬¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-1 | |
| 15640 | →¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓 | Modus ponens 15638, 15639 | |
| 15641 | →→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓 | Subs [𝜑↗¬¬¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜒↗→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-2 | |
| 15642 | →→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓 | Modus ponens 15640, 15641 | |
| 15643 | →¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓 | Modus ponens 15637, 15642 | |
| 15644 | →→¬↔𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓 | Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜒↗¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-2 | |
| 15645 | →→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓 | Modus ponens 15636, 15644 | |
| 15646 | →→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓 | Subs [𝜑↗→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬¬¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-1 | |
| 15647 | →¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓 | Modus ponens 15645, 15646 | |
| 15648 | →→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓 | Subs [𝜑↗¬¬¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜒↗→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-2 | |
| 15649 | →→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓 | Modus ponens 15647, 15648 | |
| 15650 | →¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒 | Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗¬¬¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-1 | |
| 15651 | →→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒 | Subs [𝜑↗→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒, 𝜓↗¬↔𝜑𝜒] into ax-1 | |
| 15652 | →¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒 | Modus ponens 15650, 15651 | |
| 15653 | →→¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→→¬↔𝜑𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒 | Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗¬↔𝜑𝜒, 𝜒↗→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒] into ax-2 | |
| 15654 | →→¬↔𝜑𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒 | Modus ponens 15652, 15653 | |
| 15655 | →→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓 | Subs [𝜑↗¬¬¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬↔𝜑𝜒, 𝜒↗¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-2 | |
| 15656 | →→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓 | Modus ponens 15643, 15655 | |
| 15657 | →→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓 | Subs [𝜑↗→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬↔𝜑𝜒] into ax-1 | |
| 15658 | →¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓 | Modus ponens 15656, 15657 | |
| 15659 | →→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓 | Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒, 𝜒↗→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-2 | |
| 15660 | →→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓 | Modus ponens 15658, 15659 | |
| 15661 | →¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓 | Modus ponens 15650, 15660 | |
| 15662 | →→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓 | Subs [𝜑↗¬¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗→↔𝜑𝜓¬↔𝜒𝜓] into ax-3 | |
| 15663 | →→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓 | Subs [𝜑↗→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬↔𝜑𝜒] into ax-1 | |
| 15664 | →¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓 | Modus ponens 15662, 15663 | |
| 15665 | →→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓→→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓 | Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜒↗→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-2 | |
| 15666 | →→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓 | Modus ponens 15664, 15665 | |
| 15667 | →¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓 | Modus ponens 15661, 15666 | |
| 15668 | →→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓→→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬¬→↔𝜑𝜓¬↔𝜒𝜓 | Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗→↔𝜑𝜓¬↔𝜒𝜓, 𝜒↗¬¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-2 | |
| 15669 | →→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬¬→↔𝜑𝜓¬↔𝜒𝜓 | Modus ponens 15667, 15668 | |
| 15670 | →¬↔𝜑𝜒¬¬→↔𝜑𝜓¬↔𝜒𝜓 | Modus ponens 15633, 15669 | |
| 15671 | →→¬↔𝜑𝜒¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬→↔𝜑𝜓¬↔𝜒𝜓↔𝜑𝜒 | Subs [𝜑↗↔𝜑𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-3 | |
| 15672 | →¬→↔𝜑𝜓¬↔𝜒𝜓↔𝜑𝜒 | Modus ponens 15670, 15671 | |
| 15673 | →↔⋀↔𝜑𝜓↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→⋀↔𝜑𝜓↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓 | Subs [𝜑↗⋀↔𝜑𝜓↔𝜒𝜓, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜓] into biimp | |
| 15674 | →⋀↔𝜑𝜓↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓 | Modus ponens 15588, 15673 | |
| 15675 | →→¬→↔𝜑𝜓¬↔𝜒𝜓↔𝜑𝜒→⋀↔𝜑𝜓↔𝜒𝜓→¬→↔𝜑𝜓¬↔𝜒𝜓↔𝜑𝜒 | Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜓↔𝜑𝜒, 𝜓↗⋀↔𝜑𝜓↔𝜒𝜓] into ax-1 | |
| 15676 | →⋀↔𝜑𝜓↔𝜒𝜓→¬→↔𝜑𝜓¬↔𝜒𝜓↔𝜑𝜒 | Modus ponens 15672, 15675 | |
| 15677 | →→⋀↔𝜑𝜓↔𝜒𝜓→¬→↔𝜑𝜓¬↔𝜒𝜓↔𝜑𝜒→→⋀↔𝜑𝜓↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→⋀↔𝜑𝜓↔𝜒𝜓↔𝜑𝜒 | Subs [𝜑↗⋀↔𝜑𝜓↔𝜒𝜓, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜒↗↔𝜑𝜒] into ax-2 | |
| 15678 | →→⋀↔𝜑𝜓↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→⋀↔𝜑𝜓↔𝜒𝜓↔𝜑𝜒 | Modus ponens 15676, 15677 | |
| 15679 | →⋀↔𝜑𝜓↔𝜒𝜓↔𝜑𝜒 | Modus ponens 15674, 15678 | biantr |
| 15680 | ↔→𝜓𝜒→¬𝜒¬𝜓 | Subs [𝜑↗𝜓, 𝜓↗𝜒] into con34b | |
| 15681 | →↔→𝜓𝜒→¬𝜒¬𝜓→𝜑↔→𝜓𝜒→¬𝜒¬𝜓 | Subs [𝜑↗↔→𝜓𝜒→¬𝜒¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 15682 | →𝜑↔→𝜓𝜒→¬𝜒¬𝜓 | Modus ponens 15680, 15681 | |
| 15683 | ↔→𝜑↔→𝜓𝜒→¬𝜒¬𝜓↔→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓 | Subs [𝜓↗→𝜓𝜒, 𝜒↗→¬𝜒¬𝜓] into pm5.74 | |
| 15684 | →↔→𝜑↔→𝜓𝜒→¬𝜒¬𝜓↔→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓→→𝜑↔→𝜓𝜒→¬𝜒¬𝜓↔→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓 | Subs [𝜑↗→𝜑↔→𝜓𝜒→¬𝜒¬𝜓, 𝜓↗↔→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓] into biimp | |
| 15685 | →→𝜑↔→𝜓𝜒→¬𝜒¬𝜓↔→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓 | Modus ponens 15683, 15684 | |
| 15686 | ↔→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓 | Modus ponens 15682, 15685 | |
| 15687 | ↔→⋀𝜑¬𝜒¬𝜓→𝜑→¬𝜒¬𝜓 | Subs [𝜓↗¬𝜒, 𝜒↗¬𝜓] into impexp | |
| 15688 | →↔→⋀𝜑¬𝜒¬𝜓→𝜑→¬𝜒¬𝜓↔→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓 | Subs [𝜑↗→⋀𝜑¬𝜒¬𝜓, 𝜓↗→𝜑→¬𝜒¬𝜓] into bicom1 | |
| 15689 | ↔→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓 | Modus ponens 15687, 15688 | |
| 15690 | →↔→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓→→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓 | Subs [𝜑↗→𝜑→¬𝜒¬𝜓, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into biimp | |
| 15691 | →→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓 | Modus ponens 15689, 15690 | |
| 15692 | →↔→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓→→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→¬𝜒¬𝜓] into biimp | |
| 15693 | →→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓 | Modus ponens 15686, 15692 | |
| 15694 | →→→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓→→𝜑→𝜓𝜒→→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓 | Subs [𝜑↗→→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓, 𝜓↗→𝜑→𝜓𝜒] into ax-1 | |
| 15695 | →→𝜑→𝜓𝜒→→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓 | Modus ponens 15691, 15694 | |
| 15696 | →→→𝜑→𝜓𝜒→→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓→→→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→¬𝜒¬𝜓, 𝜒↗→⋀𝜑¬𝜒¬𝜓] into ax-2 | |
| 15697 | →→→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓 | Modus ponens 15695, 15696 | |
| 15698 | →→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓 | Modus ponens 15693, 15697 | |
| 15699 | →↔→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓↔→⋀𝜑¬𝜒¬𝜓→𝜑→¬𝜒¬𝜓 | Subs [𝜑↗→𝜑→¬𝜒¬𝜓, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into bicom1 | |
| 15700 | →↔→⋀𝜑¬𝜒¬𝜓→𝜑→¬𝜒¬𝜓→→⋀𝜑¬𝜒¬𝜓→𝜑→¬𝜒¬𝜓 | Subs [𝜑↗→⋀𝜑¬𝜒¬𝜓, 𝜓↗→𝜑→¬𝜒¬𝜓] into biimp | |
| 15701 | →→⋀𝜑¬𝜒¬𝜓→𝜑→¬𝜒¬𝜓 | Modus ponens 15687, 15700 | |
| 15702 | →↔→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓↔→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→¬𝜒¬𝜓] into bicom1 | |
| 15703 | ↔→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒 | Modus ponens 15686, 15702 | |
| 15704 | →↔→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒→→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒 | Subs [𝜑↗→𝜑→¬𝜒¬𝜓, 𝜓↗→𝜑→𝜓𝜒] into biimp | |
| 15705 | →→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒 | Modus ponens 15703, 15704 | |
| 15706 | →→→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒→→⋀𝜑¬𝜒¬𝜓→→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒 | Subs [𝜑↗→→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into ax-1 | |
| 15707 | →→⋀𝜑¬𝜒¬𝜓→→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒 | Modus ponens 15705, 15706 | |
| 15708 | →→→⋀𝜑¬𝜒¬𝜓→→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒→→→⋀𝜑¬𝜒¬𝜓→𝜑→¬𝜒¬𝜓→→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒 | Subs [𝜑↗→⋀𝜑¬𝜒¬𝜓, 𝜓↗→𝜑→¬𝜒¬𝜓, 𝜒↗→𝜑→𝜓𝜒] into ax-2 | |
| 15709 | →→→⋀𝜑¬𝜒¬𝜓→𝜑→¬𝜒¬𝜓→→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒 | Modus ponens 15707, 15708 | |
| 15710 | →→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒 | Modus ponens 15701, 15709 | |
| 15711 | →→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓→→→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into impbi | |
| 15712 | →→→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓 | Modus ponens 15698, 15711 | |
| 15713 | ↔→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓 | Modus ponens 15710, 15712 | |
| 15714 | →↔→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into biimp | |
| 15715 | →↔→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒→→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒 | Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into biimp | |
| 15716 | →→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓→→⋀𝜑𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓 | Subs [𝜑↗→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓, 𝜓↗→⋀𝜑𝜓𝜒] into ax-1 | |
| 15717 | →→⋀𝜑𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓 | Modus ponens 15698, 15716 | |
| 15718 | →→→⋀𝜑𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓→→→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒→→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓 | Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→⋀𝜑¬𝜒¬𝜓] into ax-2 | |
| 15719 | →→→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒→→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓 | Modus ponens 15717, 15718 | |
| 15720 | →→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓 | Modus ponens pm3.3, 15719 | pm3.37 |
| 15721 | →↔→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓↔→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into bicom1 | |
| 15722 | ↔→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒 | Modus ponens 15713, 15721 | |
| 15723 | →↔→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒→→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒 | Subs [𝜑↗→⋀𝜑¬𝜒¬𝜓, 𝜓↗→𝜑→𝜓𝜒] into biimp | |
| 15724 | →↔→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into bicom1 | |
| 15725 | ↔→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens impexp, 15724 | |
| 15726 | →↔→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜒] into biimp | |
| 15727 | →→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑¬𝜒¬𝜓→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into ax-1 | |
| 15728 | →→⋀𝜑¬𝜒¬𝜓→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens pm3.31, 15727 | |
| 15729 | →→→⋀𝜑¬𝜒¬𝜓→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒→→→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒→→⋀𝜑¬𝜒¬𝜓→⋀𝜑𝜓𝜒 | Subs [𝜑↗→⋀𝜑¬𝜒¬𝜓, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→⋀𝜑𝜓𝜒] into ax-2 | |
| 15730 | →→→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒→→⋀𝜑¬𝜒¬𝜓→⋀𝜑𝜓𝜒 | Modus ponens 15728, 15729 | |
| 15731 | →→⋀𝜑¬𝜒¬𝜓→⋀𝜑𝜓𝜒 | Modus ponens 15710, 15730 | |
| 15732 | →→→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓→→→⋀𝜑¬𝜒¬𝜓→⋀𝜑𝜓𝜒↔→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓 | Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into impbi | |
| 15733 | →→→⋀𝜑¬𝜒¬𝜓→⋀𝜑𝜓𝜒↔→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓 | Modus ponens pm3.37, 15732 | |
| 15734 | ↔→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓 | Modus ponens 15731, 15733 | pm4.14 |
| 15735 | →↔→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓→→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓 | Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into biimp | |
| 15736 | →→𝜒𝜃→𝜒𝜃 | Subs [𝜑↗→𝜒𝜃] into id | |
| 15737 | →→𝜑→→𝜑𝜓𝜑→⋀𝜑𝜒→𝜑→→𝜑𝜓𝜑 | Subs [𝜑↗→𝜑→→𝜑𝜓𝜑, 𝜓↗⋀𝜑𝜒] into ax-1 | |
| 15738 | →⋀𝜑𝜒→𝜑→→𝜑𝜓𝜑 | Modus ponens 25, 15737 | |
| 15739 | →→⋀𝜑𝜒→𝜑→→𝜑𝜓𝜑→→⋀𝜑𝜒𝜑→⋀𝜑𝜒→→𝜑𝜓𝜑 | Subs [𝜑↗⋀𝜑𝜒, 𝜓↗𝜑, 𝜒↗→→𝜑𝜓𝜑] into ax-2 | |
| 15740 | →→⋀𝜑𝜒𝜑→⋀𝜑𝜒→→𝜑𝜓𝜑 | Modus ponens 15738, 15739 | |
| 15741 | →⋀𝜑𝜒→→𝜑𝜓𝜑 | Modus ponens 8604, 15740 | |
| 15742 | →→→→𝜑𝜓𝜑→→𝜑𝜓𝜓→⋀𝜑𝜒→→→𝜑𝜓𝜑→→𝜑𝜓𝜓 | Subs [𝜑↗→→→𝜑𝜓𝜑→→𝜑𝜓𝜓, 𝜓↗⋀𝜑𝜒] into ax-1 | |
| 15743 | →⋀𝜑𝜒→→→𝜑𝜓𝜑→→𝜑𝜓𝜓 | Modus ponens 31, 15742 | |
| 15744 | →→⋀𝜑𝜒→→→𝜑𝜓𝜑→→𝜑𝜓𝜓→→⋀𝜑𝜒→→𝜑𝜓𝜑→⋀𝜑𝜒→→𝜑𝜓𝜓 | Subs [𝜑↗⋀𝜑𝜒, 𝜓↗→→𝜑𝜓𝜑, 𝜒↗→→𝜑𝜓𝜓] into ax-2 | |
| 15745 | →→⋀𝜑𝜒→→𝜑𝜓𝜑→⋀𝜑𝜒→→𝜑𝜓𝜓 | Modus ponens 15743, 15744 | |
| 15746 | →⋀𝜑𝜒→→𝜑𝜓𝜓 | Modus ponens 15741, 15745 | |
| 15747 | →→⋀𝜑𝜒→→𝜑𝜓𝜓→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒𝜓 | Subs [𝜑↗⋀𝜑𝜒, 𝜓↗→𝜑𝜓, 𝜒↗𝜓] into ax-2 | |
| 15748 | →→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒𝜓 | Modus ponens 15746, 15747 | |
| 15749 | →→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒𝜓→→𝜑𝜓→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒𝜓 | Subs [𝜑↗→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 15750 | →→𝜑𝜓→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒𝜓 | Modus ponens 15748, 15749 | |
| 15751 | →→→𝜑𝜓→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒𝜓→→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜑𝜒→𝜑𝜓, 𝜒↗→⋀𝜑𝜒𝜓] into ax-2 | |
| 15752 | →→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜓 | Modus ponens 15750, 15751 | |
| 15753 | →→𝜑𝜓→⋀𝜑𝜒𝜓 | Modus ponens 7486, 15752 | |
| 15754 | →⋀𝜑𝜒𝜒 | Subs [𝜓↗𝜒] into simpr | |
| 15755 | →𝜒→→𝜒𝜃𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜒𝜃] into ax-1 | |
| 15756 | →→𝜒→→𝜒𝜃𝜒→⋀𝜑𝜒→𝜒→→𝜒𝜃𝜒 | Subs [𝜑↗→𝜒→→𝜒𝜃𝜒, 𝜓↗⋀𝜑𝜒] into ax-1 | |
| 15757 | →⋀𝜑𝜒→𝜒→→𝜒𝜃𝜒 | Modus ponens 15755, 15756 | |
| 15758 | →→⋀𝜑𝜒→𝜒→→𝜒𝜃𝜒→→⋀𝜑𝜒𝜒→⋀𝜑𝜒→→𝜒𝜃𝜒 | Subs [𝜑↗⋀𝜑𝜒, 𝜓↗𝜒, 𝜒↗→→𝜒𝜃𝜒] into ax-2 | |
| 15759 | →→⋀𝜑𝜒𝜒→⋀𝜑𝜒→→𝜒𝜃𝜒 | Modus ponens 15757, 15758 | |
| 15760 | →⋀𝜑𝜒→→𝜒𝜃𝜒 | Modus ponens 15754, 15759 | |
| 15761 | →→→𝜒𝜃→𝜒𝜃→→→𝜒𝜃𝜒→→𝜒𝜃𝜃 | Subs [𝜑↗→𝜒𝜃, 𝜓↗𝜒, 𝜒↗𝜃] into ax-2 | |
| 15762 | →→→𝜒𝜃𝜒→→𝜒𝜃𝜃 | Modus ponens 15736, 15761 | |
| 15763 | →→→→𝜒𝜃𝜒→→𝜒𝜃𝜃→⋀𝜑𝜒→→→𝜒𝜃𝜒→→𝜒𝜃𝜃 | Subs [𝜑↗→→→𝜒𝜃𝜒→→𝜒𝜃𝜃, 𝜓↗⋀𝜑𝜒] into ax-1 | |
| 15764 | →⋀𝜑𝜒→→→𝜒𝜃𝜒→→𝜒𝜃𝜃 | Modus ponens 15762, 15763 | |
| 15765 | →→⋀𝜑𝜒→→→𝜒𝜃𝜒→→𝜒𝜃𝜃→→⋀𝜑𝜒→→𝜒𝜃𝜒→⋀𝜑𝜒→→𝜒𝜃𝜃 | Subs [𝜑↗⋀𝜑𝜒, 𝜓↗→→𝜒𝜃𝜒, 𝜒↗→→𝜒𝜃𝜃] into ax-2 | |
| 15766 | →→⋀𝜑𝜒→→𝜒𝜃𝜒→⋀𝜑𝜒→→𝜒𝜃𝜃 | Modus ponens 15764, 15765 | |
| 15767 | →⋀𝜑𝜒→→𝜒𝜃𝜃 | Modus ponens 15760, 15766 | |
| 15768 | →→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃 | Subs [𝜑↗→𝜒𝜃, 𝜓↗⋀𝜑𝜒] into ax-1 | |
| 15769 | →→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃→→𝜒𝜃→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃 | Subs [𝜑↗→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1 | |
| 15770 | →→𝜒𝜃→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃 | Modus ponens 15768, 15769 | |
| 15771 | →→→𝜒𝜃→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃 | Subs [𝜑↗→𝜒𝜃, 𝜓↗→𝜒𝜃, 𝜒↗→⋀𝜑𝜒→𝜒𝜃] into ax-2 | |
| 15772 | →→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃 | Modus ponens 15770, 15771 | |
| 15773 | →→⋀𝜑𝜒→→𝜒𝜃𝜃→→⋀𝜑𝜒→𝜒𝜃→⋀𝜑𝜒𝜃 | Subs [𝜑↗⋀𝜑𝜒, 𝜓↗→𝜒𝜃, 𝜒↗𝜃] into ax-2 | |
| 15774 | →→⋀𝜑𝜒→𝜒𝜃→⋀𝜑𝜒𝜃 | Modus ponens 15767, 15773 | |
| 15775 | →→→⋀𝜑𝜒→𝜒𝜃→⋀𝜑𝜒𝜃→→𝜒𝜃→→⋀𝜑𝜒→𝜒𝜃→⋀𝜑𝜒𝜃 | Subs [𝜑↗→→⋀𝜑𝜒→𝜒𝜃→⋀𝜑𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1 | |
| 15776 | →→𝜒𝜃→→⋀𝜑𝜒→𝜒𝜃→⋀𝜑𝜒𝜃 | Modus ponens 15774, 15775 | |
| 15777 | →→→𝜒𝜃→→⋀𝜑𝜒→𝜒𝜃→⋀𝜑𝜒𝜃→→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃→→𝜒𝜃→⋀𝜑𝜒𝜃 | Subs [𝜑↗→𝜒𝜃, 𝜓↗→⋀𝜑𝜒→𝜒𝜃, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2 | |
| 15778 | →→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃→→𝜒𝜃→⋀𝜑𝜒𝜃 | Modus ponens 15776, 15777 | |
| 15779 | →→𝜒𝜃→⋀𝜑𝜒𝜃 | Modus ponens 15768, 15778 | |
| 15780 | →⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗⋀𝜑𝜒, 𝜒↗𝜃] into pm3.43 | |
| 15781 | ↔⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗→⋀𝜑𝜒𝜓, 𝜓↗→⋀𝜑𝜒𝜃] into df-an | |
| 15782 | →↔⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃↔¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃, 𝜓↗¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃] into bicom1 | |
| 15783 | ↔¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃 | Modus ponens 15781, 15782 | |
| 15784 | →↔¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃] into biimp | |
| 15785 | →¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃 | Modus ponens 15783, 15784 | |
| 15786 | →→⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃] into ax-1 | |
| 15787 | →¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15780, 15786 | |
| 15788 | →→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 15789 | →→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15787, 15788 | |
| 15790 | →¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15785, 15789 | |
| 15791 | →→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗→⋀𝜑𝜒𝜓, 𝜓↗→⋀𝜑𝜒𝜃] into pm3.2im | |
| 15792 | →→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→⋀𝜑𝜒𝜃→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→⋀𝜑𝜒𝜃] into ax-1 | |
| 15793 | →→⋀𝜑𝜒𝜃→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15790, 15792 | |
| 15794 | →→→⋀𝜑𝜒𝜃→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 15795 | →→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15793, 15794 | |
| 15796 | →→→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→⋀𝜑𝜒𝜓→→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→⋀𝜑𝜒𝜓] into ax-1 | |
| 15797 | →→⋀𝜑𝜒𝜓→→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15795, 15796 | |
| 15798 | →→→⋀𝜑𝜒𝜓→→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→⋀𝜑𝜒𝜓, 𝜓↗→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 15799 | →→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15797, 15798 | |
| 15800 | →→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15791, 15799 | |
| 15801 | →→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜃 | Subs [𝜑↗→⋀𝜑𝜒𝜃] into id | |
| 15802 | →→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜓] into ax-1 | |
| 15803 | →→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜃] into ax-1 | |
| 15804 | →→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃 | Modus ponens 15802, 15803 | |
| 15805 | →→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃] into ax-2 | |
| 15806 | →→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃 | Modus ponens 15804, 15805 | |
| 15807 | →→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→⋀𝜑𝜒𝜓, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 15808 | →→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15800, 15807 | |
| 15809 | →→→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃→→⋀𝜑𝜒𝜃→→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→⋀𝜑𝜒𝜃] into ax-1 | |
| 15810 | →→⋀𝜑𝜒𝜃→→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15808, 15809 | |
| 15811 | →→→⋀𝜑𝜒𝜃→→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃→→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃, 𝜒↗→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 15812 | →→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15810, 15811 | |
| 15813 | →→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15802, 15812 | |
| 15814 | →→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓 | Subs [𝜑↗→⋀𝜑𝜒𝜓, 𝜓↗→⋀𝜑𝜒𝜃] into ax-1 | |
| 15815 | →→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓 | Subs [𝜑↗→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 15816 | →→𝜑𝜓→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓 | Modus ponens 15814, 15815 | |
| 15817 | →→→𝜑𝜓→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→→𝜑𝜓→⋀𝜑𝜒𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜑𝜒𝜓, 𝜒↗→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓] into ax-2 | |
| 15818 | →→→𝜑𝜓→⋀𝜑𝜒𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓 | Modus ponens 15816, 15817 | |
| 15819 | →→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓 | Modus ponens 15753, 15818 | |
| 15820 | →→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜓, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 15821 | →→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15813, 15820 | |
| 15822 | →→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→𝜑𝜓] into ax-1 | |
| 15823 | →→𝜑𝜓→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15821, 15822 | |
| 15824 | →→→𝜑𝜓→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓, 𝜒↗→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 15825 | →→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15823, 15824 | |
| 15826 | →→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15819, 15825 | |
| 15827 | →→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1 | |
| 15828 | →→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜃] into ax-1 | |
| 15829 | →→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 15827, 15828 | |
| 15830 | →→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒𝜃] into ax-2 | |
| 15831 | →→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 15829, 15830 | |
| 15832 | →→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 15833 | →→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15826, 15832 | |
| 15834 | →→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→→⋀𝜑𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→⋀𝜑𝜒𝜃] into ax-1 | |
| 15835 | →→⋀𝜑𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15833, 15834 | |
| 15836 | →→→⋀𝜑𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 15837 | →→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15835, 15836 | |
| 15838 | →→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15827, 15837 | |
| 15839 | →→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜑𝜒𝜃] into ax-1 | |
| 15840 | →→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 15841 | →→𝜑𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓 | Modus ponens 15839, 15840 | |
| 15842 | →→→𝜑𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→⋀𝜑𝜒𝜃→𝜑𝜓] into ax-2 | |
| 15843 | →→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓 | Modus ponens 15841, 15842 | |
| 15844 | →→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→→→⋀𝜑𝜒𝜃→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 15845 | →→→⋀𝜑𝜒𝜃→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15838, 15844 | |
| 15846 | →→→→⋀𝜑𝜒𝜃→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→→→⋀𝜑𝜒𝜃→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→→→⋀𝜑𝜒𝜃→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→𝜑𝜓] into ax-1 | |
| 15847 | →→𝜑𝜓→→→⋀𝜑𝜒𝜃→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15845, 15846 | |
| 15848 | →→→𝜑𝜓→→→⋀𝜑𝜒𝜃→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→→⋀𝜑𝜒𝜃→𝜑𝜓, 𝜒↗→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 15849 | →→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15847, 15848 | |
| 15850 | ↔⋀→𝜑𝜓→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜑𝜒𝜃] into df-an | |
| 15851 | →¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜃 | Subs [𝜑↗→⋀𝜑𝜒𝜃] into notnotr | |
| 15852 | →→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗¬¬→⋀𝜑𝜒𝜃] into ax-1 | |
| 15853 | →¬¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 15827, 15852 | |
| 15854 | →→¬¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬¬→⋀𝜑𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒𝜃] into ax-2 | |
| 15855 | →→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 15853, 15854 | |
| 15856 | →¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 15851, 15855 | |
| 15857 | →→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬¬→⋀𝜑𝜒𝜃] into ax-1 | |
| 15858 | →¬¬→⋀𝜑𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15833, 15857 | |
| 15859 | →→¬¬→⋀𝜑𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗¬¬→⋀𝜑𝜒𝜃, 𝜓↗→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 15860 | →→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15858, 15859 | |
| 15861 | →¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15856, 15860 | |
| 15862 | →→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗¬¬→⋀𝜑𝜒𝜃] into ax-1 | |
| 15863 | →→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 15864 | →→𝜑𝜓→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓 | Modus ponens 15862, 15863 | |
| 15865 | →→→𝜑𝜓→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓] into ax-2 | |
| 15866 | →→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓 | Modus ponens 15864, 15865 | |
| 15867 | →→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗¬¬→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 15868 | →→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15861, 15867 | |
| 15869 | →→→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→𝜑𝜓] into ax-1 | |
| 15870 | →→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15868, 15869 | |
| 15871 | →→→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓, 𝜒↗→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 15872 | →→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15870, 15871 | |
| 15873 | →→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15862, 15872 | |
| 15874 | →→⋀𝜑𝜒⋀𝜓𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→⋀𝜑𝜒⋀𝜓𝜃] into notnot | |
| 15875 | →→→⋀𝜑𝜒⋀𝜓𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒⋀𝜓𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→→⋀𝜑𝜒⋀𝜓𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬¬→⋀𝜑𝜒𝜃] into ax-1 | |
| 15876 | →¬¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒⋀𝜓𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15874, 15875 | |
| 15877 | →→¬¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒⋀𝜓𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗¬¬→⋀𝜑𝜒𝜃, 𝜓↗→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗¬¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 15878 | →→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15876, 15877 | |
| 15879 | →→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→𝜑𝜓] into ax-1 | |
| 15880 | →→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15878, 15879 | |
| 15881 | →→→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 15882 | →→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15880, 15881 | |
| 15883 | →→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15873, 15882 | |
| 15884 | →→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-3 | |
| 15885 | →→→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃→→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗→→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1 | |
| 15886 | →→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃 | Modus ponens 15884, 15885 | |
| 15887 | →→→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃→→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃] into ax-2 | |
| 15888 | →→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃 | Modus ponens 15886, 15887 | |
| 15889 | →→𝜑𝜓→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃 | Modus ponens 15883, 15888 | |
| 15890 | →¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃] into id | |
| 15891 | →¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→𝜑𝜓] into ax-1 | |
| 15892 | →→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-1 | |
| 15893 | →¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15891, 15892 | |
| 15894 | →→¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 15895 | →→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15893, 15894 | |
| 15896 | →→→𝜑𝜓→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗¬→⋀𝜑𝜒𝜃] into ax-2 | |
| 15897 | →→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 15889, 15896 | |
| 15898 | →→→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗→→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-1 | |
| 15899 | →¬→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 15897, 15898 | |
| 15900 | →→¬→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2 | |
| 15901 | →→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 15899, 15900 | |
| 15902 | →¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 15891, 15901 | |
| 15903 | →¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into id | |
| 15904 | →→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-1 | |
| 15905 | →¬→⋀𝜑𝜒⋀𝜓𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 15903, 15904 | |
| 15906 | →¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into notnotr | |
| 15907 | →¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-1 | |
| 15908 | →→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-1 | |
| 15909 | →¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 15907, 15908 | |
| 15910 | →→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2 | |
| 15911 | →→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 15909, 15910 | |
| 15912 | →¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 15906, 15911 | |
| 15913 | →→¬→⋀𝜑𝜒⋀𝜓𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2 | |
| 15914 | →→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 15905, 15913 | |
| 15915 | →→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-1 | |
| 15916 | →¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 15914, 15915 | |
| 15917 | →→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2 | |
| 15918 | →→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 15916, 15917 | |
| 15919 | →¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-1 | |
| 15920 | →→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-1 | |
| 15921 | →¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15919, 15920 | |
| 15922 | →→¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 15923 | →→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15921, 15922 | |
| 15924 | →→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2 | |
| 15925 | →→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 15912, 15924 | |
| 15926 | →→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-1 | |
| 15927 | →¬→⋀𝜑𝜒⋀𝜓𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 15925, 15926 | |
| 15928 | →→¬→⋀𝜑𝜒⋀𝜓𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2 | |
| 15929 | →→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 15927, 15928 | |
| 15930 | →¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 15919, 15929 | |
| 15931 | →→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-3 | |
| 15932 | →→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-1 | |
| 15933 | →¬→⋀𝜑𝜒⋀𝜓𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 15931, 15932 | |
| 15934 | →→¬→⋀𝜑𝜒⋀𝜓𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2 | |
| 15935 | →→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 15933, 15934 | |
| 15936 | →¬→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 15930, 15935 | |
| 15937 | →→¬→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2 | |
| 15938 | →→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 15936, 15937 | |
| 15939 | →¬→⋀𝜑𝜒⋀𝜓𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 15902, 15938 | |
| 15940 | →→¬→⋀𝜑𝜒⋀𝜓𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-3 | |
| 15941 | →¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15939, 15940 | |
| 15942 | →↔⋀→𝜑𝜓→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗⋀→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into biimp | |
| 15943 | →⋀→𝜑𝜓→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 15850, 15942 | |
| 15944 | →→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀→𝜑𝜓→⋀𝜑𝜒𝜃] into ax-1 | |
| 15945 | →⋀→𝜑𝜓→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15941, 15944 | |
| 15946 | →→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→⋀→𝜑𝜓→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗⋀→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 15947 | →→⋀→𝜑𝜓→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15945, 15946 | |
| 15948 | →⋀→𝜑𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15943, 15947 | |
| 15949 | →→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1 | |
| 15950 | →→𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 15827, 15949 | |
| 15951 | →→→𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→→𝜒𝜃→⋀𝜑𝜒𝜃→→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗→𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒𝜃] into ax-2 | |
| 15952 | →→→𝜒𝜃→⋀𝜑𝜒𝜃→→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 15950, 15951 | |
| 15953 | →→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 15779, 15952 | |
| 15954 | ↔⋀→𝜒𝜃→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗→𝜒𝜃, 𝜓↗→𝜑𝜓] into df-an | |
| 15955 | →→→𝜑𝜓→→𝜒𝜃→𝜑𝜓→¬¬→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→→𝜒𝜃→𝜑𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1 | |
| 15956 | →¬¬→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→𝜑𝜓 | Modus ponens 196, 15955 | |
| 15957 | →→¬¬→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→𝜑𝜓→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→→𝜒𝜃→𝜑𝜓 | Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜒𝜃→𝜑𝜓] into ax-2 | |
| 15958 | →→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→→𝜒𝜃→𝜑𝜓 | Modus ponens 15956, 15957 | |
| 15959 | →¬¬→𝜑𝜓→→𝜒𝜃→𝜑𝜓 | Modus ponens 532, 15958 | |
| 15960 | →→→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃 | Subs [𝜑↗→𝜒𝜃, 𝜓↗→𝜑𝜓, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2 | |
| 15961 | →→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃 | Modus ponens 15953, 15960 | |
| 15962 | →→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃 | Subs [𝜑↗→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃, 𝜓↗¬¬→𝜑𝜓] into ax-1 | |
| 15963 | →¬¬→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃 | Modus ponens 15961, 15962 | |
| 15964 | →→¬¬→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃→→¬¬→𝜑𝜓→→𝜒𝜃→𝜑𝜓→¬¬→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→→𝜒𝜃→𝜑𝜓, 𝜒↗→→𝜒𝜃→⋀𝜑𝜒𝜃] into ax-2 | |
| 15965 | →→¬¬→𝜑𝜓→→𝜒𝜃→𝜑𝜓→¬¬→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃 | Modus ponens 15963, 15964 | |
| 15966 | →¬¬→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃 | Modus ponens 15959, 15965 | |
| 15967 | →→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃 | Subs [𝜑↗→𝜒𝜃, 𝜓↗¬¬→𝜑𝜓] into ax-1 | |
| 15968 | →→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃→→𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃 | Subs [𝜑↗→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1 | |
| 15969 | →→𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃 | Modus ponens 15967, 15968 | |
| 15970 | →→→𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃 | Subs [𝜑↗→𝜒𝜃, 𝜓↗→𝜒𝜃, 𝜒↗→¬¬→𝜑𝜓→𝜒𝜃] into ax-2 | |
| 15971 | →→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃 | Modus ponens 15969, 15970 | |
| 15972 | →→¬¬→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃→→¬¬→𝜑𝜓→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜒𝜃, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2 | |
| 15973 | →→¬¬→𝜑𝜓→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 15966, 15972 | |
| 15974 | →→→¬¬→𝜑𝜓→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜒𝜃→→¬¬→𝜑𝜓→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗→→¬¬→𝜑𝜓→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1 | |
| 15975 | →→𝜒𝜃→→¬¬→𝜑𝜓→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 15973, 15974 | |
| 15976 | →→→𝜒𝜃→→¬¬→𝜑𝜓→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗→𝜒𝜃, 𝜓↗→¬¬→𝜑𝜓→𝜒𝜃, 𝜒↗→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃] into ax-2 | |
| 15977 | →→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 15975, 15976 | |
| 15978 | →→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 15967, 15977 | |
| 15979 | →→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗→⋀𝜑𝜒𝜃] into notnot | |
| 15980 | →→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃, 𝜓↗¬¬→𝜑𝜓] into ax-1 | |
| 15981 | →¬¬→𝜑𝜓→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃 | Modus ponens 15979, 15980 | |
| 15982 | →→¬¬→𝜑𝜓→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃→→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗¬¬→⋀𝜑𝜒𝜃] into ax-2 | |
| 15983 | →→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃 | Modus ponens 15981, 15982 | |
| 15984 | →→→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→→𝜒𝜃→→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗→→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1 | |
| 15985 | →→𝜒𝜃→→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃 | Modus ponens 15983, 15984 | |
| 15986 | →→→𝜒𝜃→→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→→→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗→𝜒𝜃, 𝜓↗→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜒↗→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃] into ax-2 | |
| 15987 | →→→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃 | Modus ponens 15985, 15986 | |
| 15988 | →→𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃 | Modus ponens 15978, 15987 | |
| 15989 | →→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-3 | |
| 15990 | →→→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓→→𝜒𝜃→→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗→→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓, 𝜓↗→𝜒𝜃] into ax-1 | |
| 15991 | →→𝜒𝜃→→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓 | Modus ponens 15989, 15990 | |
| 15992 | →→→𝜒𝜃→→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓→→→𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗→𝜒𝜃, 𝜓↗→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃, 𝜒↗→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓] into ax-2 | |
| 15993 | →→→𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓 | Modus ponens 15991, 15992 | |
| 15994 | →→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓 | Modus ponens 15988, 15993 | |
| 15995 | →¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒𝜃] into id | |
| 15996 | →¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1 | |
| 15997 | →→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1 | |
| 15998 | →¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃 | Modus ponens 15996, 15997 | |
| 15999 | →→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃, 𝜒↗→→𝜒𝜃¬→⋀𝜑𝜒𝜃] into ax-2 | |
| 16000 | →→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃 | Modus ponens 15998, 15999 | |
| 16001 | →→→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓→→→𝜒𝜃¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗→𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃, 𝜒↗¬→𝜑𝜓] into ax-2 | |
| 16002 | →→→𝜒𝜃¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓 | Modus ponens 15994, 16001 | |
| 16003 | →→→→𝜒𝜃¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃→→→𝜒𝜃¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗→→→𝜒𝜃¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1 | |
| 16004 | →¬→⋀𝜑𝜒𝜃→→→𝜒𝜃¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓 | Modus ponens 16002, 16003 | |
| 16005 | →→¬→⋀𝜑𝜒𝜃→→→𝜒𝜃¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓→→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→→𝜒𝜃¬→⋀𝜑𝜒𝜃, 𝜒↗→→𝜒𝜃¬→𝜑𝜓] into ax-2 | |
| 16006 | →→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓 | Modus ponens 16004, 16005 | |
| 16007 | →¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓 | Modus ponens 15996, 16006 | |
| 16008 | →¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗¬→→𝜒𝜃¬→𝜑𝜓] into id | |
| 16009 | →→¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃→¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗→¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1 | |
| 16010 | →¬→⋀𝜑𝜒𝜃→¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓 | Modus ponens 16008, 16009 | |
| 16011 | →¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗¬→→𝜒𝜃¬→𝜑𝜓] into notnotr | |
| 16012 | →¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1 | |
| 16013 | →→¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗→¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬¬¬→→𝜒𝜃¬→𝜑𝜓] into ax-1 | |
| 16014 | →¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓 | Modus ponens 16012, 16013 | |
| 16015 | →→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗¬¬¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬→→𝜒𝜃¬→𝜑𝜓, 𝜒↗→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓] into ax-2 | |
| 16016 | →→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓 | Modus ponens 16014, 16015 | |
| 16017 | →¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓 | Modus ponens 16011, 16016 | |
| 16018 | →→¬→⋀𝜑𝜒𝜃→¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜒𝜃¬→𝜑𝜓, 𝜒↗¬→→𝜒𝜃¬→𝜑𝜓] into ax-2 | |
| 16019 | →→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓 | Modus ponens 16010, 16018 | |
| 16020 | →→→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬¬¬→→𝜒𝜃¬→𝜑𝜓→→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗→→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬¬¬→→𝜒𝜃¬→𝜑𝜓] into ax-1 | |
| 16021 | →¬¬¬→→𝜒𝜃¬→𝜑𝜓→→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓 | Modus ponens 16019, 16020 | |
| 16022 | →→¬¬¬→→𝜒𝜃¬→𝜑𝜓→→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗¬¬¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓, 𝜒↗→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓] into ax-2 | |
| 16023 | →→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓 | Modus ponens 16021, 16022 | |
| 16024 | →¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬¬¬→→𝜒𝜃¬→𝜑𝜓] into ax-1 | |
| 16025 | →→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1 | |
| 16026 | →¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 16024, 16025 | |
| 16027 | →→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃, 𝜒↗→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2 | |
| 16028 | →→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 16026, 16027 | |
| 16029 | →→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗¬¬¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒𝜃, 𝜒↗¬→→𝜒𝜃¬→𝜑𝜓] into ax-2 | |
| 16030 | →→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓 | Modus ponens 16017, 16029 | |
| 16031 | →→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1 | |
| 16032 | →¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓 | Modus ponens 16030, 16031 | |
| 16033 | →→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓] into ax-2 | |
| 16034 | →→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓 | Modus ponens 16032, 16033 | |
| 16035 | →¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓 | Modus ponens 16024, 16034 | |
| 16036 | →→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗¬¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗→→𝜒𝜃¬→𝜑𝜓] into ax-3 | |
| 16037 | →→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1 | |
| 16038 | →¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓 | Modus ponens 16036, 16037 | |
| 16039 | →→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓→→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓, 𝜒↗→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓] into ax-2 | |
| 16040 | →→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓 | Modus ponens 16038, 16039 | |
| 16041 | →¬→⋀𝜑𝜒𝜃→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓 | Modus ponens 16035, 16040 | |
| 16042 | →→¬→⋀𝜑𝜒𝜃→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓→→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬¬→→𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→→𝜒𝜃¬→𝜑𝜓, 𝜒↗¬¬→→𝜒𝜃¬→𝜑𝜓] into ax-2 | |
| 16043 | →→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬¬→→𝜒𝜃¬→𝜑𝜓 | Modus ponens 16041, 16042 | |
| 16044 | →¬→⋀𝜑𝜒𝜃¬¬→→𝜒𝜃¬→𝜑𝜓 | Modus ponens 16007, 16043 | |
| 16045 | →→¬→⋀𝜑𝜒𝜃¬¬→→𝜒𝜃¬→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜒𝜃¬→𝜑𝜓] into ax-3 | |
| 16046 | →¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 16044, 16045 | |
| 16047 | →↔⋀→𝜒𝜃→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→⋀→𝜒𝜃→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗⋀→𝜒𝜃→𝜑𝜓, 𝜓↗¬→→𝜒𝜃¬→𝜑𝜓] into biimp | |
| 16048 | →⋀→𝜒𝜃→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓 | Modus ponens 15954, 16047 | |
| 16049 | →→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃→⋀→𝜒𝜃→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗⋀→𝜒𝜃→𝜑𝜓] into ax-1 | |
| 16050 | →⋀→𝜒𝜃→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 16046, 16049 | |
| 16051 | →→⋀→𝜒𝜃→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃→→⋀→𝜒𝜃→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→⋀→𝜒𝜃→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗⋀→𝜒𝜃→𝜑𝜓, 𝜓↗¬→→𝜒𝜃¬→𝜑𝜓, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2 | |
| 16052 | →→⋀→𝜒𝜃→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→⋀→𝜒𝜃→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 16050, 16051 | |
| 16053 | →⋀→𝜒𝜃→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 16048, 16052 | |
| 16054 | →↔⋀→𝜒𝜃→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓↔¬→→𝜒𝜃¬→𝜑𝜓⋀→𝜒𝜃→𝜑𝜓 | Subs [𝜑↗⋀→𝜒𝜃→𝜑𝜓, 𝜓↗¬→→𝜒𝜃¬→𝜑𝜓] into bicom1 | |
| 16055 | ↔¬→→𝜒𝜃¬→𝜑𝜓⋀→𝜒𝜃→𝜑𝜓 | Modus ponens 15954, 16054 | |
| 16056 | →↔¬→→𝜒𝜃¬→𝜑𝜓⋀→𝜒𝜃→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓⋀→𝜒𝜃→𝜑𝜓 | Subs [𝜑↗¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗⋀→𝜒𝜃→𝜑𝜓] into biimp | |
| 16057 | →¬→→𝜒𝜃¬→𝜑𝜓⋀→𝜒𝜃→𝜑𝜓 | Modus ponens 16055, 16056 | |
| 16058 | →→⋀→𝜒𝜃→𝜑𝜓→⋀𝜑𝜒𝜃→¬→→𝜒𝜃¬→𝜑𝜓→⋀→𝜒𝜃→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗→⋀→𝜒𝜃→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜒𝜃¬→𝜑𝜓] into ax-1 | |
| 16059 | →¬→→𝜒𝜃¬→𝜑𝜓→⋀→𝜒𝜃→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 16053, 16058 | |
| 16060 | →→¬→→𝜒𝜃¬→𝜑𝜓→⋀→𝜒𝜃→𝜑𝜓→⋀𝜑𝜒𝜃→→¬→→𝜒𝜃¬→𝜑𝜓⋀→𝜒𝜃→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗⋀→𝜒𝜃→𝜑𝜓, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2 | |
| 16061 | →→¬→→𝜒𝜃¬→𝜑𝜓⋀→𝜒𝜃→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 16059, 16060 | |
| 16062 | →→𝜒𝜃→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓 | Subs [𝜑↗→𝜒𝜃, 𝜓↗→𝜑𝜓] into pm3.2im | |
| 16063 | →→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1 | |
| 16064 | →→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 16046, 16063 | |
| 16065 | →→→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→→𝜒𝜃¬→𝜑𝜓, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2 | |
| 16066 | →→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 16064, 16065 | |
| 16067 | →→→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜒𝜃→→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗→→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1 | |
| 16068 | →→𝜒𝜃→→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 16066, 16067 | |
| 16069 | →→→𝜒𝜃→→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜃→→→𝜒𝜃→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗→𝜒𝜃, 𝜓↗→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒𝜃] into ax-2 | |
| 16070 | →→→𝜒𝜃→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 16068, 16069 | |
| 16071 | →→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃→→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃 | Subs [𝜑↗→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1 | |
| 16072 | →→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃 | Modus ponens 15961, 16071 | |
| 16073 | →→→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃→→→𝜑𝜓→→𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜒𝜃→𝜑𝜓, 𝜒↗→→𝜒𝜃→⋀𝜑𝜒𝜃] into ax-2 | |
| 16074 | →→→𝜑𝜓→→𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃 | Modus ponens 16072, 16073 | |
| 16075 | →→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃 | Modus ponens 196, 16074 | |
| 16076 | ↔⋀→𝜑𝜓→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒𝜃] into df-an | |
| 16077 | →¬¬→𝜒𝜃→𝜒𝜃 | Subs [𝜑↗→𝜒𝜃] into notnotr | |
| 16078 | →→𝜒𝜃→→𝜑𝜓→𝜒𝜃 | Subs [𝜑↗→𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1 | |
| 16079 | →→→𝜒𝜃→→𝜑𝜓→𝜒𝜃→¬¬→𝜒𝜃→→𝜒𝜃→→𝜑𝜓→𝜒𝜃 | Subs [𝜑↗→→𝜒𝜃→→𝜑𝜓→𝜒𝜃, 𝜓↗¬¬→𝜒𝜃] into ax-1 | |
| 16080 | →¬¬→𝜒𝜃→→𝜒𝜃→→𝜑𝜓→𝜒𝜃 | Modus ponens 16078, 16079 | |
| 16081 | →→¬¬→𝜒𝜃→→𝜒𝜃→→𝜑𝜓→𝜒𝜃→→¬¬→𝜒𝜃→𝜒𝜃→¬¬→𝜒𝜃→→𝜑𝜓→𝜒𝜃 | Subs [𝜑↗¬¬→𝜒𝜃, 𝜓↗→𝜒𝜃, 𝜒↗→→𝜑𝜓→𝜒𝜃] into ax-2 | |
| 16082 | →→¬¬→𝜒𝜃→𝜒𝜃→¬¬→𝜒𝜃→→𝜑𝜓→𝜒𝜃 | Modus ponens 16080, 16081 | |
| 16083 | →¬¬→𝜒𝜃→→𝜑𝜓→𝜒𝜃 | Modus ponens 16077, 16082 | |
| 16084 | →→→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃→→→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒𝜃, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2 | |
| 16085 | →→→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 16075, 16084 | |
| 16086 | →→→→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃→→→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗→→→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗¬¬→𝜒𝜃] into ax-1 | |
| 16087 | →¬¬→𝜒𝜃→→→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 16085, 16086 | |
| 16088 | →→¬¬→𝜒𝜃→→→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→¬¬→𝜒𝜃→→𝜑𝜓→𝜒𝜃→¬¬→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬¬→𝜒𝜃, 𝜓↗→→𝜑𝜓→𝜒𝜃, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒𝜃] into ax-2 | |
| 16089 | →→¬¬→𝜒𝜃→→𝜑𝜓→𝜒𝜃→¬¬→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 16087, 16088 | |
| 16090 | →¬¬→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 16083, 16089 | |
| 16091 | →→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗¬¬→𝜒𝜃] into ax-1 | |
| 16092 | →→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 16093 | →→𝜑𝜓→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓 | Modus ponens 16091, 16092 | |
| 16094 | →→→𝜑𝜓→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→¬¬→𝜒𝜃→𝜑𝜓] into ax-2 | |
| 16095 | →→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓 | Modus ponens 16093, 16094 | |
| 16096 | →→¬¬→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→¬¬→𝜒𝜃→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬¬→𝜒𝜃, 𝜓↗→𝜑𝜓, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2 | |
| 16097 | →→¬¬→𝜒𝜃→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃 | Modus ponens 16090, 16096 | |
| 16098 | →→→¬¬→𝜒𝜃→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→→𝜑𝜓→→¬¬→𝜒𝜃→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃 | Subs [𝜑↗→→¬¬→𝜒𝜃→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1 | |
| 16099 | →→𝜑𝜓→→¬¬→𝜒𝜃→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃 | Modus ponens 16097, 16098 | |
| 16100 | →→→𝜑𝜓→→¬¬→𝜒𝜃→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓→→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜒𝜃→𝜑𝜓, 𝜒↗→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃] into ax-2 | |
| 16101 | →→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓→→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃 | Modus ponens 16099, 16100 | |
| 16102 | →→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃 | Modus ponens 16091, 16101 | |
| 16103 | →→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃, 𝜓↗¬¬→𝜒𝜃] into ax-1 | |
| 16104 | →¬¬→𝜒𝜃→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃 | Modus ponens 15979, 16103 | |
| 16105 | →→¬¬→𝜒𝜃→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃→→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬¬→𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗¬¬→⋀𝜑𝜒𝜃] into ax-2 | |
| 16106 | →→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃 | Modus ponens 16104, 16105 | |
| 16107 | →→→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗→→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1 | |
| 16108 | →→𝜑𝜓→→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃 | Modus ponens 16106, 16107 | |
| 16109 | →→→𝜑𝜓→→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→→→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→→𝜑𝜓→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃, 𝜒↗→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃] into ax-2 | |
| 16110 | →→→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→→𝜑𝜓→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃 | Modus ponens 16108, 16109 | |
| 16111 | →→𝜑𝜓→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃 | Modus ponens 16102, 16110 | |
| 16112 | →→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃 | Subs [𝜑↗¬→𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-3 | |
| 16113 | →→→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃→→𝜑𝜓→→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃 | Subs [𝜑↗→→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1 | |
| 16114 | →→𝜑𝜓→→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃 | Modus ponens 16112, 16113 | |
| 16115 | →→→𝜑𝜓→→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃→→→𝜑𝜓→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃, 𝜒↗→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃] into ax-2 | |
| 16116 | →→→𝜑𝜓→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃 | Modus ponens 16114, 16115 | |
| 16117 | →→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃 | Modus ponens 16111, 16116 | |
| 16118 | →¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1 | |
| 16119 | →→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1 | |
| 16120 | →¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 16118, 16119 | |
| 16121 | →→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2 | |
| 16122 | →→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Modus ponens 16120, 16121 | |
| 16123 | →→→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃 | Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒𝜃, 𝜒↗¬→𝜒𝜃] into ax-2 | |
| 16124 | →→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃 | Modus ponens 16117, 16123 | |
| 16125 | →→→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃 | Subs [𝜑↗→→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1 | |
| 16126 | →¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃 | Modus ponens 16124, 16125 | |
| 16127 | →→¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃→→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓¬→𝜒𝜃] into ax-2 | |
| 16128 | →→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃 | Modus ponens 16126, 16127 | |
| 16129 | →¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃 | Modus ponens 16118, 16128 | |
| 16130 | →¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Subs [𝜑↗¬→→𝜑𝜓¬→𝜒𝜃] into id | |
| 16131 | →→¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Subs [𝜑↗→¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1 | |
| 16132 | →¬→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Modus ponens 16130, 16131 | |
| 16133 | →¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Subs [𝜑↗¬→→𝜑𝜓¬→𝜒𝜃] into notnotr | |
| 16134 | →¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Subs [𝜑↗¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1 | |
| 16135 | →→¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Subs [𝜑↗→¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜒𝜃] into ax-1 | |
| 16136 | →¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Modus ponens 16134, 16135 | |
| 16137 | →→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→𝜒𝜃, 𝜒↗→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃] into ax-2 | |
| 16138 | →→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Modus ponens 16136, 16137 | |
| 16139 | →¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Modus ponens 16133, 16138 | |
| 16140 | →→¬→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→𝜒𝜃, 𝜒↗¬→→𝜑𝜓¬→𝜒𝜃] into ax-2 | |
| 16141 | →→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Modus ponens 16132, 16140 | |
| 16142 | →→→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃→→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Subs [𝜑↗→→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜒𝜃] into ax-1 | |
| 16143 | →¬¬¬→→𝜑𝜓¬→𝜒𝜃→→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Modus ponens 16141, 16142 | |
| 16144 | →→¬¬¬→→𝜑𝜓¬→𝜒𝜃→→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃, 𝜒↗→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃] into ax-2 | |
| 16145 | →→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Modus ponens 16143, 16144 | |
| 16146 | →¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜒𝜃] into ax-1 | |
| 16147 | →→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1 | |
| 16148 | →¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃 | Modus ponens 16146, 16147 | |
| 16149 | →→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃, 𝜒↗→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃] into ax-2 | |
| 16150 | →→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃 | Modus ponens 16148, 16149 | |
| 16151 | →→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃, 𝜒↗¬→→𝜑𝜓¬→𝜒𝜃] into ax-2 | |
| 16152 | →→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Modus ponens 16139, 16151 | |
| 16153 | →→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1 | |
| 16154 | →¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Modus ponens 16152, 16153 | |
| 16155 | →→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃, 𝜒↗→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃] into ax-2 | |
| 16156 | →→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Modus ponens 16154, 16155 | |
| 16157 | →¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Modus ponens 16146, 16156 | |
| 16158 | →→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃 | Subs [𝜑↗¬¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗→→𝜑𝜓¬→𝜒𝜃] into ax-3 | |
| 16159 | →→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃 | Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1 | |
| 16160 | →¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃 | Modus ponens 16158, 16159 | |
| 16161 | →→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃→→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃, 𝜒↗→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃] into ax-2 | |
| 16162 | →→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃 | Modus ponens 16160, 16161 | |
| 16163 | →¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃 | Modus ponens 16157, 16162 | |
| 16164 | →→¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃→→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃 | Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→→𝜑𝜓¬→𝜒𝜃, 𝜒↗¬¬→→𝜑𝜓¬→𝜒𝜃] into ax-2 | |
| 16165 | →→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃 | Modus ponens 16163, 16164 | |
| 16166 | →¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃 | Modus ponens 16129, 16165 | |
| 16167 | →→¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃→⋀𝜑𝜒𝜃 | Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→𝜒𝜃] into ax-3 | |
| 16168 | →¬→→𝜑𝜓¬→𝜒𝜃→⋀𝜑𝜒𝜃 | Modus ponens 16166, 16167 | |
| 16169 | →↔⋀→𝜑𝜓→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Subs [𝜑↗⋀→𝜑𝜓→𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→𝜒𝜃] into biimp | |
| 16170 | →⋀→𝜑𝜓→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃 | Modus ponens 16076, 16169 | |
| 16171 | →→¬→→𝜑𝜓¬→𝜒𝜃→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃→⋀𝜑𝜒𝜃 | Subs [𝜑↗→¬→→𝜑𝜓¬→𝜒𝜃→⋀𝜑𝜒𝜃, 𝜓↗⋀→𝜑𝜓→𝜒𝜃] into ax-1 | |
| 16172 | →⋀→𝜑𝜓→𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃→⋀𝜑𝜒𝜃 | Modus ponens 16168, 16171 | |
| 16173 | →→⋀→𝜑𝜓→𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃→⋀𝜑𝜒𝜃→→⋀→𝜑𝜓→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒𝜃 | Subs [𝜑↗⋀→𝜑𝜓→𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→𝜒𝜃, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2 | |
| 16174 | →→⋀→𝜑𝜓→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒𝜃 | Modus ponens 16172, 16173 | |
| 16175 | →⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒𝜃 | Modus ponens 16170, 16174 | |
| 16176 | →⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒𝜃] into simpl | |
| 16177 | →↔⋀→𝜑𝜓→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃↔¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃⋀→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗⋀→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into bicom1 | |
| 16178 | ↔¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃⋀→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 15850, 16177 | |
| 16179 | →↔¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃⋀→𝜑𝜓→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃⋀→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗⋀→𝜑𝜓→⋀𝜑𝜒𝜃] into biimp | |
| 16180 | →¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃⋀→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 16178, 16179 | |
| 16181 | →→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-1 | |
| 16182 | →¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15948, 16181 | |
| 16183 | →→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃⋀→𝜑𝜓→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗⋀→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 16184 | →→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃⋀→𝜑𝜓→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 16182, 16183 | |
| 16185 | →→𝜑𝜓→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜑𝜒𝜃] into pm3.2im | |
| 16186 | →→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→⋀𝜑𝜒𝜃] into ax-1 | |
| 16187 | →→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15941, 16186 | |
| 16188 | →→→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 16189 | →→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 16187, 16188 | |
| 16190 | →→→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→𝜑𝜓] into ax-1 | |
| 16191 | →→𝜑𝜓→→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 16189, 16190 | |
| 16192 | →→→𝜑𝜓→→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 16193 | →→→𝜑𝜓→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 16191, 16192 | |
| 16194 | →→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗⋀→𝜑𝜓→𝜒𝜃] into ax-1 | |
| 16195 | →⋀→𝜑𝜓→𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 15827, 16194 | |
| 16196 | →→⋀→𝜑𝜓→𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Subs [𝜑↗⋀→𝜑𝜓→𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒𝜃] into ax-2 | |
| 16197 | →→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 16195, 16196 | |
| 16198 | →⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃 | Modus ponens 16175, 16197 | |
| 16199 | →→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→⋀→𝜑𝜓→𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀→𝜑𝜓→𝜒𝜃] into ax-1 | |
| 16200 | →⋀→𝜑𝜓→𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 15833, 16199 | |
| 16201 | →→⋀→𝜑𝜓→𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗⋀→𝜑𝜓→𝜒𝜃, 𝜓↗→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 16202 | →→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 16200, 16201 | |
| 16203 | →⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 16198, 16202 | |
| 16204 | →→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀→𝜑𝜓→𝜒𝜃] into ax-1 | |
| 16205 | →→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 16206 | →→𝜑𝜓→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓 | Modus ponens 16204, 16205 | |
| 16207 | →→→𝜑𝜓→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓] into ax-2 | |
| 16208 | →→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓 | Modus ponens 16206, 16207 | |
| 16209 | →→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗⋀→𝜑𝜓→𝜒𝜃, 𝜓↗→𝜑𝜓, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 16210 | →→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 16203, 16209 | |
| 16211 | →→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→𝜑𝜓] into ax-1 | |
| 16212 | →→𝜑𝜓→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 16210, 16211 | |
| 16213 | →→→𝜑𝜓→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓, 𝜒↗→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 16214 | →→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 16212, 16213 | |
| 16215 | →→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 16204, 16214 | |
| 16216 | →→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀→𝜑𝜓→𝜒𝜃] into ax-1 | |
| 16217 | →⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 16215, 16216 | |
| 16218 | →→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗⋀→𝜑𝜓→𝜒𝜃, 𝜓↗→𝜑𝜓, 𝜒↗→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 16219 | →→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 16217, 16218 | |
| 16220 | →⋀→𝜑𝜓→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 16176, 16219 | |
| 16221 | →⋀→𝜑𝜓→𝜒𝜃⋀→𝜑𝜓→𝜒𝜃 | Subs [𝜑↗⋀→𝜑𝜓→𝜒𝜃] into id | |
| 16222 | →→⋀→𝜑𝜓→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→⋀→𝜑𝜓→𝜒𝜃⋀→𝜑𝜓→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Subs [𝜑↗⋀→𝜑𝜓→𝜒𝜃, 𝜓↗⋀→𝜑𝜓→𝜒𝜃, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2 | |
| 16223 | →→⋀→𝜑𝜓→𝜒𝜃⋀→𝜑𝜓→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 16220, 16222 | |
| 16224 | →⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃 | Modus ponens 16221, 16223 | anim12 |
| 16225 | →→𝜓→𝜑𝜓→⋀𝜑𝜓→𝜓→𝜑𝜓 | Subs [𝜑↗→𝜓→𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 16226 | →⋀𝜑𝜓→𝜓→𝜑𝜓 | Modus ponens 208, 16225 | |
| 16227 | →→⋀𝜑𝜓→𝜓→𝜑𝜓→→⋀𝜑𝜓𝜓→⋀𝜑𝜓→𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2 | |
| 16228 | →→⋀𝜑𝜓𝜓→⋀𝜑𝜓→𝜑𝜓 | Modus ponens 16226, 16227 | |
| 16229 | →⋀𝜑𝜓→𝜑𝜓 | Modus ponens simpr, 16228 | pm3.4 |
| 16230 | ↔↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑𝜑 | Subs [𝜓↗⋀𝜓𝜑] into bicom | |
| 16231 | ↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Subs [𝜓↗⋀𝜓𝜒] into bicom | |
| 16232 | →↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into id | |
| 16233 | →↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into ax-1 | |
| 16234 | →↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 7683, 16233 | |
| 16235 | ↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔𝜑⋀𝜓𝜒, 𝜒↗→𝜓↔𝜑𝜒] into pm5.74 | |
| 16236 | →↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒] into biimp | |
| 16237 | →→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒 | Modus ponens 16235, 16236 | |
| 16238 | ↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒 | Modus ponens 16232, 16237 | |
| 16239 | ↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗→𝜓↔𝜑𝜒, 𝜒↗↔⋀𝜓𝜑⋀𝜓𝜒] into pm5.74 | |
| 16240 | →↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp | |
| 16241 | →→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16239, 16240 | |
| 16242 | ↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16234, 16241 | |
| 16243 | →↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp | |
| 16244 | →→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16242, 16243 | |
| 16245 | →↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒] into biimp | |
| 16246 | →→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒 | Modus ponens 16238, 16245 | |
| 16247 | →→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into ax-1 | |
| 16248 | →→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16244, 16247 | |
| 16249 | →→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒, 𝜒↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into ax-2 | |
| 16250 | →→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16248, 16249 | |
| 16251 | →→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16246, 16250 | |
| 16252 | →↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1 | |
| 16253 | ↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒 | Modus ponens 16242, 16252 | |
| 16254 | →↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒] into biimp | |
| 16255 | →→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒 | Modus ponens 16253, 16254 | |
| 16256 | →↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒] into bicom1 | |
| 16257 | ↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16238, 16256 | |
| 16258 | →↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into biimp | |
| 16259 | →→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16257, 16258 | |
| 16260 | →→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into ax-1 | |
| 16261 | →→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16259, 16260 | |
| 16262 | →→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒, 𝜒↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into ax-2 | |
| 16263 | →→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16261, 16262 | |
| 16264 | →→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16255, 16263 | |
| 16265 | →→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into impbi | |
| 16266 | →→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16251, 16265 | |
| 16267 | ↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16264, 16266 | |
| 16268 | ↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔𝜑⋀𝜓𝜒, 𝜒↗↔⋀𝜓𝜑⋀𝜓𝜒] into pm5.74 | |
| 16269 | →↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1 | |
| 16270 | ↔↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16268, 16269 | |
| 16271 | →↔↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp | |
| 16272 | →↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16270, 16271 | |
| 16273 | →↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16267, 16272 | |
| 16274 | →↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into id | |
| 16275 | →↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗→𝜓↔𝜑𝜒, 𝜓↗↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1 | |
| 16276 | ↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Modus ponens 7683, 16275 | |
| 16277 | →↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into ax-1 | |
| 16278 | →↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Modus ponens 16276, 16277 | |
| 16279 | ↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜒, 𝜒↗↔⋀𝜓𝜑⋀𝜓𝜒] into pm5.74 | |
| 16280 | →↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp | |
| 16281 | →→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16279, 16280 | |
| 16282 | ↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16274, 16281 | |
| 16283 | ↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗→𝜓↔𝜑𝜒] into pm5.74 | |
| 16284 | →↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into biimp | |
| 16285 | →→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Modus ponens 16283, 16284 | |
| 16286 | ↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Modus ponens 16278, 16285 | |
| 16287 | →↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into biimp | |
| 16288 | →→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Modus ponens 16286, 16287 | |
| 16289 | →↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp | |
| 16290 | →→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16282, 16289 | |
| 16291 | →→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into ax-1 | |
| 16292 | →→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Modus ponens 16288, 16291 | |
| 16293 | →→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into ax-2 | |
| 16294 | →→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Modus ponens 16292, 16293 | |
| 16295 | →→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Modus ponens 16290, 16294 | |
| 16296 | →↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into bicom1 | |
| 16297 | ↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16286, 16296 | |
| 16298 | →↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp | |
| 16299 | →→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16297, 16298 | |
| 16300 | →↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1 | |
| 16301 | ↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16282, 16300 | |
| 16302 | →↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into biimp | |
| 16303 | →→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16301, 16302 | |
| 16304 | →→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into ax-1 | |
| 16305 | →→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16303, 16304 | |
| 16306 | →→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into ax-2 | |
| 16307 | →→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16305, 16306 | |
| 16308 | →→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16299, 16307 | |
| 16309 | →→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into impbi | |
| 16310 | →→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Modus ponens 16295, 16309 | |
| 16311 | ↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Modus ponens 16308, 16310 | |
| 16312 | ↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜒, 𝜒↗→𝜓↔𝜑𝜒] into pm5.74 | |
| 16313 | →↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into bicom1 | |
| 16314 | ↔↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Modus ponens 16312, 16313 | |
| 16315 | →↔↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into biimp | |
| 16316 | →↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Modus ponens 16314, 16315 | |
| 16317 | →↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Modus ponens 16311, 16316 | |
| 16318 | →→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into impbi | |
| 16319 | →→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16273, 16318 | |
| 16320 | ↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16317, 16319 | |
| 16321 | ↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑⋀𝜓𝜒] into bicom | |
| 16322 | →↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into id | |
| 16323 | →↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into ax-1 | |
| 16324 | →↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Modus ponens 16231, 16323 | |
| 16325 | ↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗↔𝜑⋀𝜓𝜒] into pm5.74 | |
| 16326 | →↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into biimp | |
| 16327 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16325, 16326 | |
| 16328 | ↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16322, 16327 | |
| 16329 | ↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜒, 𝜒↗↔⋀𝜓𝜒𝜑] into pm5.74 | |
| 16330 | →↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into biimp | |
| 16331 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Modus ponens 16329, 16330 | |
| 16332 | ↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Modus ponens 16324, 16331 | |
| 16333 | →↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into biimp | |
| 16334 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Modus ponens 16332, 16333 | |
| 16335 | →↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into biimp | |
| 16336 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16328, 16335 | |
| 16337 | →→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Subs [𝜑↗→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into ax-1 | |
| 16338 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Modus ponens 16334, 16337 | |
| 16339 | →→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜒↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into ax-2 | |
| 16340 | →→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Modus ponens 16338, 16339 | |
| 16341 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Modus ponens 16336, 16340 | |
| 16342 | →↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into bicom1 | |
| 16343 | ↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16332, 16342 | |
| 16344 | →↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into biimp | |
| 16345 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16343, 16344 | |
| 16346 | →↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into bicom1 | |
| 16347 | ↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16328, 16346 | |
| 16348 | →↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp | |
| 16349 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16347, 16348 | |
| 16350 | →→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into ax-1 | |
| 16351 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16349, 16350 | |
| 16352 | →→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜒↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into ax-2 | |
| 16353 | →→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16351, 16352 | |
| 16354 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16345, 16353 | |
| 16355 | →→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into impbi | |
| 16356 | →→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Modus ponens 16341, 16355 | |
| 16357 | ↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Modus ponens 16354, 16356 | |
| 16358 | ↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗↔⋀𝜓𝜒𝜑] into pm5.74 | |
| 16359 | →↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into bicom1 | |
| 16360 | ↔↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Modus ponens 16358, 16359 | |
| 16361 | →↔↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Subs [𝜑↗↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into biimp | |
| 16362 | →↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Modus ponens 16360, 16361 | |
| 16363 | →↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Modus ponens 16357, 16362 | |
| 16364 | →↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into id | |
| 16365 | →↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜒𝜑] into bicom1 | |
| 16366 | ↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒 | Modus ponens 16231, 16365 | |
| 16367 | →↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into ax-1 | |
| 16368 | →↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒 | Modus ponens 16366, 16367 | |
| 16369 | ↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑 | Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗↔⋀𝜓𝜒𝜑] into pm5.74 | |
| 16370 | →↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑] into biimp | |
| 16371 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑 | Modus ponens 16369, 16370 | |
| 16372 | ↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑 | Modus ponens 16364, 16371 | |
| 16373 | ↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔⋀𝜓𝜒𝜑, 𝜒↗↔𝜑⋀𝜓𝜒] into pm5.74 | |
| 16374 | →↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒, 𝜓↗↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒] into biimp | |
| 16375 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒 | Modus ponens 16373, 16374 | |
| 16376 | ↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒 | Modus ponens 16368, 16375 | |
| 16377 | →↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒] into biimp | |
| 16378 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒 | Modus ponens 16376, 16377 | |
| 16379 | →↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑] into biimp | |
| 16380 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑 | Modus ponens 16372, 16379 | |
| 16381 | →→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into ax-1 | |
| 16382 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒 | Modus ponens 16378, 16381 | |
| 16383 | →→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑, 𝜒↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒] into ax-2 | |
| 16384 | →→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒 | Modus ponens 16382, 16383 | |
| 16385 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒 | Modus ponens 16380, 16384 | |
| 16386 | →↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒] into bicom1 | |
| 16387 | ↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑 | Modus ponens 16376, 16386 | |
| 16388 | →↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑] into biimp | |
| 16389 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑 | Modus ponens 16387, 16388 | |
| 16390 | →↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑] into bicom1 | |
| 16391 | ↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16372, 16390 | |
| 16392 | →↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into biimp | |
| 16393 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16391, 16392 | |
| 16394 | →→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒] into ax-1 | |
| 16395 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16393, 16394 | |
| 16396 | →→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑, 𝜒↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into ax-2 | |
| 16397 | →→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16395, 16396 | |
| 16398 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16389, 16397 | |
| 16399 | →→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒] into impbi | |
| 16400 | →→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒 | Modus ponens 16385, 16399 | |
| 16401 | ↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒 | Modus ponens 16398, 16400 | |
| 16402 | ↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗↔𝜑⋀𝜓𝜒] into pm5.74 | |
| 16403 | →↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒↔↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒] into bicom1 | |
| 16404 | ↔↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16402, 16403 | |
| 16405 | →↔↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into biimp | |
| 16406 | →↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16404, 16405 | |
| 16407 | →↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16401, 16406 | |
| 16408 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into impbi | |
| 16409 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Modus ponens 16363, 16408 | |
| 16410 | ↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Modus ponens 16407, 16409 | |
| 16411 | ↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜒𝜑] into bicom | |
| 16412 | →↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into biimp | |
| 16413 | →↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16411, 16412 | |
| 16414 | →↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into biimp | |
| 16415 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into ax-1 | |
| 16416 | →↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16413, 16415 | |
| 16417 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜒↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into ax-2 | |
| 16418 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16416, 16417 | |
| 16419 | →↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16363, 16418 | |
| 16420 | →↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1 | |
| 16421 | ↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Modus ponens 16411, 16420 | |
| 16422 | →↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into biimp | |
| 16423 | →↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑 | Modus ponens 16421, 16422 | |
| 16424 | →↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into bicom1 | |
| 16425 | ↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16410, 16424 | |
| 16426 | →↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into biimp | |
| 16427 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into ax-1 | |
| 16428 | →↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16407, 16427 | |
| 16429 | →→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜒↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into ax-2 | |
| 16430 | →→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16428, 16429 | |
| 16431 | →↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16423, 16430 | |
| 16432 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into impbi | |
| 16433 | →→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16419, 16432 | |
| 16434 | ↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16431, 16433 | |
| 16435 | →↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into biimp | |
| 16436 | →↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into biimp | |
| 16437 | →↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16321, 16436 | |
| 16438 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into ax-1 | |
| 16439 | →↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16419, 16438 | |
| 16440 | →→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜒↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into ax-2 | |
| 16441 | →→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16439, 16440 | |
| 16442 | →↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16437, 16441 | |
| 16443 | →↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1 | |
| 16444 | ↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16434, 16443 | |
| 16445 | →↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into biimp | |
| 16446 | →↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into bicom1 | |
| 16447 | ↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16321, 16446 | |
| 16448 | →↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp | |
| 16449 | →↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16447, 16448 | |
| 16450 | →→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into ax-1 | |
| 16451 | →↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16449, 16450 | |
| 16452 | →→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜒↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into ax-2 | |
| 16453 | →→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16451, 16452 | |
| 16454 | →↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16431, 16453 | |
| 16455 | →→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into impbi | |
| 16456 | →→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16442, 16455 | |
| 16457 | ↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16454, 16456 | |
| 16458 | →↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into biimp | |
| 16459 | →↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp | |
| 16460 | →→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into ax-1 | |
| 16461 | →↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16442, 16460 | |
| 16462 | →→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into ax-2 | |
| 16463 | →→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16461, 16462 | |
| 16464 | →↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16273, 16463 | |
| 16465 | →↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1 | |
| 16466 | ↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16457, 16465 | |
| 16467 | →↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp | |
| 16468 | →↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1 | |
| 16469 | ↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Modus ponens 16320, 16468 | |
| 16470 | →↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into biimp | |
| 16471 | →→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into ax-1 | |
| 16472 | →↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Modus ponens 16317, 16471 | |
| 16473 | →→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into ax-2 | |
| 16474 | →→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Modus ponens 16472, 16473 | |
| 16475 | →↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Modus ponens 16454, 16474 | |
| 16476 | →→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into impbi | |
| 16477 | →→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16464, 16476 | |
| 16478 | ↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16475, 16477 | |
| 16479 | ↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗→𝜓↔𝜑𝜒, 𝜓↗↔𝜑⋀𝜓𝜒] into bicom | |
| 16480 | ↔↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜑, 𝜓↗𝜑, 𝜒↗⋀𝜓𝜒] into biluk | |
| 16481 | →↔↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑 | Subs [𝜑↗↔⋀𝜓𝜑𝜑, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1 | |
| 16482 | ↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑 | Modus ponens 16480, 16481 | |
| 16483 | →↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑 | Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into biimp | |
| 16484 | →↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑 | Modus ponens 16482, 16483 | |
| 16485 | →↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into biimp | |
| 16486 | →→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑 | Subs [𝜑↗→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into ax-1 | |
| 16487 | →↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑 | Modus ponens 16484, 16486 | |
| 16488 | →→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗↔⋀𝜓𝜑𝜑] into ax-2 | |
| 16489 | →→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑 | Modus ponens 16487, 16488 | |
| 16490 | →↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑 | Modus ponens 16464, 16489 | |
| 16491 | →↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into bicom1 | |
| 16492 | →↔↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Subs [𝜑↗↔⋀𝜓𝜑𝜑, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into biimp | |
| 16493 | →↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒 | Modus ponens 16480, 16492 | |
| 16494 | →↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1 | |
| 16495 | ↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Modus ponens 16478, 16494 | |
| 16496 | →↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into biimp | |
| 16497 | →→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔⋀𝜓𝜑𝜑→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into ax-1 | |
| 16498 | →↔⋀𝜓𝜑𝜑→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Modus ponens 16475, 16497 | |
| 16499 | →→↔⋀𝜓𝜑𝜑→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗↔⋀𝜓𝜑𝜑, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into ax-2 | |
| 16500 | →→↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Modus ponens 16498, 16499 | |
| 16501 | →↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Modus ponens 16493, 16500 | |
| 16502 | →→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑→→↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into impbi | |
| 16503 | →→↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑 | Modus ponens 16490, 16502 | |
| 16504 | ↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑 | Modus ponens 16501, 16503 | |
| 16505 | →↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into biimp | |
| 16506 | →↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into biimp | |
| 16507 | →↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Modus ponens 16479, 16506 | |
| 16508 | →→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into ax-1 | |
| 16509 | →↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑 | Modus ponens 16490, 16508 | |
| 16510 | →→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑 | Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜒↗↔⋀𝜓𝜑𝜑] into ax-2 | |
| 16511 | →→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑 | Modus ponens 16509, 16510 | |
| 16512 | →↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑 | Modus ponens 16507, 16511 | |
| 16513 | →↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into bicom1 | |
| 16514 | ↔↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Modus ponens 16504, 16513 | |
| 16515 | →↔↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒 | Subs [𝜑↗↔⋀𝜓𝜑𝜑, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into biimp | |
| 16516 | →↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into bicom1 | |
| 16517 | ↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16479, 16516 | |
| 16518 | →↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into biimp | |
| 16519 | →↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16517, 16518 | |
| 16520 | →→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔⋀𝜓𝜑𝜑→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into ax-1 | |
| 16521 | →↔⋀𝜓𝜑𝜑→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16519, 16520 | |
| 16522 | →→↔⋀𝜓𝜑𝜑→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔⋀𝜓𝜑𝜑, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜒↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into ax-2 | |
| 16523 | →→↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16521, 16522 | |
| 16524 | →↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16501, 16523 | |
| 16525 | →→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑→→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑 | Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into impbi | |
| 16526 | →→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑 | Modus ponens 16512, 16525 | |
| 16527 | ↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑 | Modus ponens 16524, 16526 | |
| 16528 | →↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into bicom1 | |
| 16529 | ↔↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16527, 16528 | |
| 16530 | →↔↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔⋀𝜓𝜑𝜑, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into biimp | |
| 16531 | →↔↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑𝜑 | Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗↔⋀𝜓𝜑𝜑] into biimp | |
| 16532 | →↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑𝜑 | Modus ponens 16230, 16531 | |
| 16533 | →→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜑→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜑] into ax-1 | |
| 16534 | →↔𝜑⋀𝜓𝜑→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16524, 16533 | |
| 16535 | →→↔𝜑⋀𝜓𝜑→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗↔⋀𝜓𝜑𝜑, 𝜒↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into ax-2 | |
| 16536 | →→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16534, 16535 | |
| 16537 | →↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16532, 16536 | |
| 16538 | →↔↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑 | Subs [𝜑↗↔⋀𝜓𝜑𝜑, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into bicom1 | |
| 16539 | →↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑 | Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into biimp | |
| 16540 | →↔↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑 | Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗↔⋀𝜓𝜑𝜑] into bicom1 | |
| 16541 | ↔↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑 | Modus ponens 16230, 16540 | |
| 16542 | →↔↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑→↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑 | Subs [𝜑↗↔⋀𝜓𝜑𝜑, 𝜓↗↔𝜑⋀𝜓𝜑] into biimp | |
| 16543 | →↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑 | Modus ponens 16541, 16542 | |
| 16544 | →→↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑 | Subs [𝜑↗→↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into ax-1 | |
| 16545 | →↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑 | Modus ponens 16543, 16544 | |
| 16546 | →→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑 | Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑𝜑, 𝜒↗↔𝜑⋀𝜓𝜑] into ax-2 | |
| 16547 | →→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑 | Modus ponens 16545, 16546 | |
| 16548 | →↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑 | Modus ponens 16512, 16547 | |
| 16549 | →→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑↔↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into impbi | |
| 16550 | →→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑↔↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16537, 16549 | |
| 16551 | ↔↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16548, 16550 | |
| 16552 | →↔↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into biimp | |
| 16553 | →↔→𝜑𝜓↔𝜑⋀𝜓𝜑→→𝜑𝜓↔𝜑⋀𝜓𝜑 | Subs [𝜑↗→𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑] into biimp | |
| 16554 | →→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→𝜑𝜓→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 16555 | →→𝜑𝜓→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16537, 16554 | |
| 16556 | →→→𝜑𝜓→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→→𝜑𝜓↔𝜑⋀𝜓𝜑→→𝜑𝜓↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑, 𝜒↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into ax-2 | |
| 16557 | →→→𝜑𝜓↔𝜑⋀𝜓𝜑→→𝜑𝜓↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16555, 16556 | |
| 16558 | →→𝜑𝜓↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 6441, 16557 | |
| 16559 | →↔↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑 | Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into bicom1 | |
| 16560 | ↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑 | Modus ponens 16551, 16559 | |
| 16561 | →↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑 | Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜑] into biimp | |
| 16562 | →↔→𝜑𝜓↔𝜑⋀𝜓𝜑↔↔𝜑⋀𝜓𝜑→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑] into bicom1 | |
| 16563 | ↔↔𝜑⋀𝜓𝜑→𝜑𝜓 | Modus ponens pm4.71r, 16562 | |
| 16564 | →↔↔𝜑⋀𝜓𝜑→𝜑𝜓→↔𝜑⋀𝜓𝜑→𝜑𝜓 | Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗→𝜑𝜓] into biimp | |
| 16565 | →→↔𝜑⋀𝜓𝜑→𝜑𝜓→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜑→𝜑𝜓 | Subs [𝜑↗→↔𝜑⋀𝜓𝜑→𝜑𝜓, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into ax-1 | |
| 16566 | →↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜑→𝜑𝜓 | Modus ponens 6452, 16565 | |
| 16567 | →→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜑→𝜑𝜓→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→𝜑𝜓 | Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜑, 𝜒↗→𝜑𝜓] into ax-2 | |
| 16568 | →→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→𝜑𝜓 | Modus ponens 16566, 16567 | |
| 16569 | →↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→𝜑𝜓 | Modus ponens 16548, 16568 | |
| 16570 | →→→𝜑𝜓↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→𝜑𝜓↔→𝜑𝜓↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into impbi | |
| 16571 | →→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→𝜑𝜓↔→𝜑𝜓↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16558, 16570 | |
| 16572 | ↔→𝜑𝜓↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒 | Modus ponens 16569, 16571 | biadan |
| 16573 | →↔𝜓↔𝜑𝜓→𝜓↔𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗↔𝜑𝜓] into biimp | |
| 16574 | →→↔𝜓↔𝜑𝜓→𝜓↔𝜑𝜓→𝜑→↔𝜓↔𝜑𝜓→𝜓↔𝜑𝜓 | Subs [𝜑↗→↔𝜓↔𝜑𝜓→𝜓↔𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 16575 | →𝜑→↔𝜓↔𝜑𝜓→𝜓↔𝜑𝜓 | Modus ponens 16573, 16574 | |
| 16576 | →→𝜑→↔𝜓↔𝜑𝜓→𝜓↔𝜑𝜓→→𝜑↔𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓 | Subs [𝜓↗↔𝜓↔𝜑𝜓, 𝜒↗→𝜓↔𝜑𝜓] into ax-2 | |
| 16577 | →→𝜑↔𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓 | Modus ponens 16575, 16576 | |
| 16578 | →→𝜑→𝜓↔𝜑𝜓→→𝜑𝜓→𝜑↔𝜑𝜓 | Subs [𝜒↗↔𝜑𝜓] into ax-2 | |
| 16579 | →→→𝜑𝜓→𝜑↔𝜑𝜓→¬¬𝜓→→𝜑𝜓→𝜑↔𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗¬¬𝜓] into ax-1 | |
| 16580 | →¬¬𝜓→→𝜑𝜓→𝜑↔𝜑𝜓 | Modus ponens 1697, 16579 | |
| 16581 | →→¬¬𝜓→→𝜑𝜓→𝜑↔𝜑𝜓→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑↔𝜑𝜓 | Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑↔𝜑𝜓] into ax-2 | |
| 16582 | →→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑↔𝜑𝜓 | Modus ponens 16580, 16581 | |
| 16583 | →¬¬𝜓→𝜑↔𝜑𝜓 | Modus ponens 575, 16582 | |
| 16584 | →→¬¬𝜓→𝜑↔𝜑𝜓→→¬¬𝜓𝜑→¬¬𝜓↔𝜑𝜓 | Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑, 𝜒↗↔𝜑𝜓] into ax-2 | |
| 16585 | →→¬¬𝜓𝜑→¬¬𝜓↔𝜑𝜓 | Modus ponens 16583, 16584 | |
| 16586 | →→→¬¬𝜓𝜑→¬¬𝜓↔𝜑𝜓→𝜑→→¬¬𝜓𝜑→¬¬𝜓↔𝜑𝜓 | Subs [𝜑↗→→¬¬𝜓𝜑→¬¬𝜓↔𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 16587 | →𝜑→→¬¬𝜓𝜑→¬¬𝜓↔𝜑𝜓 | Modus ponens 16585, 16586 | |
| 16588 | →→𝜑→→¬¬𝜓𝜑→¬¬𝜓↔𝜑𝜓→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓↔𝜑𝜓 | Subs [𝜓↗→¬¬𝜓𝜑, 𝜒↗→¬¬𝜓↔𝜑𝜓] into ax-2 | |
| 16589 | →→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓↔𝜑𝜓 | Modus ponens 16587, 16588 | |
| 16590 | →𝜑→¬¬𝜓↔𝜑𝜓 | Modus ponens 581, 16589 | |
| 16591 | →↔𝜑𝜓¬¬↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓] into notnot | |
| 16592 | →→↔𝜑𝜓¬¬↔𝜑𝜓→¬¬𝜓→↔𝜑𝜓¬¬↔𝜑𝜓 | Subs [𝜑↗→↔𝜑𝜓¬¬↔𝜑𝜓, 𝜓↗¬¬𝜓] into ax-1 | |
| 16593 | →¬¬𝜓→↔𝜑𝜓¬¬↔𝜑𝜓 | Modus ponens 16591, 16592 | |
| 16594 | →→¬¬𝜓→↔𝜑𝜓¬¬↔𝜑𝜓→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬↔𝜑𝜓 | Subs [𝜑↗¬¬𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗¬¬↔𝜑𝜓] into ax-2 | |
| 16595 | →→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬↔𝜑𝜓 | Modus ponens 16593, 16594 | |
| 16596 | →→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬↔𝜑𝜓→𝜑→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬↔𝜑𝜓 | Subs [𝜑↗→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬↔𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 16597 | →𝜑→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬↔𝜑𝜓 | Modus ponens 16595, 16596 | |
| 16598 | →→𝜑→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬↔𝜑𝜓→→𝜑→¬¬𝜓↔𝜑𝜓→𝜑→¬¬𝜓¬¬↔𝜑𝜓 | Subs [𝜓↗→¬¬𝜓↔𝜑𝜓, 𝜒↗→¬¬𝜓¬¬↔𝜑𝜓] into ax-2 | |
| 16599 | →→𝜑→¬¬𝜓↔𝜑𝜓→𝜑→¬¬𝜓¬¬↔𝜑𝜓 | Modus ponens 16597, 16598 | |
| 16600 | →𝜑→¬¬𝜓¬¬↔𝜑𝜓 | Modus ponens 16590, 16599 | |
| 16601 | →→¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-3 | |
| 16602 | →→→¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬𝜓→𝜑→→¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬𝜓 | Subs [𝜑↗→→¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 16603 | →𝜑→→¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬𝜓 | Modus ponens 16601, 16602 | |
| 16604 | →→𝜑→→¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬𝜓→→𝜑→¬¬𝜓¬¬↔𝜑𝜓→𝜑→¬↔𝜑𝜓¬𝜓 | Subs [𝜓↗→¬¬𝜓¬¬↔𝜑𝜓, 𝜒↗→¬↔𝜑𝜓¬𝜓] into ax-2 | |
| 16605 | →→𝜑→¬¬𝜓¬¬↔𝜑𝜓→𝜑→¬↔𝜑𝜓¬𝜓 | Modus ponens 16603, 16604 | |
| 16606 | →𝜑→¬↔𝜑𝜓¬𝜓 | Modus ponens 16600, 16605 | |
| 16607 | →¬↔𝜑𝜓¬↔𝜑𝜓 | Subs [𝜑↗¬↔𝜑𝜓] into id | |
| 16608 | →¬↔𝜑𝜓→𝜑¬↔𝜑𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 16609 | →→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓→¬↔𝜑𝜓→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓 | Subs [𝜑↗→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1 | |
| 16610 | →¬↔𝜑𝜓→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓 | Modus ponens 16608, 16609 | |
| 16611 | →→¬↔𝜑𝜓→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓→→¬↔𝜑𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓, 𝜒↗→𝜑¬↔𝜑𝜓] into ax-2 | |
| 16612 | →→¬↔𝜑𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓 | Modus ponens 16610, 16611 | |
| 16613 | →→𝜑→¬↔𝜑𝜓¬𝜓→→𝜑¬↔𝜑𝜓→𝜑¬𝜓 | Subs [𝜓↗¬↔𝜑𝜓, 𝜒↗¬𝜓] into ax-2 | |
| 16614 | →→𝜑¬↔𝜑𝜓→𝜑¬𝜓 | Modus ponens 16606, 16613 | |
| 16615 | →→→𝜑¬↔𝜑𝜓→𝜑¬𝜓→¬↔𝜑𝜓→→𝜑¬↔𝜑𝜓→𝜑¬𝜓 | Subs [𝜑↗→→𝜑¬↔𝜑𝜓→𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1 | |
| 16616 | →¬↔𝜑𝜓→→𝜑¬↔𝜑𝜓→𝜑¬𝜓 | Modus ponens 16614, 16615 | |
| 16617 | →→¬↔𝜑𝜓→→𝜑¬↔𝜑𝜓→𝜑¬𝜓→→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓→¬↔𝜑𝜓→𝜑¬𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→𝜑¬↔𝜑𝜓, 𝜒↗→𝜑¬𝜓] into ax-2 | |
| 16618 | →→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓→¬↔𝜑𝜓→𝜑¬𝜓 | Modus ponens 16616, 16617 | |
| 16619 | →¬↔𝜑𝜓→𝜑¬𝜓 | Modus ponens 16608, 16618 | |
| 16620 | →→¬→𝜑¬𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓→¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1 | |
| 16621 | →¬↔𝜑𝜓→¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 619, 16620 | |
| 16622 | →¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓 | Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1 | |
| 16623 | →→¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1 | |
| 16624 | →¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓 | Modus ponens 16622, 16623 | |
| 16625 | →→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓 | Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→¬↔𝜑𝜓¬→𝜑¬𝜓] into ax-2 | |
| 16626 | →→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓 | Modus ponens 16624, 16625 | |
| 16627 | →¬¬¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓 | Modus ponens 622, 16626 | |
| 16628 | →→¬↔𝜑𝜓→¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬↔𝜑𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗¬→𝜑¬𝜓] into ax-2 | |
| 16629 | →→¬↔𝜑𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓 | Modus ponens 16621, 16628 | |
| 16630 | →→→¬↔𝜑𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→→¬↔𝜑𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→→¬↔𝜑𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1 | |
| 16631 | →¬¬¬→𝜑¬𝜓→→¬↔𝜑𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓 | Modus ponens 16629, 16630 | |
| 16632 | →→¬¬¬→𝜑¬𝜓→→¬↔𝜑𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓 | Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗→¬↔𝜑𝜓¬→𝜑¬𝜓, 𝜒↗→¬↔𝜑𝜓¬→𝜑¬𝜓] into ax-2 | |
| 16633 | →→¬¬¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓 | Modus ponens 16631, 16632 | |
| 16634 | →¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1 | |
| 16635 | →→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓 | Subs [𝜑↗→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1 | |
| 16636 | →¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓 | Modus ponens 16634, 16635 | |
| 16637 | →→¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→→¬↔𝜑𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓, 𝜒↗→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓] into ax-2 | |
| 16638 | →→¬↔𝜑𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓 | Modus ponens 16636, 16637 | |
| 16639 | →→¬¬¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓, 𝜒↗¬→𝜑¬𝜓] into ax-2 | |
| 16640 | →→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 16627, 16639 | |
| 16641 | →→→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓→→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1 | |
| 16642 | →¬↔𝜑𝜓→→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 16640, 16641 | |
| 16643 | →→¬↔𝜑𝜓→→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓, 𝜒↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓] into ax-2 | |
| 16644 | →→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 16642, 16643 | |
| 16645 | →¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓 | Modus ponens 16634, 16644 | |
| 16646 | →→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→¬↔𝜑𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1 | |
| 16647 | →¬↔𝜑𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Modus ponens 647, 16646 | |
| 16648 | →→¬↔𝜑𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜒↗→→𝜑¬𝜓¬¬→𝜑¬𝜓] into ax-2 | |
| 16649 | →→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Modus ponens 16647, 16648 | |
| 16650 | →¬↔𝜑𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓 | Modus ponens 16645, 16649 | |
| 16651 | →→¬↔𝜑𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬↔𝜑𝜓→𝜑¬𝜓→¬↔𝜑𝜓¬¬→𝜑¬𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→𝜑¬𝜓, 𝜒↗¬¬→𝜑¬𝜓] into ax-2 | |
| 16652 | →→¬↔𝜑𝜓→𝜑¬𝜓→¬↔𝜑𝜓¬¬→𝜑¬𝜓 | Modus ponens 16650, 16651 | |
| 16653 | →¬↔𝜑𝜓¬¬→𝜑¬𝜓 | Modus ponens 16619, 16652 | |
| 16654 | →→¬↔𝜑𝜓¬¬→𝜑¬𝜓→¬→𝜑¬𝜓↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→𝜑¬𝜓] into ax-3 | |
| 16655 | →¬→𝜑¬𝜓↔𝜑𝜓 | Modus ponens 16653, 16654 | |
| 16656 | →→¬→𝜑¬𝜓↔𝜑𝜓→⋀𝜑𝜓→¬→𝜑¬𝜓↔𝜑𝜓 | Subs [𝜑↗→¬→𝜑¬𝜓↔𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 16657 | →⋀𝜑𝜓→¬→𝜑¬𝜓↔𝜑𝜓 | Modus ponens 16655, 16656 | |
| 16658 | →→⋀𝜑𝜓→¬→𝜑¬𝜓↔𝜑𝜓→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓↔𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗↔𝜑𝜓] into ax-2 | |
| 16659 | →→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓↔𝜑𝜓 | Modus ponens 16657, 16658 | |
| 16660 | →⋀𝜑𝜓↔𝜑𝜓 | Modus ponens 4842, 16659 | pm5.1 |
| 16661 | ↔⋀¬𝜑¬𝜓¬→¬𝜑¬¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓] into df-an | |
| 16662 | →¬¬¬𝜓¬𝜓 | Subs [𝜑↗¬𝜓] into notnotr | |
| 16663 | →¬𝜓→¬𝜑¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 16664 | →→¬𝜓→¬𝜑¬𝜓→¬¬¬𝜓→¬𝜓→¬𝜑¬𝜓 | Subs [𝜑↗→¬𝜓→¬𝜑¬𝜓, 𝜓↗¬¬¬𝜓] into ax-1 | |
| 16665 | →¬¬¬𝜓→¬𝜓→¬𝜑¬𝜓 | Modus ponens 16663, 16664 | |
| 16666 | →→¬¬¬𝜓→¬𝜓→¬𝜑¬𝜓→→¬¬¬𝜓¬𝜓→¬¬¬𝜓→¬𝜑¬𝜓 | Subs [𝜑↗¬¬¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬𝜑¬𝜓] into ax-2 | |
| 16667 | →→¬¬¬𝜓¬𝜓→¬¬¬𝜓→¬𝜑¬𝜓 | Modus ponens 16665, 16666 | |
| 16668 | →¬¬¬𝜓→¬𝜑¬𝜓 | Modus ponens 16662, 16667 | |
| 16669 | →→¬𝜑→¬𝜓↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓, 𝜒↗↔𝜑𝜓] into ax-2 | |
| 16670 | →→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬¬¬𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗¬¬¬𝜓] into ax-1 | |
| 16671 | →¬¬¬𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 3133, 16670 | |
| 16672 | →→¬¬¬𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→¬¬¬𝜓→¬𝜑¬𝜓→¬¬¬𝜓→¬𝜑↔𝜑𝜓 | Subs [𝜑↗¬¬¬𝜓, 𝜓↗→¬𝜑¬𝜓, 𝜒↗→¬𝜑↔𝜑𝜓] into ax-2 | |
| 16673 | →→¬¬¬𝜓→¬𝜑¬𝜓→¬¬¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 16671, 16672 | |
| 16674 | →¬¬¬𝜓→¬𝜑↔𝜑𝜓 | Modus ponens 16668, 16673 | |
| 16675 | →¬𝜑→¬¬¬𝜓¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬𝜓] into ax-1 | |
| 16676 | →→¬𝜑→¬¬¬𝜓¬𝜑→¬𝜑→¬𝜑→¬¬¬𝜓¬𝜑 | Subs [𝜑↗→¬𝜑→¬¬¬𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1 | |
| 16677 | →¬𝜑→¬𝜑→¬¬¬𝜓¬𝜑 | Modus ponens 16675, 16676 | |
| 16678 | →→¬𝜑→¬𝜑→¬¬¬𝜓¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬𝜓¬𝜑 | Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬𝜓¬𝜑] into ax-2 | |
| 16679 | →→¬𝜑¬𝜑→¬𝜑→¬¬¬𝜓¬𝜑 | Modus ponens 16677, 16678 | |
| 16680 | →→¬¬¬𝜓→¬𝜑↔𝜑𝜓→→¬¬¬𝜓¬𝜑→¬¬¬𝜓↔𝜑𝜓 | Subs [𝜑↗¬¬¬𝜓, 𝜓↗¬𝜑, 𝜒↗↔𝜑𝜓] into ax-2 | |
| 16681 | →→¬¬¬𝜓¬𝜑→¬¬¬𝜓↔𝜑𝜓 | Modus ponens 16674, 16680 | |
| 16682 | →→→¬¬¬𝜓¬𝜑→¬¬¬𝜓↔𝜑𝜓→¬𝜑→→¬¬¬𝜓¬𝜑→¬¬¬𝜓↔𝜑𝜓 | Subs [𝜑↗→→¬¬¬𝜓¬𝜑→¬¬¬𝜓↔𝜑𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 16683 | →¬𝜑→→¬¬¬𝜓¬𝜑→¬¬¬𝜓↔𝜑𝜓 | Modus ponens 16681, 16682 | |
| 16684 | →→¬𝜑→→¬¬¬𝜓¬𝜑→¬¬¬𝜓↔𝜑𝜓→→¬𝜑→¬¬¬𝜓¬𝜑→¬𝜑→¬¬¬𝜓↔𝜑𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬𝜓¬𝜑, 𝜒↗→¬¬¬𝜓↔𝜑𝜓] into ax-2 | |
| 16685 | →→¬𝜑→¬¬¬𝜓¬𝜑→¬𝜑→¬¬¬𝜓↔𝜑𝜓 | Modus ponens 16683, 16684 | |
| 16686 | →¬𝜑→¬¬¬𝜓↔𝜑𝜓 | Modus ponens 16675, 16685 | |
| 16687 | →→↔𝜑𝜓¬¬↔𝜑𝜓→¬¬¬𝜓→↔𝜑𝜓¬¬↔𝜑𝜓 | Subs [𝜑↗→↔𝜑𝜓¬¬↔𝜑𝜓, 𝜓↗¬¬¬𝜓] into ax-1 | |
| 16688 | →¬¬¬𝜓→↔𝜑𝜓¬¬↔𝜑𝜓 | Modus ponens 16591, 16687 | |
| 16689 | →→¬¬¬𝜓→↔𝜑𝜓¬¬↔𝜑𝜓→→¬¬¬𝜓↔𝜑𝜓→¬¬¬𝜓¬¬↔𝜑𝜓 | Subs [𝜑↗¬¬¬𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗¬¬↔𝜑𝜓] into ax-2 | |
| 16690 | →→¬¬¬𝜓↔𝜑𝜓→¬¬¬𝜓¬¬↔𝜑𝜓 | Modus ponens 16688, 16689 | |
| 16691 | →→→¬¬¬𝜓↔𝜑𝜓→¬¬¬𝜓¬¬↔𝜑𝜓→¬𝜑→→¬¬¬𝜓↔𝜑𝜓→¬¬¬𝜓¬¬↔𝜑𝜓 | Subs [𝜑↗→→¬¬¬𝜓↔𝜑𝜓→¬¬¬𝜓¬¬↔𝜑𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 16692 | →¬𝜑→→¬¬¬𝜓↔𝜑𝜓→¬¬¬𝜓¬¬↔𝜑𝜓 | Modus ponens 16690, 16691 | |
| 16693 | →→¬𝜑→→¬¬¬𝜓↔𝜑𝜓→¬¬¬𝜓¬¬↔𝜑𝜓→→¬𝜑→¬¬¬𝜓↔𝜑𝜓→¬𝜑→¬¬¬𝜓¬¬↔𝜑𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬𝜓↔𝜑𝜓, 𝜒↗→¬¬¬𝜓¬¬↔𝜑𝜓] into ax-2 | |
| 16694 | →→¬𝜑→¬¬¬𝜓↔𝜑𝜓→¬𝜑→¬¬¬𝜓¬¬↔𝜑𝜓 | Modus ponens 16692, 16693 | |
| 16695 | →¬𝜑→¬¬¬𝜓¬¬↔𝜑𝜓 | Modus ponens 16686, 16694 | |
| 16696 | →→¬¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬¬𝜓 | Subs [𝜑↗¬¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-3 | |
| 16697 | →→→¬¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬¬𝜓→¬𝜑→→¬¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬¬𝜓 | Subs [𝜑↗→→¬¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬¬𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 16698 | →¬𝜑→→¬¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬¬𝜓 | Modus ponens 16696, 16697 | |
| 16699 | →→¬𝜑→→¬¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬¬𝜓→→¬𝜑→¬¬¬𝜓¬¬↔𝜑𝜓→¬𝜑→¬↔𝜑𝜓¬¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬𝜓¬¬↔𝜑𝜓, 𝜒↗→¬↔𝜑𝜓¬¬𝜓] into ax-2 | |
| 16700 | →→¬𝜑→¬¬¬𝜓¬¬↔𝜑𝜓→¬𝜑→¬↔𝜑𝜓¬¬𝜓 | Modus ponens 16698, 16699 | |
| 16701 | →¬𝜑→¬↔𝜑𝜓¬¬𝜓 | Modus ponens 16695, 16700 | |
| 16702 | →¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬𝜑] into ax-1 | |
| 16703 | →→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓→¬↔𝜑𝜓→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓 | Subs [𝜑↗→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1 | |
| 16704 | →¬↔𝜑𝜓→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓 | Modus ponens 16702, 16703 | |
| 16705 | →→¬↔𝜑𝜓→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓→→¬↔𝜑𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓, 𝜒↗→¬𝜑¬↔𝜑𝜓] into ax-2 | |
| 16706 | →→¬↔𝜑𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓 | Modus ponens 16704, 16705 | |
| 16707 | →→¬𝜑→¬↔𝜑𝜓¬¬𝜓→→¬𝜑¬↔𝜑𝜓→¬𝜑¬¬𝜓 | Subs [𝜑↗¬𝜑, 𝜓↗¬↔𝜑𝜓, 𝜒↗¬¬𝜓] into ax-2 | |
| 16708 | →→¬𝜑¬↔𝜑𝜓→¬𝜑¬¬𝜓 | Modus ponens 16701, 16707 | |
| 16709 | →→→¬𝜑¬↔𝜑𝜓→¬𝜑¬¬𝜓→¬↔𝜑𝜓→→¬𝜑¬↔𝜑𝜓→¬𝜑¬¬𝜓 | Subs [𝜑↗→→¬𝜑¬↔𝜑𝜓→¬𝜑¬¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1 | |
| 16710 | →¬↔𝜑𝜓→→¬𝜑¬↔𝜑𝜓→¬𝜑¬¬𝜓 | Modus ponens 16708, 16709 | |
| 16711 | →→¬↔𝜑𝜓→→¬𝜑¬↔𝜑𝜓→¬𝜑¬¬𝜓→→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓→¬↔𝜑𝜓→¬𝜑¬¬𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→¬𝜑¬↔𝜑𝜓, 𝜒↗→¬𝜑¬¬𝜓] into ax-2 | |
| 16712 | →→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓→¬↔𝜑𝜓→¬𝜑¬¬𝜓 | Modus ponens 16710, 16711 | |
| 16713 | →¬↔𝜑𝜓→¬𝜑¬¬𝜓 | Modus ponens 16702, 16712 | |
| 16714 | →¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓 | Subs [𝜑↗¬→¬𝜑¬¬𝜓] into id | |
| 16715 | →→¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓→¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓 | Subs [𝜑↗→¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1 | |
| 16716 | →¬↔𝜑𝜓→¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓 | Modus ponens 16714, 16715 | |
| 16717 | →¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓 | Subs [𝜑↗¬→¬𝜑¬¬𝜓] into notnotr | |
| 16718 | →¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓 | Subs [𝜑↗¬→¬𝜑¬¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1 | |
| 16719 | →→¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬¬¬→¬𝜑¬¬𝜓→¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓 | Subs [𝜑↗→¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓, 𝜓↗¬¬¬→¬𝜑¬¬𝜓] into ax-1 | |
| 16720 | →¬¬¬→¬𝜑¬¬𝜓→¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓 | Modus ponens 16718, 16719 | |
| 16721 | →→¬¬¬→¬𝜑¬¬𝜓→¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→¬¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓 | Subs [𝜑↗¬¬¬→¬𝜑¬¬𝜓, 𝜓↗¬→¬𝜑¬¬𝜓, 𝜒↗→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓] into ax-2 | |
| 16722 | →→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→¬¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓 | Modus ponens 16720, 16721 | |
| 16723 | →¬¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓 | Modus ponens 16717, 16722 | |
| 16724 | →→¬↔𝜑𝜓→¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬→¬𝜑¬¬𝜓, 𝜒↗¬→¬𝜑¬¬𝜓] into ax-2 | |
| 16725 | →→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓 | Modus ponens 16716, 16724 | |
| 16726 | →→→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬¬¬→¬𝜑¬¬𝜓→→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓 | Subs [𝜑↗→→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓, 𝜓↗¬¬¬→¬𝜑¬¬𝜓] into ax-1 | |
| 16727 | →¬¬¬→¬𝜑¬¬𝜓→→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓 | Modus ponens 16725, 16726 | |
| 16728 | →→¬¬¬→¬𝜑¬¬𝜓→→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→→¬¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓 | Subs [𝜑↗¬¬¬→¬𝜑¬¬𝜓, 𝜓↗→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓, 𝜒↗→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓] into ax-2 | |
| 16729 | →→¬¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓 | Modus ponens 16727, 16728 | |
| 16730 | →¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬¬¬→¬𝜑¬¬𝜓] into ax-1 | |
| 16731 | →→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓 | Subs [𝜑↗→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1 | |
| 16732 | →¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓 | Modus ponens 16730, 16731 | |
| 16733 | →→¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→→¬↔𝜑𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓, 𝜒↗→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓] into ax-2 | |
| 16734 | →→¬↔𝜑𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓 | Modus ponens 16732, 16733 | |
| 16735 | →→¬¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓 | Subs [𝜑↗¬¬¬→¬𝜑¬¬𝜓, 𝜓↗¬↔𝜑𝜓, 𝜒↗¬→¬𝜑¬¬𝜓] into ax-2 | |
| 16736 | →→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓 | Modus ponens 16723, 16735 | |
| 16737 | →→→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓→→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓 | Subs [𝜑↗→→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1 | |
| 16738 | →¬↔𝜑𝜓→→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓 | Modus ponens 16736, 16737 | |
| 16739 | →→¬↔𝜑𝜓→→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓, 𝜒↗→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓] into ax-2 | |
| 16740 | →→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓 | Modus ponens 16738, 16739 | |
| 16741 | →¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓 | Modus ponens 16730, 16740 | |
| 16742 | →→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓 | Subs [𝜑↗¬¬→¬𝜑¬¬𝜓, 𝜓↗→¬𝜑¬¬𝜓] into ax-3 | |
| 16743 | →→→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓→→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓 | Subs [𝜑↗→→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1 | |
| 16744 | →¬↔𝜑𝜓→→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓 | Modus ponens 16742, 16743 | |
| 16745 | →→¬↔𝜑𝜓→→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓→→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓, 𝜒↗→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓] into ax-2 | |
| 16746 | →→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓 | Modus ponens 16744, 16745 | |
| 16747 | →¬↔𝜑𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓 | Modus ponens 16741, 16746 | |
| 16748 | →→¬↔𝜑𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓→→¬↔𝜑𝜓→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬¬→¬𝜑¬¬𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→¬𝜑¬¬𝜓, 𝜒↗¬¬→¬𝜑¬¬𝜓] into ax-2 | |
| 16749 | →→¬↔𝜑𝜓→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬¬→¬𝜑¬¬𝜓 | Modus ponens 16747, 16748 | |
| 16750 | →¬↔𝜑𝜓¬¬→¬𝜑¬¬𝜓 | Modus ponens 16713, 16749 | |
| 16751 | →→¬↔𝜑𝜓¬¬→¬𝜑¬¬𝜓→¬→¬𝜑¬¬𝜓↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→¬𝜑¬¬𝜓] into ax-3 | |
| 16752 | →¬→¬𝜑¬¬𝜓↔𝜑𝜓 | Modus ponens 16750, 16751 | |
| 16753 | →↔⋀¬𝜑¬𝜓¬→¬𝜑¬¬𝜓→⋀¬𝜑¬𝜓¬→¬𝜑¬¬𝜓 | Subs [𝜑↗⋀¬𝜑¬𝜓, 𝜓↗¬→¬𝜑¬¬𝜓] into biimp | |
| 16754 | →⋀¬𝜑¬𝜓¬→¬𝜑¬¬𝜓 | Modus ponens 16661, 16753 | |
| 16755 | →→¬→¬𝜑¬¬𝜓↔𝜑𝜓→⋀¬𝜑¬𝜓→¬→¬𝜑¬¬𝜓↔𝜑𝜓 | Subs [𝜑↗→¬→¬𝜑¬¬𝜓↔𝜑𝜓, 𝜓↗⋀¬𝜑¬𝜓] into ax-1 | |
| 16756 | →⋀¬𝜑¬𝜓→¬→¬𝜑¬¬𝜓↔𝜑𝜓 | Modus ponens 16752, 16755 | |
| 16757 | →→⋀¬𝜑¬𝜓→¬→¬𝜑¬¬𝜓↔𝜑𝜓→→⋀¬𝜑¬𝜓¬→¬𝜑¬¬𝜓→⋀¬𝜑¬𝜓↔𝜑𝜓 | Subs [𝜑↗⋀¬𝜑¬𝜓, 𝜓↗¬→¬𝜑¬¬𝜓, 𝜒↗↔𝜑𝜓] into ax-2 | |
| 16758 | →→⋀¬𝜑¬𝜓¬→¬𝜑¬¬𝜓→⋀¬𝜑¬𝜓↔𝜑𝜓 | Modus ponens 16756, 16757 | |
| 16759 | →⋀¬𝜑¬𝜓↔𝜑𝜓 | Modus ponens 16754, 16758 | pm5.21 |
| 16760 | →⋀→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒] into pm5.1 | |
| 16761 | →→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒→⋀→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒 | Subs [𝜑↗→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒, 𝜓↗⋀→𝜑𝜓→𝜑𝜒] into ax-1 | |
| 16762 | →⋀→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒 | Modus ponens 1905, 16761 | |
| 16763 | →→⋀→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒→→⋀→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→⋀→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒 | Subs [𝜑↗⋀→𝜑𝜓→𝜑𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜑↔𝜓𝜒] into ax-2 | |
| 16764 | →→⋀→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→⋀→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒 | Modus ponens 16762, 16763 | |
| 16765 | →⋀→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒 | Modus ponens 16760, 16764 | pm5.35 |
| 16766 | ↔→𝜑↔𝜓→𝜑𝜓↔⋀𝜑𝜓⋀𝜑→𝜑𝜓 | Subs [𝜒↗→𝜑𝜓] into pm5.32 | |
| 16767 | →↔→𝜑↔𝜓→𝜑𝜓↔⋀𝜑𝜓⋀𝜑→𝜑𝜓→→𝜑↔𝜓→𝜑𝜓↔⋀𝜑𝜓⋀𝜑→𝜑𝜓 | Subs [𝜑↗→𝜑↔𝜓→𝜑𝜓, 𝜓↗↔⋀𝜑𝜓⋀𝜑→𝜑𝜓] into biimp | |
| 16768 | →→𝜑↔𝜓→𝜑𝜓↔⋀𝜑𝜓⋀𝜑→𝜑𝜓 | Modus ponens 16766, 16767 | |
| 16769 | ↔⋀𝜑𝜓⋀𝜑→𝜑𝜓 | Modus ponens biimt, 16768 | abai |
| 16770 | ↔→𝜑→𝜓𝜑↔𝜑⋀𝜑→𝜓𝜑 | Subs [𝜓↗→𝜓𝜑] into pm4.71 | |
| 16771 | →↔→𝜑→𝜓𝜑↔𝜑⋀𝜑→𝜓𝜑→→𝜑→𝜓𝜑↔𝜑⋀𝜑→𝜓𝜑 | Subs [𝜑↗→𝜑→𝜓𝜑, 𝜓↗↔𝜑⋀𝜑→𝜓𝜑] into biimp | |
| 16772 | →→𝜑→𝜓𝜑↔𝜑⋀𝜑→𝜓𝜑 | Modus ponens 16770, 16771 | |
| 16773 | ↔𝜑⋀𝜑→𝜓𝜑 | Modus ponens ax-1, 16772 | pm4.45im |
| 16774 | →⋀→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜑] into pm5.1 | |
| 16775 | →↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀→𝜑𝜓→𝜓𝜑] into biimp | |
| 16776 | →→⋀→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑→↔𝜑𝜓→⋀→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗→⋀→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1 | |
| 16777 | →↔𝜑𝜓→⋀→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑 | Modus ponens 16774, 16776 | |
| 16778 | →→↔𝜑𝜓→⋀→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑→→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀→𝜑𝜓→𝜓𝜑, 𝜒↗↔→𝜑𝜓→𝜓𝜑] into ax-2 | |
| 16779 | →→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔→𝜑𝜓→𝜓𝜑 | Modus ponens 16777, 16778 | |
| 16780 | →↔𝜑𝜓↔→𝜑𝜓→𝜓𝜑 | Modus ponens 5712, 16779 | |
| 16781 | →→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑 | Subs [𝜑↗→𝜓𝜑, 𝜓↗¬↔𝜑𝜓] into ax-1 | |
| 16782 | →→→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑→¬→𝜑𝜓→→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑 | Subs [𝜑↗→→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 16783 | →¬→𝜑𝜓→→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑 | Modus ponens 16781, 16782 | |
| 16784 | →→¬→𝜑𝜓→→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑→→¬→𝜑𝜓→𝜓𝜑→¬→𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→𝜓𝜑, 𝜒↗→¬↔𝜑𝜓→𝜓𝜑] into ax-2 | |
| 16785 | →→¬→𝜑𝜓→𝜓𝜑→¬→𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑 | Modus ponens 16783, 16784 | |
| 16786 | →¬→𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑 | Modus ponens pm2.521, 16785 | |
| 16787 | →→𝜓𝜑¬¬→𝜓𝜑 | Subs [𝜑↗→𝜓𝜑] into notnot | |
| 16788 | →→→𝜓𝜑¬¬→𝜓𝜑→¬↔𝜑𝜓→→𝜓𝜑¬¬→𝜓𝜑 | Subs [𝜑↗→→𝜓𝜑¬¬→𝜓𝜑, 𝜓↗¬↔𝜑𝜓] into ax-1 | |
| 16789 | →¬↔𝜑𝜓→→𝜓𝜑¬¬→𝜓𝜑 | Modus ponens 16787, 16788 | |
| 16790 | →→¬↔𝜑𝜓→→𝜓𝜑¬¬→𝜓𝜑→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬¬→𝜓𝜑 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→𝜓𝜑, 𝜒↗¬¬→𝜓𝜑] into ax-2 | |
| 16791 | →→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬¬→𝜓𝜑 | Modus ponens 16789, 16790 | |
| 16792 | →→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬¬→𝜓𝜑 | Subs [𝜑↗→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬¬→𝜓𝜑, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 16793 | →¬→𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬¬→𝜓𝜑 | Modus ponens 16791, 16792 | |
| 16794 | →→¬→𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬¬→𝜓𝜑→→¬→𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑→¬→𝜑𝜓→¬↔𝜑𝜓¬¬→𝜓𝜑 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬↔𝜑𝜓→𝜓𝜑, 𝜒↗→¬↔𝜑𝜓¬¬→𝜓𝜑] into ax-2 | |
| 16795 | →→¬→𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑→¬→𝜑𝜓→¬↔𝜑𝜓¬¬→𝜓𝜑 | Modus ponens 16793, 16794 | |
| 16796 | →¬→𝜑𝜓→¬↔𝜑𝜓¬¬→𝜓𝜑 | Modus ponens 16786, 16795 | |
| 16797 | →→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→𝜓𝜑] into ax-3 | |
| 16798 | →→→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓→¬→𝜑𝜓→→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 16799 | →¬→𝜑𝜓→→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 16797, 16798 | |
| 16800 | →→¬→𝜑𝜓→→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓→→¬→𝜑𝜓→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬↔𝜑𝜓¬¬→𝜓𝜑, 𝜒↗→¬→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 16801 | →→¬→𝜑𝜓→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 16799, 16800 | |
| 16802 | →¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 16796, 16801 | |
| 16803 | →↔→𝜑𝜓→𝜓𝜑→→𝜓𝜑→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜑] into biimpr | |
| 16804 | →→→𝜓𝜑→→𝜑𝜓→𝜓𝜑→→𝜓𝜑→→𝜓𝜑→→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗→→𝜓𝜑→→𝜑𝜓→𝜓𝜑, 𝜓↗→𝜓𝜑] into ax-1 | |
| 16805 | →→𝜓𝜑→→𝜓𝜑→→𝜑𝜓→𝜓𝜑 | Modus ponens 1674, 16804 | |
| 16806 | →→→𝜓𝜑→→𝜓𝜑→→𝜑𝜓→𝜓𝜑→→→𝜓𝜑→𝜓𝜑→→𝜓𝜑→→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗→𝜓𝜑, 𝜓↗→𝜓𝜑, 𝜒↗→→𝜑𝜓→𝜓𝜑] into ax-2 | |
| 16807 | →→→𝜓𝜑→𝜓𝜑→→𝜓𝜑→→𝜑𝜓→𝜓𝜑 | Modus ponens 16805, 16806 | |
| 16808 | →→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓→→𝜓𝜑→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓 | Subs [𝜑↗→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓, 𝜓↗→𝜓𝜑] into ax-1 | |
| 16809 | →→𝜓𝜑→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓 | Modus ponens 1681, 16808 | |
| 16810 | →→→𝜓𝜑→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓→→→𝜓𝜑→→𝜑𝜓→𝜓𝜑→→𝜓𝜑→→𝜑𝜓↔𝜑𝜓 | Subs [𝜑↗→𝜓𝜑, 𝜓↗→→𝜑𝜓→𝜓𝜑, 𝜒↗→→𝜑𝜓↔𝜑𝜓] into ax-2 | |
| 16811 | →→→𝜓𝜑→→𝜑𝜓→𝜓𝜑→→𝜓𝜑→→𝜑𝜓↔𝜑𝜓 | Modus ponens 16809, 16810 | |
| 16812 | →→𝜓𝜑→→𝜑𝜓↔𝜑𝜓 | Modus ponens 1674, 16811 | |
| 16813 | →→→𝜓𝜑→→𝜑𝜓↔𝜑𝜓→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→𝜓𝜑, 𝜓↗→𝜑𝜓, 𝜒↗↔𝜑𝜓] into ax-2 | |
| 16814 | →→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜑𝜓 | Modus ponens 16812, 16813 | |
| 16815 | →→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1 | |
| 16816 | →↔→𝜑𝜓→𝜓𝜑→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜑𝜓 | Modus ponens 16814, 16815 | |
| 16817 | →→↔→𝜑𝜓→𝜓𝜑→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→→𝜓𝜑→𝜑𝜓, 𝜒↗→→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 16818 | →→↔→𝜑𝜓→𝜓𝜑→→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→𝜓𝜑↔𝜑𝜓 | Modus ponens 16816, 16817 | |
| 16819 | →↔→𝜑𝜓→𝜓𝜑→→𝜓𝜑↔𝜑𝜓 | Modus ponens 16803, 16818 | |
| 16820 | →↔→𝜑𝜓→𝜓𝜑→→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜑] into biimp | |
| 16821 | →→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1 | |
| 16822 | →→→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→¬¬→𝜑𝜓→→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1 | |
| 16823 | →¬¬→𝜑𝜓→→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓 | Modus ponens 16821, 16822 | |
| 16824 | →→¬¬→𝜑𝜓→→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓 | Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓] into ax-2 | |
| 16825 | →→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓 | Modus ponens 16823, 16824 | |
| 16826 | →¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓 | Modus ponens 532, 16825 | |
| 16827 | →→↔→𝜑𝜓→𝜓𝜑→→𝜑𝜓→𝜓𝜑→→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑 | Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→𝜑𝜓, 𝜒↗→𝜓𝜑] into ax-2 | |
| 16828 | →→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑 | Modus ponens 16820, 16827 | |
| 16829 | →→→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑→¬¬→𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑 | Subs [𝜑↗→→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑, 𝜓↗¬¬→𝜑𝜓] into ax-1 | |
| 16830 | →¬¬→𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑 | Modus ponens 16828, 16829 | |
| 16831 | →→¬¬→𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑→→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑 | Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓, 𝜒↗→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑] into ax-2 | |
| 16832 | →→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑 | Modus ponens 16830, 16831 | |
| 16833 | →¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑 | Modus ponens 16826, 16832 | |
| 16834 | →↔→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑] into id | |
| 16835 | →↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗¬¬→𝜑𝜓] into ax-1 | |
| 16836 | →→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1 | |
| 16837 | →↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑 | Modus ponens 16835, 16836 | |
| 16838 | →→↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→→↔→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜓𝜑, 𝜒↗→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑] into ax-2 | |
| 16839 | →→↔→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑 | Modus ponens 16837, 16838 | |
| 16840 | →→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑→→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑, 𝜒↗→𝜓𝜑] into ax-2 | |
| 16841 | →→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑 | Modus ponens 16833, 16840 | |
| 16842 | →→→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗→→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1 | |
| 16843 | →↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑 | Modus ponens 16841, 16842 | |
| 16844 | →→↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑→→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑, 𝜒↗→¬¬→𝜑𝜓→𝜓𝜑] into ax-2 | |
| 16845 | →→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑 | Modus ponens 16843, 16844 | |
| 16846 | →↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑 | Modus ponens 16835, 16845 | |
| 16847 | →→→𝜓𝜑¬¬→𝜓𝜑→¬¬→𝜑𝜓→→𝜓𝜑¬¬→𝜓𝜑 | Subs [𝜑↗→→𝜓𝜑¬¬→𝜓𝜑, 𝜓↗¬¬→𝜑𝜓] into ax-1 | |
| 16848 | →¬¬→𝜑𝜓→→𝜓𝜑¬¬→𝜓𝜑 | Modus ponens 16787, 16847 | |
| 16849 | →→¬¬→𝜑𝜓→→𝜓𝜑¬¬→𝜓𝜑→→¬¬→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑 | Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜓𝜑, 𝜒↗¬¬→𝜓𝜑] into ax-2 | |
| 16850 | →→¬¬→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑 | Modus ponens 16848, 16849 | |
| 16851 | →→→¬¬→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑 | Subs [𝜑↗→→¬¬→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1 | |
| 16852 | →↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑 | Modus ponens 16850, 16851 | |
| 16853 | →→↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑→→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑 | Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬¬→𝜑𝜓→𝜓𝜑, 𝜒↗→¬¬→𝜑𝜓¬¬→𝜓𝜑] into ax-2 | |
| 16854 | →→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑 | Modus ponens 16852, 16853 | |
| 16855 | →↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑 | Modus ponens 16846, 16854 | |
| 16856 | →→¬¬→𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜓𝜑] into ax-3 | |
| 16857 | →→→¬¬→𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓 | Subs [𝜑↗→→¬¬→𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1 | |
| 16858 | →↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓 | Modus ponens 16856, 16857 | |
| 16859 | →→↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬¬→𝜑𝜓¬¬→𝜓𝜑, 𝜒↗→¬→𝜓𝜑¬→𝜑𝜓] into ax-2 | |
| 16860 | →→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓 | Modus ponens 16858, 16859 | |
| 16861 | →↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓 | Modus ponens 16855, 16860 | |
| 16862 | →¬→𝜓𝜑¬→𝜓𝜑 | Subs [𝜑↗¬→𝜓𝜑] into id | |
| 16863 | →¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬→𝜓𝜑, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 16864 | →→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜓𝜑→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→𝜓𝜑] into ax-1 | |
| 16865 | →¬→𝜓𝜑→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑 | Modus ponens 16863, 16864 | |
| 16866 | →→¬→𝜓𝜑→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑→→¬→𝜓𝜑¬→𝜓𝜑→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑 | Subs [𝜑↗¬→𝜓𝜑, 𝜓↗¬→𝜓𝜑, 𝜒↗→¬→𝜑𝜓¬→𝜓𝜑] into ax-2 | |
| 16867 | →→¬→𝜓𝜑¬→𝜓𝜑→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑 | Modus ponens 16865, 16866 | |
| 16868 | →→¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓→→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜓𝜑, 𝜒↗↔𝜑𝜓] into ax-2 | |
| 16869 | →→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓 | Modus ponens 16802, 16868 | |
| 16870 | →→→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓→¬→𝜓𝜑→→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓 | Subs [𝜑↗→→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓, 𝜓↗¬→𝜓𝜑] into ax-1 | |
| 16871 | →¬→𝜓𝜑→→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓 | Modus ponens 16869, 16870 | |
| 16872 | →→¬→𝜓𝜑→→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓→→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓 | Subs [𝜑↗¬→𝜓𝜑, 𝜓↗→¬→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬→𝜑𝜓↔𝜑𝜓] into ax-2 | |
| 16873 | →→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓 | Modus ponens 16871, 16872 | |
| 16874 | →¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓 | Modus ponens 16863, 16873 | |
| 16875 | →→¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓→→¬→𝜓𝜑¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗¬→𝜓𝜑, 𝜓↗¬→𝜑𝜓, 𝜒↗↔𝜑𝜓] into ax-2 | |
| 16876 | →→¬→𝜓𝜑¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 16874, 16875 | |
| 16877 | →→→¬→𝜓𝜑¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→¬→𝜓𝜑¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1 | |
| 16878 | →↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 16876, 16877 | |
| 16879 | →→↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬→𝜓𝜑¬→𝜑𝜓, 𝜒↗→¬→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 16880 | →→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 16878, 16879 | |
| 16881 | →↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓 | Modus ponens 16861, 16880 | |
| 16882 | →→↔𝜑𝜓¬¬↔𝜑𝜓→¬→𝜓𝜑→↔𝜑𝜓¬¬↔𝜑𝜓 | Subs [𝜑↗→↔𝜑𝜓¬¬↔𝜑𝜓, 𝜓↗¬→𝜓𝜑] into ax-1 | |
| 16883 | →¬→𝜓𝜑→↔𝜑𝜓¬¬↔𝜑𝜓 | Modus ponens 16591, 16882 | |
| 16884 | →→¬→𝜓𝜑→↔𝜑𝜓¬¬↔𝜑𝜓→→¬→𝜓𝜑↔𝜑𝜓→¬→𝜓𝜑¬¬↔𝜑𝜓 | Subs [𝜑↗¬→𝜓𝜑, 𝜓↗↔𝜑𝜓, 𝜒↗¬¬↔𝜑𝜓] into ax-2 | |
| 16885 | →→¬→𝜓𝜑↔𝜑𝜓→¬→𝜓𝜑¬¬↔𝜑𝜓 | Modus ponens 16883, 16884 | |
| 16886 | →→→¬→𝜓𝜑↔𝜑𝜓→¬→𝜓𝜑¬¬↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑↔𝜑𝜓→¬→𝜓𝜑¬¬↔𝜑𝜓 | Subs [𝜑↗→→¬→𝜓𝜑↔𝜑𝜓→¬→𝜓𝜑¬¬↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1 | |
| 16887 | →↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑↔𝜑𝜓→¬→𝜓𝜑¬¬↔𝜑𝜓 | Modus ponens 16885, 16886 | |
| 16888 | →→↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑↔𝜑𝜓→¬→𝜓𝜑¬¬↔𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬¬↔𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬→𝜓𝜑¬¬↔𝜑𝜓] into ax-2 | |
| 16889 | →→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬¬↔𝜑𝜓 | Modus ponens 16887, 16888 | |
| 16890 | →↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬¬↔𝜑𝜓 | Modus ponens 16881, 16889 | |
| 16891 | →→¬→𝜓𝜑¬¬↔𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑 | Subs [𝜑↗→𝜓𝜑, 𝜓↗¬↔𝜑𝜓] into ax-3 | |
| 16892 | →→→¬→𝜓𝜑¬¬↔𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑¬¬↔𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑 | Subs [𝜑↗→→¬→𝜓𝜑¬¬↔𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1 | |
| 16893 | →↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑¬¬↔𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑 | Modus ponens 16891, 16892 | |
| 16894 | →→↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑¬¬↔𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑→→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬¬↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑 | Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬→𝜓𝜑¬¬↔𝜑𝜓, 𝜒↗→¬↔𝜑𝜓→𝜓𝜑] into ax-2 | |
| 16895 | →→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬¬↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑 | Modus ponens 16893, 16894 | |
| 16896 | →↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑 | Modus ponens 16890, 16895 | |
| 16897 | →→→𝜓𝜑↔𝜑𝜓→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1 | |
| 16898 | →→→→𝜓𝜑↔𝜑𝜓→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→→𝜓𝜑↔𝜑𝜓→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→→𝜓𝜑↔𝜑𝜓→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1 | |
| 16899 | →↔→𝜑𝜓→𝜓𝜑→→→𝜓𝜑↔𝜑𝜓→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓 | Modus ponens 16897, 16898 | |
| 16900 | →→↔→𝜑𝜓→𝜓𝜑→→→𝜓𝜑↔𝜑𝜓→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 16901 | →→↔→𝜑𝜓→𝜓𝜑→→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓 | Modus ponens 16899, 16900 | |
| 16902 | →↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓 | Modus ponens 16819, 16901 | |
| 16903 | →→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→𝜓𝜑, 𝜒↗↔𝜑𝜓] into ax-2 | |
| 16904 | →→→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓 | Subs [𝜑↗→→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1 | |
| 16905 | →↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓 | Modus ponens 16903, 16904 | |
| 16906 | →→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓, 𝜒↗→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓] into ax-2 | |
| 16907 | →→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓 | Modus ponens 16905, 16906 | |
| 16908 | →↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓 | Modus ponens 16902, 16907 | |
| 16909 | →→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬↔𝜑𝜓→𝜓𝜑, 𝜒↗→¬↔𝜑𝜓↔𝜑𝜓] into ax-2 | |
| 16910 | →→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓 | Modus ponens 16908, 16909 | |
| 16911 | →↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓 | Modus ponens 16896, 16910 | |
| 16912 | →¬↔𝜑𝜓→↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬↔→𝜑𝜓→𝜓𝜑] into pm2.21 | |
| 16913 | →→¬↔𝜑𝜓→↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓↔𝜑𝜓→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗¬↔→𝜑𝜓→𝜓𝜑] into ax-2 | |
| 16914 | →→¬↔𝜑𝜓↔𝜑𝜓→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑 | Modus ponens 16912, 16913 | |
| 16915 | →→→¬↔𝜑𝜓↔𝜑𝜓→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓↔𝜑𝜓→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗→→¬↔𝜑𝜓↔𝜑𝜓→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1 | |
| 16916 | →↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓↔𝜑𝜓→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑 | Modus ponens 16914, 16915 | |
| 16917 | →→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓↔𝜑𝜓→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬↔𝜑𝜓↔𝜑𝜓, 𝜒↗→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑] into ax-2 | |
| 16918 | →→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑 | Modus ponens 16916, 16917 | |
| 16919 | →↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑 | Modus ponens 16911, 16918 | |
| 16920 | →→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-3 | |
| 16921 | →→→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗→→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1 | |
| 16922 | →↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓 | Modus ponens 16920, 16921 | |
| 16923 | →→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑, 𝜒↗→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓] into ax-2 | |
| 16924 | →→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓 | Modus ponens 16922, 16923 | |
| 16925 | →↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓 | Modus ponens 16919, 16924 | |
| 16926 | →→↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓 | Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜓𝜑, 𝜒↗↔𝜑𝜓] into ax-2 | |
| 16927 | →→↔→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓 | Modus ponens 16925, 16926 | |
| 16928 | →↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓 | Modus ponens 16834, 16927 | |
| 16929 | →→↔𝜑𝜓↔→𝜑𝜓→𝜓𝜑→→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓↔→𝜑𝜓→𝜓𝜑 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into impbi | |
| 16930 | →→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓↔→𝜑𝜓→𝜓𝜑 | Modus ponens 16780, 16929 | |
| 16931 | ↔↔𝜑𝜓↔→𝜑𝜓→𝜓𝜑 | Modus ponens 16928, 16930 | impimprbi |
| 16932 | ↔→⋀𝜑𝜓¬𝜒→𝜑→𝜓¬𝜒 | Subs [𝜒↗¬𝜒] into impexp | |
| 16933 | ↔→𝜓¬𝜒¬⋀𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗𝜒] into imnan | |
| 16934 | →↔→𝜓¬𝜒¬⋀𝜓𝜒→𝜑↔→𝜓¬𝜒¬⋀𝜓𝜒 | Subs [𝜑↗↔→𝜓¬𝜒¬⋀𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 16935 | →𝜑↔→𝜓¬𝜒¬⋀𝜓𝜒 | Modus ponens 16933, 16934 | |
| 16936 | ↔→𝜑↔→𝜓¬𝜒¬⋀𝜓𝜒↔→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒 | Subs [𝜓↗→𝜓¬𝜒, 𝜒↗¬⋀𝜓𝜒] into pm5.74 | |
| 16937 | →↔→𝜑↔→𝜓¬𝜒¬⋀𝜓𝜒↔→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒→→𝜑↔→𝜓¬𝜒¬⋀𝜓𝜒↔→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→𝜑↔→𝜓¬𝜒¬⋀𝜓𝜒, 𝜓↗↔→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒] into biimp | |
| 16938 | →→𝜑↔→𝜓¬𝜒¬⋀𝜓𝜒↔→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒 | Modus ponens 16936, 16937 | |
| 16939 | ↔→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒 | Modus ponens 16935, 16938 | |
| 16940 | →↔→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒→→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→𝜑→𝜓¬𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒] into biimp | |
| 16941 | →→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒 | Modus ponens 16939, 16940 | |
| 16942 | →↔→⋀𝜑𝜓¬𝜒→𝜑→𝜓¬𝜒→→⋀𝜑𝜓¬𝜒→𝜑→𝜓¬𝜒 | Subs [𝜑↗→⋀𝜑𝜓¬𝜒, 𝜓↗→𝜑→𝜓¬𝜒] into biimp | |
| 16943 | →→⋀𝜑𝜓¬𝜒→𝜑→𝜓¬𝜒 | Modus ponens 16932, 16942 | |
| 16944 | →→→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒→→⋀𝜑𝜓¬𝜒→→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒, 𝜓↗→⋀𝜑𝜓¬𝜒] into ax-1 | |
| 16945 | →→⋀𝜑𝜓¬𝜒→→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒 | Modus ponens 16941, 16944 | |
| 16946 | →→→⋀𝜑𝜓¬𝜒→→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒→→→⋀𝜑𝜓¬𝜒→𝜑→𝜓¬𝜒→→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→⋀𝜑𝜓¬𝜒, 𝜓↗→𝜑→𝜓¬𝜒, 𝜒↗→𝜑¬⋀𝜓𝜒] into ax-2 | |
| 16947 | →→→⋀𝜑𝜓¬𝜒→𝜑→𝜓¬𝜒→→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒 | Modus ponens 16945, 16946 | |
| 16948 | →→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒 | Modus ponens 16943, 16947 | |
| 16949 | →↔→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒↔→𝜑¬⋀𝜓𝜒→𝜑→𝜓¬𝜒 | Subs [𝜑↗→𝜑→𝜓¬𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒] into bicom1 | |
| 16950 | ↔→𝜑¬⋀𝜓𝜒→𝜑→𝜓¬𝜒 | Modus ponens 16939, 16949 | |
| 16951 | →↔→𝜑¬⋀𝜓𝜒→𝜑→𝜓¬𝜒→→𝜑¬⋀𝜓𝜒→𝜑→𝜓¬𝜒 | Subs [𝜑↗→𝜑¬⋀𝜓𝜒, 𝜓↗→𝜑→𝜓¬𝜒] into biimp | |
| 16952 | →→𝜑¬⋀𝜓𝜒→𝜑→𝜓¬𝜒 | Modus ponens 16950, 16951 | |
| 16953 | →↔→⋀𝜑𝜓¬𝜒→𝜑→𝜓¬𝜒↔→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→⋀𝜑𝜓¬𝜒, 𝜓↗→𝜑→𝜓¬𝜒] into bicom1 | |
| 16954 | ↔→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒 | Modus ponens 16932, 16953 | |
| 16955 | →↔→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒→→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→𝜑→𝜓¬𝜒, 𝜓↗→⋀𝜑𝜓¬𝜒] into biimp | |
| 16956 | →→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒 | Modus ponens 16954, 16955 | |
| 16957 | →→→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒→→𝜑¬⋀𝜓𝜒→→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒] into ax-1 | |
| 16958 | →→𝜑¬⋀𝜓𝜒→→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒 | Modus ponens 16956, 16957 | |
| 16959 | →→→𝜑¬⋀𝜓𝜒→→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒→→→𝜑¬⋀𝜓𝜒→𝜑→𝜓¬𝜒→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→𝜑¬⋀𝜓𝜒, 𝜓↗→𝜑→𝜓¬𝜒, 𝜒↗→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 16960 | →→→𝜑¬⋀𝜓𝜒→𝜑→𝜓¬𝜒→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒 | Modus ponens 16958, 16959 | |
| 16961 | →→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒 | Modus ponens 16952, 16960 | |
| 16962 | →→→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒→→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒↔→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→⋀𝜑𝜓¬𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒] into impbi | |
| 16963 | →→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒↔→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒 | Modus ponens 16948, 16962 | |
| 16964 | ↔→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒 | Modus ponens 16961, 16963 | |
| 16965 | →↔→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒↔→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→⋀𝜑𝜓¬𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒] into bicom1 | |
| 16966 | ↔→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒 | Modus ponens 16964, 16965 | nan |
| 16967 | →⋀𝜒→𝜑𝜓→𝜑𝜓 | Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜓] into simpr | |
| 16968 | →⋀𝜒→𝜑𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜓] into simpl | |
| 16969 | →→𝜒→𝜑𝜒→⋀𝜒→𝜑𝜓→𝜒→𝜑𝜒 | Subs [𝜑↗→𝜒→𝜑𝜒, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1 | |
| 16970 | →⋀𝜒→𝜑𝜓→𝜒→𝜑𝜒 | Modus ponens 1834, 16969 | |
| 16971 | →→⋀𝜒→𝜑𝜓→𝜒→𝜑𝜒→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→𝜑𝜒] into ax-2 | |
| 16972 | →→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑𝜒 | Modus ponens 16970, 16971 | |
| 16973 | →⋀𝜒→𝜑𝜓→𝜑𝜒 | Modus ponens 16968, 16972 | |
| 16974 | →→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→⋀𝜒→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒 | Subs [𝜑↗→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1 | |
| 16975 | →⋀𝜒→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒 | Modus ponens 5594, 16974 | |
| 16976 | →→⋀𝜒→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→→⋀𝜒→𝜑𝜓→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒 | Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑→𝜒⋀𝜓𝜒] into ax-2 | |
| 16977 | →→⋀𝜒→𝜑𝜓→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒 | Modus ponens 16975, 16976 | |
| 16978 | →⋀𝜒→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒 | Modus ponens 16967, 16977 | |
| 16979 | →→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒→⋀𝜒→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1 | |
| 16980 | →⋀𝜒→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒 | Modus ponens 5595, 16979 | |
| 16981 | →→⋀𝜒→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒→→⋀𝜒→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→⋀𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗→𝜑→𝜒⋀𝜓𝜒, 𝜒↗→→𝜑𝜒→𝜑⋀𝜓𝜒] into ax-2 | |
| 16982 | →→⋀𝜒→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→⋀𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜓𝜒 | Modus ponens 16980, 16981 | |
| 16983 | →⋀𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜓𝜒 | Modus ponens 16978, 16982 | |
| 16984 | →→⋀𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜓𝜒→→⋀𝜒→𝜑𝜓→𝜑𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜓𝜒 | Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2 | |
| 16985 | →→⋀𝜒→𝜑𝜓→𝜑𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜓𝜒 | Modus ponens 16983, 16984 | |
| 16986 | →⋀𝜒→𝜑𝜓→𝜑⋀𝜓𝜒 | Modus ponens 16973, 16985 | pm5.31 |
| 16987 | →⋀→𝜑𝜒→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜓↗𝜒, 𝜒↗𝜓] into pm3.43 | |
| 16988 | ↔⋀→𝜑𝜒→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓 | Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜑𝜓] into df-an | |
| 16989 | →↔⋀→𝜑𝜒→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓↔¬→→𝜑𝜒¬→𝜑𝜓⋀→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗⋀→𝜑𝜒→𝜑𝜓, 𝜓↗¬→→𝜑𝜒¬→𝜑𝜓] into bicom1 | |
| 16990 | ↔¬→→𝜑𝜒¬→𝜑𝜓⋀→𝜑𝜒→𝜑𝜓 | Modus ponens 16988, 16989 | |
| 16991 | →↔¬→→𝜑𝜒¬→𝜑𝜓⋀→𝜑𝜒→𝜑𝜓→¬→→𝜑𝜒¬→𝜑𝜓⋀→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗¬→→𝜑𝜒¬→𝜑𝜓, 𝜓↗⋀→𝜑𝜒→𝜑𝜓] into biimp | |
| 16992 | →¬→→𝜑𝜒¬→𝜑𝜓⋀→𝜑𝜒→𝜑𝜓 | Modus ponens 16990, 16991 | |
| 16993 | →→⋀→𝜑𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→¬→→𝜑𝜒¬→𝜑𝜓→⋀→𝜑𝜒→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗→⋀→𝜑𝜒→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗¬→→𝜑𝜒¬→𝜑𝜓] into ax-1 | |
| 16994 | →¬→→𝜑𝜒¬→𝜑𝜓→⋀→𝜑𝜒→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 16987, 16993 | |
| 16995 | →→¬→→𝜑𝜒¬→𝜑𝜓→⋀→𝜑𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→→¬→→𝜑𝜒¬→𝜑𝜓⋀→𝜑𝜒→𝜑𝜓→¬→→𝜑𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗¬→→𝜑𝜒¬→𝜑𝜓, 𝜓↗⋀→𝜑𝜒→𝜑𝜓, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2 | |
| 16996 | →→¬→→𝜑𝜒¬→𝜑𝜓⋀→𝜑𝜒→𝜑𝜓→¬→→𝜑𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 16994, 16995 | |
| 16997 | →¬→→𝜑𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 16992, 16996 | |
| 16998 | →→𝜑𝜒→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓 | Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜑𝜓] into pm3.2im | |
| 16999 | →→¬→→𝜑𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜑𝜓→¬→→𝜑𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗→¬→→𝜑𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 17000 | →→𝜑𝜓→¬→→𝜑𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 16997, 16999 | |
| 17001 | →→→𝜑𝜓→¬→→𝜑𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓→→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→→𝜑𝜒¬→𝜑𝜓, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2 | |
| 17002 | →→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17000, 17001 | |
| 17003 | →→→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜑𝜒→→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗→→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗→𝜑𝜒] into ax-1 | |
| 17004 | →→𝜑𝜒→→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17002, 17003 | |
| 17005 | →→→𝜑𝜒→→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓→→→𝜑𝜒→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗→𝜑𝜒, 𝜓↗→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓, 𝜒↗→→𝜑𝜓→𝜑⋀𝜒𝜓] into ax-2 | |
| 17006 | →→→𝜑𝜒→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17004, 17005 | |
| 17007 | →→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 16998, 17006 | |
| 17008 | →→𝜑𝜓→→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒] into ax-1 | |
| 17009 | →→→𝜑𝜓→→𝜑𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 17010 | →→𝜑𝜓→→𝜑𝜓→→𝜑𝜒→𝜑𝜓 | Modus ponens 17008, 17009 | |
| 17011 | →→→𝜑𝜓→→𝜑𝜓→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜑𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜑𝜒→𝜑𝜓] into ax-2 | |
| 17012 | →→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜑𝜒→𝜑𝜓 | Modus ponens 17010, 17011 | |
| 17013 | →→→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓→→→𝜑𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓 | Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2 | |
| 17014 | →→→𝜑𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓 | Modus ponens 17007, 17013 | |
| 17015 | →→→→𝜑𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓→→𝜑𝜓→→→𝜑𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓 | Subs [𝜑↗→→→𝜑𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 17016 | →→𝜑𝜓→→→𝜑𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓 | Modus ponens 17014, 17015 | |
| 17017 | →→→𝜑𝜓→→→𝜑𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓→→→𝜑𝜓→→𝜑𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜑𝜒→𝜑𝜓, 𝜒↗→→𝜑𝜒→𝜑⋀𝜒𝜓] into ax-2 | |
| 17018 | →→→𝜑𝜓→→𝜑𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓 | Modus ponens 17016, 17017 | |
| 17019 | →→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓 | Modus ponens 17008, 17018 | |
| 17020 | →→→𝜑𝜒→→𝜑𝜓→𝜑𝜒→𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗→→𝜑𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗𝜒] into ax-1 | |
| 17021 | →𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 5603, 17020 | |
| 17022 | →→𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→𝜒→𝜑𝜒→𝜒→→𝜑𝜓→𝜑𝜒 | Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜒] into ax-2 | |
| 17023 | →→𝜒→𝜑𝜒→𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 17021, 17022 | |
| 17024 | →𝜒→→𝜑𝜓→𝜑𝜒 | Modus ponens 1834, 17023 | |
| 17025 | →→→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2 | |
| 17026 | →→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17019, 17025 | |
| 17027 | →→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓→𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗𝜒] into ax-1 | |
| 17028 | →𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17026, 17027 | |
| 17029 | →→𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜒→→𝜑𝜓→𝜑𝜒→𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒, 𝜒↗→→𝜑𝜓→𝜑⋀𝜒𝜓] into ax-2 | |
| 17030 | →→𝜒→→𝜑𝜓→𝜑𝜒→𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17028, 17029 | |
| 17031 | →𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17024, 17030 | |
| 17032 | →→𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓 | Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2 | |
| 17033 | →→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓 | Modus ponens 17031, 17032 | |
| 17034 | →→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓 | Subs [𝜑↗→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 17035 | →→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓 | Modus ponens 17033, 17034 | |
| 17036 | →→→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→→→𝜑𝜓→𝜒→𝜑𝜓→→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→𝜑𝜓, 𝜒↗→𝜒→𝜑⋀𝜒𝜓] into ax-2 | |
| 17037 | →→→𝜑𝜓→𝜒→𝜑𝜓→→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓 | Modus ponens 17035, 17036 | |
| 17038 | →→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓 | Modus ponens 39, 17037 | |
| 17039 | →→→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2 | |
| 17040 | →→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17038, 17039 | |
| 17041 | →→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗𝜒] into ax-1 | |
| 17042 | →𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17040, 17041 | |
| 17043 | →→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜒→→𝜑𝜓𝜒→𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜑⋀𝜒𝜓] into ax-2 | |
| 17044 | →→𝜒→→𝜑𝜓𝜒→𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17042, 17043 | |
| 17045 | ↔⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜓] into df-an | |
| 17046 | →→→𝜑𝜓→𝜒→𝜑𝜓→¬¬→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→𝜒→𝜑𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1 | |
| 17047 | →¬¬→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓 | Modus ponens 39, 17046 | |
| 17048 | →→¬¬→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→𝜒→𝜑𝜓 | Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜒→𝜑𝜓] into ax-2 | |
| 17049 | →→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→𝜒→𝜑𝜓 | Modus ponens 17047, 17048 | |
| 17050 | →¬¬→𝜑𝜓→𝜒→𝜑𝜓 | Modus ponens 532, 17049 | |
| 17051 | →→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓 | Subs [𝜑↗→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1 | |
| 17052 | →¬¬→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓 | Modus ponens 17033, 17051 | |
| 17053 | →→¬¬→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→→¬¬→𝜑𝜓→𝜒→𝜑𝜓→¬¬→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓 | Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜒→𝜑𝜓, 𝜒↗→𝜒→𝜑⋀𝜒𝜓] into ax-2 | |
| 17054 | →→¬¬→𝜑𝜓→𝜒→𝜑𝜓→¬¬→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓 | Modus ponens 17052, 17053 | |
| 17055 | →¬¬→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓 | Modus ponens 17050, 17054 | |
| 17056 | →𝜒→¬¬→𝜑𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗¬¬→𝜑𝜓] into ax-1 | |
| 17057 | →→𝜒→¬¬→𝜑𝜓𝜒→𝜒→𝜒→¬¬→𝜑𝜓𝜒 | Subs [𝜑↗→𝜒→¬¬→𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 17058 | →𝜒→𝜒→¬¬→𝜑𝜓𝜒 | Modus ponens 17056, 17057 | |
| 17059 | →→𝜒→𝜒→¬¬→𝜑𝜓𝜒→→𝜒𝜒→𝜒→¬¬→𝜑𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗𝜒, 𝜒↗→¬¬→𝜑𝜓𝜒] into ax-2 | |
| 17060 | →→𝜒𝜒→𝜒→¬¬→𝜑𝜓𝜒 | Modus ponens 17058, 17059 | |
| 17061 | →→¬¬→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2 | |
| 17062 | →→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17055, 17061 | |
| 17063 | →→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→𝜒→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗𝜒] into ax-1 | |
| 17064 | →𝜒→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17062, 17063 | |
| 17065 | →→𝜒→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜒→¬¬→𝜑𝜓𝜒→𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗𝜒, 𝜓↗→¬¬→𝜑𝜓𝜒, 𝜒↗→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓] into ax-2 | |
| 17066 | →→𝜒→¬¬→𝜑𝜓𝜒→𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17064, 17065 | |
| 17067 | →𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17056, 17066 | |
| 17068 | →→𝜑⋀𝜒𝜓¬¬→𝜑⋀𝜒𝜓 | Subs [𝜑↗→𝜑⋀𝜒𝜓] into notnot | |
| 17069 | →→→𝜑⋀𝜒𝜓¬¬→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓→→𝜑⋀𝜒𝜓¬¬→𝜑⋀𝜒𝜓 | Subs [𝜑↗→→𝜑⋀𝜒𝜓¬¬→𝜑⋀𝜒𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1 | |
| 17070 | →¬¬→𝜑𝜓→→𝜑⋀𝜒𝜓¬¬→𝜑⋀𝜒𝜓 | Modus ponens 17068, 17069 | |
| 17071 | →→¬¬→𝜑𝜓→→𝜑⋀𝜒𝜓¬¬→𝜑⋀𝜒𝜓→→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓 | Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑⋀𝜒𝜓, 𝜒↗¬¬→𝜑⋀𝜒𝜓] into ax-2 | |
| 17072 | →→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓 | Modus ponens 17070, 17071 | |
| 17073 | →→→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→𝜒→→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓 | Subs [𝜑↗→→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓, 𝜓↗𝜒] into ax-1 | |
| 17074 | →𝜒→→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓 | Modus ponens 17072, 17073 | |
| 17075 | →→𝜒→→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→→𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→𝜒→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓 | Subs [𝜑↗𝜒, 𝜓↗→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜒↗→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓] into ax-2 | |
| 17076 | →→𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→𝜒→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓 | Modus ponens 17074, 17075 | |
| 17077 | →𝜒→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓 | Modus ponens 17067, 17076 | |
| 17078 | →→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓] into ax-3 | |
| 17079 | →→→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓→𝜒→→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓 | Subs [𝜑↗→→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓, 𝜓↗𝜒] into ax-1 | |
| 17080 | →𝜒→→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓 | Modus ponens 17078, 17079 | |
| 17081 | →→𝜒→→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓→→𝜒→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→𝜒→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓 | Subs [𝜑↗𝜒, 𝜓↗→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓, 𝜒↗→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓] into ax-2 | |
| 17082 | →→𝜒→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→𝜒→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓 | Modus ponens 17080, 17081 | |
| 17083 | →𝜒→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓 | Modus ponens 17077, 17082 | |
| 17084 | →¬→𝜑⋀𝜒𝜓¬→𝜑⋀𝜒𝜓 | Subs [𝜑↗¬→𝜑⋀𝜒𝜓] into id | |
| 17085 | →¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓 | Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗𝜒] into ax-1 | |
| 17086 | →→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓 | Subs [𝜑↗→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓] into ax-1 | |
| 17087 | →¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓 | Modus ponens 17085, 17086 | |
| 17088 | →→¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓→→¬→𝜑⋀𝜒𝜓¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓 | Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓, 𝜒↗→𝜒¬→𝜑⋀𝜒𝜓] into ax-2 | |
| 17089 | →→¬→𝜑⋀𝜒𝜓¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓 | Modus ponens 17087, 17088 | |
| 17090 | →→𝜒→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓→→𝜒¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓 | Subs [𝜑↗𝜒, 𝜓↗¬→𝜑⋀𝜒𝜓, 𝜒↗¬→𝜑𝜓] into ax-2 | |
| 17091 | →→𝜒¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓 | Modus ponens 17083, 17090 | |
| 17092 | →→→𝜒¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓→→𝜒¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓 | Subs [𝜑↗→→𝜒¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓] into ax-1 | |
| 17093 | →¬→𝜑⋀𝜒𝜓→→𝜒¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓 | Modus ponens 17091, 17092 | |
| 17094 | →→¬→𝜑⋀𝜒𝜓→→𝜒¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓→→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗→𝜒¬→𝜑⋀𝜒𝜓, 𝜒↗→𝜒¬→𝜑𝜓] into ax-2 | |
| 17095 | →→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓 | Modus ponens 17093, 17094 | |
| 17096 | →¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓 | Modus ponens 17085, 17095 | |
| 17097 | →¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→𝜒¬→𝜑𝜓] into id | |
| 17098 | →→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓] into ax-1 | |
| 17099 | →¬→𝜑⋀𝜒𝜓→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Modus ponens 17097, 17098 | |
| 17100 | →¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→𝜒¬→𝜑𝜓] into notnotr | |
| 17101 | →¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓] into ax-1 | |
| 17102 | →→¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗→¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓, 𝜓↗¬¬¬→𝜒¬→𝜑𝜓] into ax-1 | |
| 17103 | →¬¬¬→𝜒¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓 | Modus ponens 17101, 17102 | |
| 17104 | →→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗¬¬¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓, 𝜒↗→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓] into ax-2 | |
| 17105 | →→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓 | Modus ponens 17103, 17104 | |
| 17106 | →¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓 | Modus ponens 17100, 17105 | |
| 17107 | →→¬→𝜑⋀𝜒𝜓→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓, 𝜒↗¬→𝜒¬→𝜑𝜓] into ax-2 | |
| 17108 | →→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓 | Modus ponens 17099, 17107 | |
| 17109 | →→→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗→→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓, 𝜓↗¬¬¬→𝜒¬→𝜑𝜓] into ax-1 | |
| 17110 | →¬¬¬→𝜒¬→𝜑𝜓→→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓 | Modus ponens 17108, 17109 | |
| 17111 | →→¬¬¬→𝜒¬→𝜑𝜓→→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗¬¬¬→𝜒¬→𝜑𝜓, 𝜓↗→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓, 𝜒↗→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓] into ax-2 | |
| 17112 | →→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓 | Modus ponens 17110, 17111 | |
| 17113 | →¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓 | Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗¬¬¬→𝜒¬→𝜑𝜓] into ax-1 | |
| 17114 | →→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓 | Subs [𝜑↗→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓] into ax-1 | |
| 17115 | →¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓 | Modus ponens 17113, 17114 | |
| 17116 | →→¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→→¬→𝜑⋀𝜒𝜓¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓 | Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓, 𝜒↗→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓] into ax-2 | |
| 17117 | →→¬→𝜑⋀𝜒𝜓¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓 | Modus ponens 17115, 17116 | |
| 17118 | →→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗¬¬¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓, 𝜒↗¬→𝜒¬→𝜑𝜓] into ax-2 | |
| 17119 | →→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Modus ponens 17106, 17118 | |
| 17120 | →→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓] into ax-1 | |
| 17121 | →¬→𝜑⋀𝜒𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Modus ponens 17119, 17120 | |
| 17122 | →→¬→𝜑⋀𝜒𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓, 𝜒↗→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓] into ax-2 | |
| 17123 | →→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Modus ponens 17121, 17122 | |
| 17124 | →¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Modus ponens 17113, 17123 | |
| 17125 | →→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗¬¬→𝜒¬→𝜑𝜓, 𝜓↗→𝜒¬→𝜑𝜓] into ax-3 | |
| 17126 | →→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓] into ax-1 | |
| 17127 | →¬→𝜑⋀𝜒𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓 | Modus ponens 17125, 17126 | |
| 17128 | →→¬→𝜑⋀𝜒𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓→→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜒↗→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓] into ax-2 | |
| 17129 | →→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓 | Modus ponens 17127, 17128 | |
| 17130 | →¬→𝜑⋀𝜒𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓 | Modus ponens 17124, 17129 | |
| 17131 | →→¬→𝜑⋀𝜒𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓→→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗→𝜒¬→𝜑𝜓, 𝜒↗¬¬→𝜒¬→𝜑𝜓] into ax-2 | |
| 17132 | →→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬¬→𝜒¬→𝜑𝜓 | Modus ponens 17130, 17131 | |
| 17133 | →¬→𝜑⋀𝜒𝜓¬¬→𝜒¬→𝜑𝜓 | Modus ponens 17096, 17132 | |
| 17134 | →→¬→𝜑⋀𝜒𝜓¬¬→𝜒¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗→𝜑⋀𝜒𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓] into ax-3 | |
| 17135 | →¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17133, 17134 | |
| 17136 | →↔⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓→⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓] into biimp | |
| 17137 | →⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Modus ponens 17045, 17136 | |
| 17138 | →→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓→⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1 | |
| 17139 | →⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17135, 17138 | |
| 17140 | →→⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓→→⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2 | |
| 17141 | →→⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17139, 17140 | |
| 17142 | →⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17137, 17141 | pm5.31r |
| 17143 | ↔⋀→𝜑𝜓𝜒¬→→𝜑𝜓¬𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒] into df-an | |
| 17144 | →→𝜒→→𝜑𝜓𝜒→¬¬𝜒→𝜒→→𝜑𝜓𝜒 | Subs [𝜑↗→𝜒→→𝜑𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1 | |
| 17145 | →¬¬𝜒→𝜒→→𝜑𝜓𝜒 | Modus ponens 7185, 17144 | |
| 17146 | →→¬¬𝜒→𝜒→→𝜑𝜓𝜒→→¬¬𝜒𝜒→¬¬𝜒→→𝜑𝜓𝜒 | Subs [𝜑↗¬¬𝜒, 𝜓↗𝜒, 𝜒↗→→𝜑𝜓𝜒] into ax-2 | |
| 17147 | →→¬¬𝜒𝜒→¬¬𝜒→→𝜑𝜓𝜒 | Modus ponens 17145, 17146 | |
| 17148 | →¬¬𝜒→→𝜑𝜓𝜒 | Modus ponens 5153, 17147 | |
| 17149 | →→→𝜑𝜓→𝜒→𝜑𝜓→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→𝜑𝜓] into ax-2 | |
| 17150 | →→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓 | Modus ponens 39, 17149 | |
| 17151 | →→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓→¬¬𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓, 𝜓↗¬¬𝜒] into ax-1 | |
| 17152 | →¬¬𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓 | Modus ponens 17150, 17151 | |
| 17153 | →→¬¬𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓→→¬¬𝜒→→𝜑𝜓𝜒→¬¬𝜒→→𝜑𝜓→𝜑𝜓 | Subs [𝜑↗¬¬𝜒, 𝜓↗→→𝜑𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜓] into ax-2 | |
| 17154 | →→¬¬𝜒→→𝜑𝜓𝜒→¬¬𝜒→→𝜑𝜓→𝜑𝜓 | Modus ponens 17152, 17153 | |
| 17155 | →¬¬𝜒→→𝜑𝜓→𝜑𝜓 | Modus ponens 17148, 17154 | |
| 17156 | →→𝜑𝜓→¬¬𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗¬¬𝜒] into ax-1 | |
| 17157 | →→→𝜑𝜓→¬¬𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→¬¬𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→¬¬𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 17158 | →→𝜑𝜓→→𝜑𝜓→¬¬𝜒→𝜑𝜓 | Modus ponens 17156, 17157 | |
| 17159 | →→→𝜑𝜓→→𝜑𝜓→¬¬𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→¬¬𝜒→𝜑𝜓] into ax-2 | |
| 17160 | →→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬𝜒→𝜑𝜓 | Modus ponens 17158, 17159 | |
| 17161 | →→¬¬𝜒→→𝜑𝜓→𝜑𝜓→→¬¬𝜒→𝜑𝜓→¬¬𝜒→𝜑𝜓 | Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2 | |
| 17162 | →→¬¬𝜒→𝜑𝜓→¬¬𝜒→𝜑𝜓 | Modus ponens 17155, 17161 | |
| 17163 | →→→¬¬𝜒→𝜑𝜓→¬¬𝜒→𝜑𝜓→→𝜑𝜓→→¬¬𝜒→𝜑𝜓→¬¬𝜒→𝜑𝜓 | Subs [𝜑↗→→¬¬𝜒→𝜑𝜓→¬¬𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 17164 | →→𝜑𝜓→→¬¬𝜒→𝜑𝜓→¬¬𝜒→𝜑𝜓 | Modus ponens 17162, 17163 | |
| 17165 | →→→𝜑𝜓→→¬¬𝜒→𝜑𝜓→¬¬𝜒→𝜑𝜓→→→𝜑𝜓→¬¬𝜒→𝜑𝜓→→𝜑𝜓→¬¬𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬𝜒→𝜑𝜓, 𝜒↗→¬¬𝜒→𝜑𝜓] into ax-2 | |
| 17166 | →→→𝜑𝜓→¬¬𝜒→𝜑𝜓→→𝜑𝜓→¬¬𝜒→𝜑𝜓 | Modus ponens 17164, 17165 | |
| 17167 | →→𝜑𝜓¬¬→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓] into notnot | |
| 17168 | →→→𝜑𝜓¬¬→𝜑𝜓→¬¬𝜒→→𝜑𝜓¬¬→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓¬¬→𝜑𝜓, 𝜓↗¬¬𝜒] into ax-1 | |
| 17169 | →¬¬𝜒→→𝜑𝜓¬¬→𝜑𝜓 | Modus ponens 17167, 17168 | |
| 17170 | →→¬¬𝜒→→𝜑𝜓¬¬→𝜑𝜓→→¬¬𝜒→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓 | Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜑𝜓, 𝜒↗¬¬→𝜑𝜓] into ax-2 | |
| 17171 | →→¬¬𝜒→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓 | Modus ponens 17169, 17170 | |
| 17172 | →→→¬¬𝜒→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓→→𝜑𝜓→→¬¬𝜒→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓 | Subs [𝜑↗→→¬¬𝜒→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 17173 | →→𝜑𝜓→→¬¬𝜒→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓 | Modus ponens 17171, 17172 | |
| 17174 | →→→𝜑𝜓→→¬¬𝜒→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓→→→𝜑𝜓→¬¬𝜒→𝜑𝜓→→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬𝜒→𝜑𝜓, 𝜒↗→¬¬𝜒¬¬→𝜑𝜓] into ax-2 | |
| 17175 | →→→𝜑𝜓→¬¬𝜒→𝜑𝜓→→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓 | Modus ponens 17173, 17174 | |
| 17176 | →→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓 | Modus ponens 17156, 17175 | |
| 17177 | →→¬¬𝜒¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜒 | Subs [𝜑↗¬𝜒, 𝜓↗¬→𝜑𝜓] into ax-3 | |
| 17178 | →→→¬¬𝜒¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜒→→𝜑𝜓→→¬¬𝜒¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜒 | Subs [𝜑↗→→¬¬𝜒¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜒, 𝜓↗→𝜑𝜓] into ax-1 | |
| 17179 | →→𝜑𝜓→→¬¬𝜒¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜒 | Modus ponens 17177, 17178 | |
| 17180 | →→→𝜑𝜓→→¬¬𝜒¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜒→→→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓→→𝜑𝜓→¬→𝜑𝜓¬𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬𝜒¬¬→𝜑𝜓, 𝜒↗→¬→𝜑𝜓¬𝜒] into ax-2 | |
| 17181 | →→→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓→→𝜑𝜓→¬→𝜑𝜓¬𝜒 | Modus ponens 17179, 17180 | |
| 17182 | →→𝜑𝜓→¬→𝜑𝜓¬𝜒 | Modus ponens 17176, 17181 | |
| 17183 | →¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 17184 | →→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓 | Subs [𝜑↗→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 17185 | →¬→𝜑𝜓→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓 | Modus ponens 17183, 17184 | |
| 17186 | →→¬→𝜑𝜓→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗→→𝜑𝜓¬→𝜑𝜓] into ax-2 | |
| 17187 | →→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓 | Modus ponens 17185, 17186 | |
| 17188 | →→→𝜑𝜓→¬→𝜑𝜓¬𝜒→→→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗¬𝜒] into ax-2 | |
| 17189 | →→→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬𝜒 | Modus ponens 17182, 17188 | |
| 17190 | →→→→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬𝜒→¬→𝜑𝜓→→→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬𝜒 | Subs [𝜑↗→→→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬𝜒, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 17191 | →¬→𝜑𝜓→→→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬𝜒 | Modus ponens 17189, 17190 | |
| 17192 | →→¬→𝜑𝜓→→→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬𝜒→→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→→𝜑𝜓¬𝜒 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→→𝜑𝜓¬→𝜑𝜓, 𝜒↗→→𝜑𝜓¬𝜒] into ax-2 | |
| 17193 | →→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→→𝜑𝜓¬𝜒 | Modus ponens 17191, 17192 | |
| 17194 | →¬→𝜑𝜓→→𝜑𝜓¬𝜒 | Modus ponens 17183, 17193 | |
| 17195 | →¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒 | Subs [𝜑↗¬→→𝜑𝜓¬𝜒] into id | |
| 17196 | →→¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓→¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒 | Subs [𝜑↗→¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 17197 | →¬→𝜑𝜓→¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒 | Modus ponens 17195, 17196 | |
| 17198 | →¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒 | Subs [𝜑↗¬→→𝜑𝜓¬𝜒] into notnotr | |
| 17199 | →¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒 | Subs [𝜑↗¬→→𝜑𝜓¬𝜒, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 17200 | →→¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬¬¬→→𝜑𝜓¬𝜒→¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒 | Subs [𝜑↗→¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒, 𝜓↗¬¬¬→→𝜑𝜓¬𝜒] into ax-1 | |
| 17201 | →¬¬¬→→𝜑𝜓¬𝜒→¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒 | Modus ponens 17199, 17200 | |
| 17202 | →→¬¬¬→→𝜑𝜓¬𝜒→¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→¬¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒 | Subs [𝜑↗¬¬¬→→𝜑𝜓¬𝜒, 𝜓↗¬→→𝜑𝜓¬𝜒, 𝜒↗→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒] into ax-2 | |
| 17203 | →→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→¬¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒 | Modus ponens 17201, 17202 | |
| 17204 | →¬¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒 | Modus ponens 17198, 17203 | |
| 17205 | →→¬→𝜑𝜓→¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬𝜒, 𝜒↗¬→→𝜑𝜓¬𝜒] into ax-2 | |
| 17206 | →→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒 | Modus ponens 17197, 17205 | |
| 17207 | →→→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬¬¬→→𝜑𝜓¬𝜒→→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒 | Subs [𝜑↗→→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒, 𝜓↗¬¬¬→→𝜑𝜓¬𝜒] into ax-1 | |
| 17208 | →¬¬¬→→𝜑𝜓¬𝜒→→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒 | Modus ponens 17206, 17207 | |
| 17209 | →→¬¬¬→→𝜑𝜓¬𝜒→→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→→¬¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒 | Subs [𝜑↗¬¬¬→→𝜑𝜓¬𝜒, 𝜓↗→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒, 𝜒↗→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒] into ax-2 | |
| 17210 | →→¬¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒 | Modus ponens 17208, 17209 | |
| 17211 | →¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬¬¬→→𝜑𝜓¬𝜒] into ax-1 | |
| 17212 | →→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓 | Subs [𝜑↗→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 17213 | →¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓 | Modus ponens 17211, 17212 | |
| 17214 | →→¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓] into ax-2 | |
| 17215 | →→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓 | Modus ponens 17213, 17214 | |
| 17216 | →→¬¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒 | Subs [𝜑↗¬¬¬→→𝜑𝜓¬𝜒, 𝜓↗¬→𝜑𝜓, 𝜒↗¬→→𝜑𝜓¬𝜒] into ax-2 | |
| 17217 | →→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒 | Modus ponens 17204, 17216 | |
| 17218 | →→→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓→→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒 | Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 17219 | →¬→𝜑𝜓→→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒 | Modus ponens 17217, 17218 | |
| 17220 | →→¬→𝜑𝜓→→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓, 𝜒↗→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒] into ax-2 | |
| 17221 | →→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒 | Modus ponens 17219, 17220 | |
| 17222 | →¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒 | Modus ponens 17211, 17221 | |
| 17223 | →→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒 | Subs [𝜑↗¬¬→→𝜑𝜓¬𝜒, 𝜓↗→→𝜑𝜓¬𝜒] into ax-3 | |
| 17224 | →→→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓→→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒 | Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 17225 | →¬→𝜑𝜓→→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒 | Modus ponens 17223, 17224 | |
| 17226 | →→¬→𝜑𝜓→→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒→→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒, 𝜒↗→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒] into ax-2 | |
| 17227 | →→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒 | Modus ponens 17225, 17226 | |
| 17228 | →¬→𝜑𝜓→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒 | Modus ponens 17222, 17227 | |
| 17229 | →→¬→𝜑𝜓→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒→→¬→𝜑𝜓→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬¬→→𝜑𝜓¬𝜒 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→→𝜑𝜓¬𝜒, 𝜒↗¬¬→→𝜑𝜓¬𝜒] into ax-2 | |
| 17230 | →→¬→𝜑𝜓→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬¬→→𝜑𝜓¬𝜒 | Modus ponens 17228, 17229 | |
| 17231 | →¬→𝜑𝜓¬¬→→𝜑𝜓¬𝜒 | Modus ponens 17194, 17230 | |
| 17232 | →→¬→𝜑𝜓¬¬→→𝜑𝜓¬𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬𝜒] into ax-3 | |
| 17233 | →¬→→𝜑𝜓¬𝜒→𝜑𝜓 | Modus ponens 17231, 17232 | |
| 17234 | →↔⋀→𝜑𝜓𝜒¬→→𝜑𝜓¬𝜒→⋀→𝜑𝜓𝜒¬→→𝜑𝜓¬𝜒 | Subs [𝜑↗⋀→𝜑𝜓𝜒, 𝜓↗¬→→𝜑𝜓¬𝜒] into biimp | |
| 17235 | →⋀→𝜑𝜓𝜒¬→→𝜑𝜓¬𝜒 | Modus ponens 17143, 17234 | |
| 17236 | →→¬→→𝜑𝜓¬𝜒→𝜑𝜓→⋀→𝜑𝜓𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓 | Subs [𝜑↗→¬→→𝜑𝜓¬𝜒→𝜑𝜓, 𝜓↗⋀→𝜑𝜓𝜒] into ax-1 | |
| 17237 | →⋀→𝜑𝜓𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓 | Modus ponens 17233, 17236 | |
| 17238 | →→⋀→𝜑𝜓𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓→→⋀→𝜑𝜓𝜒¬→→𝜑𝜓¬𝜒→⋀→𝜑𝜓𝜒→𝜑𝜓 | Subs [𝜑↗⋀→𝜑𝜓𝜒, 𝜓↗¬→→𝜑𝜓¬𝜒, 𝜒↗→𝜑𝜓] into ax-2 | |
| 17239 | →→⋀→𝜑𝜓𝜒¬→→𝜑𝜓¬𝜒→⋀→𝜑𝜓𝜒→𝜑𝜓 | Modus ponens 17237, 17238 | |
| 17240 | →⋀→𝜑𝜓𝜒→𝜑𝜓 | Modus ponens 17235, 17239 | |
| 17241 | →↔⋀→𝜑𝜓𝜒¬→→𝜑𝜓¬𝜒↔¬→→𝜑𝜓¬𝜒⋀→𝜑𝜓𝜒 | Subs [𝜑↗⋀→𝜑𝜓𝜒, 𝜓↗¬→→𝜑𝜓¬𝜒] into bicom1 | |
| 17242 | ↔¬→→𝜑𝜓¬𝜒⋀→𝜑𝜓𝜒 | Modus ponens 17143, 17241 | |
| 17243 | →↔¬→→𝜑𝜓¬𝜒⋀→𝜑𝜓𝜒→¬→→𝜑𝜓¬𝜒⋀→𝜑𝜓𝜒 | Subs [𝜑↗¬→→𝜑𝜓¬𝜒, 𝜓↗⋀→𝜑𝜓𝜒] into biimp | |
| 17244 | →¬→→𝜑𝜓¬𝜒⋀→𝜑𝜓𝜒 | Modus ponens 17242, 17243 | |
| 17245 | →→⋀→𝜑𝜓𝜒→𝜑𝜓→¬→→𝜑𝜓¬𝜒→⋀→𝜑𝜓𝜒→𝜑𝜓 | Subs [𝜑↗→⋀→𝜑𝜓𝜒→𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬𝜒] into ax-1 | |
| 17246 | →¬→→𝜑𝜓¬𝜒→⋀→𝜑𝜓𝜒→𝜑𝜓 | Modus ponens 17240, 17245 | |
| 17247 | →→¬→→𝜑𝜓¬𝜒→⋀→𝜑𝜓𝜒→𝜑𝜓→→¬→→𝜑𝜓¬𝜒⋀→𝜑𝜓𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓 | Subs [𝜑↗¬→→𝜑𝜓¬𝜒, 𝜓↗⋀→𝜑𝜓𝜒, 𝜒↗→𝜑𝜓] into ax-2 | |
| 17248 | →→¬→→𝜑𝜓¬𝜒⋀→𝜑𝜓𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓 | Modus ponens 17246, 17247 | |
| 17249 | →→𝜑𝜓→𝜒¬→→𝜑𝜓¬𝜒 | Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒] into pm3.2im | |
| 17250 | →→¬→→𝜑𝜓¬𝜒→𝜑𝜓→𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓 | Subs [𝜑↗→¬→→𝜑𝜓¬𝜒→𝜑𝜓, 𝜓↗𝜒] into ax-1 | |
| 17251 | →𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓 | Modus ponens 17233, 17250 | |
| 17252 | →→𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓→→𝜒¬→→𝜑𝜓¬𝜒→𝜒→𝜑𝜓 | Subs [𝜑↗𝜒, 𝜓↗¬→→𝜑𝜓¬𝜒, 𝜒↗→𝜑𝜓] into ax-2 | |
| 17253 | →→𝜒¬→→𝜑𝜓¬𝜒→𝜒→𝜑𝜓 | Modus ponens 17251, 17252 | |
| 17254 | →→→𝜒¬→→𝜑𝜓¬𝜒→𝜒→𝜑𝜓→→𝜑𝜓→→𝜒¬→→𝜑𝜓¬𝜒→𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜒¬→→𝜑𝜓¬𝜒→𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 17255 | →→𝜑𝜓→→𝜒¬→→𝜑𝜓¬𝜒→𝜒→𝜑𝜓 | Modus ponens 17253, 17254 | |
| 17256 | →→→𝜑𝜓→→𝜒¬→→𝜑𝜓¬𝜒→𝜒→𝜑𝜓→→→𝜑𝜓→𝜒¬→→𝜑𝜓¬𝜒→→𝜑𝜓→𝜒→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒¬→→𝜑𝜓¬𝜒, 𝜒↗→𝜒→𝜑𝜓] into ax-2 | |
| 17257 | →→→𝜑𝜓→𝜒¬→→𝜑𝜓¬𝜒→→𝜑𝜓→𝜒→𝜑𝜓 | Modus ponens 17255, 17256 | |
| 17258 | →→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓, 𝜓↗𝜒] into ax-1 | |
| 17259 | →𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓 | Modus ponens 17150, 17258 | |
| 17260 | →→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓→→𝜒→→𝜑𝜓𝜒→𝜒→→𝜑𝜓→𝜑𝜓 | Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜓] into ax-2 | |
| 17261 | →→𝜒→→𝜑𝜓𝜒→𝜒→→𝜑𝜓→𝜑𝜓 | Modus ponens 17259, 17260 | |
| 17262 | →𝜒→→𝜑𝜓→𝜑𝜓 | Modus ponens 7185, 17261 | |
| 17263 | →→𝜒→→𝜑𝜓→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑𝜓 | Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2 | |
| 17264 | →→𝜒→𝜑𝜓→𝜒→𝜑𝜓 | Modus ponens 17262, 17263 | |
| 17265 | →→→𝜒→𝜑𝜓→𝜒→𝜑𝜓→¬¬→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜒→𝜑𝜓→𝜒→𝜑𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1 | |
| 17266 | →¬¬→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑𝜓 | Modus ponens 17264, 17265 | |
| 17267 | →→¬¬→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑𝜓→→¬¬→𝜑𝜓→𝜒→𝜑𝜓→¬¬→𝜑𝜓→𝜒→𝜑𝜓 | Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜒→𝜑𝜓, 𝜒↗→𝜒→𝜑𝜓] into ax-2 | |
| 17268 | →→¬¬→𝜑𝜓→𝜒→𝜑𝜓→¬¬→𝜑𝜓→𝜒→𝜑𝜓 | Modus ponens 17266, 17267 | |
| 17269 | →→¬¬→𝜑𝜓→𝜒→𝜑𝜓→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜓 | Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→𝜑𝜓] into ax-2 | |
| 17270 | →→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜓 | Modus ponens 17050, 17269 | |
| 17271 | →→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜓→𝜒→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜓, 𝜓↗𝜒] into ax-1 | |
| 17272 | →𝜒→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜓 | Modus ponens 17270, 17271 | |
| 17273 | →→𝜒→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜓→→𝜒→¬¬→𝜑𝜓𝜒→𝜒→¬¬→𝜑𝜓→𝜑𝜓 | Subs [𝜑↗𝜒, 𝜓↗→¬¬→𝜑𝜓𝜒, 𝜒↗→¬¬→𝜑𝜓→𝜑𝜓] into ax-2 | |
| 17274 | →→𝜒→¬¬→𝜑𝜓𝜒→𝜒→¬¬→𝜑𝜓→𝜑𝜓 | Modus ponens 17272, 17273 | |
| 17275 | →𝜒→¬¬→𝜑𝜓→𝜑𝜓 | Modus ponens 17056, 17274 | |
| 17276 | →→→𝜑𝜓¬¬→𝜑𝜓→¬¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓¬¬→𝜑𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1 | |
| 17277 | →¬¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓 | Modus ponens 17167, 17276 | |
| 17278 | →→¬¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓¬¬→𝜑𝜓 | Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗¬¬→𝜑𝜓] into ax-2 | |
| 17279 | →→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓¬¬→𝜑𝜓 | Modus ponens 17277, 17278 | |
| 17280 | →→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓¬¬→𝜑𝜓→𝜒→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓¬¬→𝜑𝜓 | Subs [𝜑↗→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓¬¬→𝜑𝜓, 𝜓↗𝜒] into ax-1 | |
| 17281 | →𝜒→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓¬¬→𝜑𝜓 | Modus ponens 17279, 17280 | |
| 17282 | →→𝜒→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓¬¬→𝜑𝜓→→𝜒→¬¬→𝜑𝜓→𝜑𝜓→𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜓 | Subs [𝜑↗𝜒, 𝜓↗→¬¬→𝜑𝜓→𝜑𝜓, 𝜒↗→¬¬→𝜑𝜓¬¬→𝜑𝜓] into ax-2 | |
| 17283 | →→𝜒→¬¬→𝜑𝜓→𝜑𝜓→𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜓 | Modus ponens 17281, 17282 | |
| 17284 | →𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜓 | Modus ponens 17275, 17283 | |
| 17285 | →→¬¬→𝜑𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-3 | |
| 17286 | →→→¬¬→𝜑𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬→𝜑𝜓→𝜒→→¬¬→𝜑𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬→𝜑𝜓 | Subs [𝜑↗→→¬¬→𝜑𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬→𝜑𝜓, 𝜓↗𝜒] into ax-1 | |
| 17287 | →𝜒→→¬¬→𝜑𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬→𝜑𝜓 | Modus ponens 17285, 17286 | |
| 17288 | →→𝜒→→¬¬→𝜑𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬→𝜑𝜓→→𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜓→𝜒→¬→𝜑𝜓¬→𝜑𝜓 | Subs [𝜑↗𝜒, 𝜓↗→¬¬→𝜑𝜓¬¬→𝜑𝜓, 𝜒↗→¬→𝜑𝜓¬→𝜑𝜓] into ax-2 | |
| 17289 | →→𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜓→𝜒→¬→𝜑𝜓¬→𝜑𝜓 | Modus ponens 17287, 17288 | |
| 17290 | →𝜒→¬→𝜑𝜓¬→𝜑𝜓 | Modus ponens 17284, 17289 | |
| 17291 | →¬→𝜑𝜓→𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗𝜒] into ax-1 | |
| 17292 | →→¬→𝜑𝜓→𝜒¬→𝜑𝜓→¬→𝜑𝜓→¬→𝜑𝜓→𝜒¬→𝜑𝜓 | Subs [𝜑↗→¬→𝜑𝜓→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 17293 | →¬→𝜑𝜓→¬→𝜑𝜓→𝜒¬→𝜑𝜓 | Modus ponens 17291, 17292 | |
| 17294 | →→¬→𝜑𝜓→¬→𝜑𝜓→𝜒¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗→𝜒¬→𝜑𝜓] into ax-2 | |
| 17295 | →→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→𝜒¬→𝜑𝜓 | Modus ponens 17293, 17294 | |
| 17296 | →→𝜒→¬→𝜑𝜓¬→𝜑𝜓→→𝜒¬→𝜑𝜓→𝜒¬→𝜑𝜓 | Subs [𝜑↗𝜒, 𝜓↗¬→𝜑𝜓, 𝜒↗¬→𝜑𝜓] into ax-2 | |
| 17297 | →→𝜒¬→𝜑𝜓→𝜒¬→𝜑𝜓 | Modus ponens 17290, 17296 | |
| 17298 | →→→𝜒¬→𝜑𝜓→𝜒¬→𝜑𝜓→¬→𝜑𝜓→→𝜒¬→𝜑𝜓→𝜒¬→𝜑𝜓 | Subs [𝜑↗→→𝜒¬→𝜑𝜓→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 17299 | →¬→𝜑𝜓→→𝜒¬→𝜑𝜓→𝜒¬→𝜑𝜓 | Modus ponens 17297, 17298 | |
| 17300 | →→¬→𝜑𝜓→→𝜒¬→𝜑𝜓→𝜒¬→𝜑𝜓→→¬→𝜑𝜓→𝜒¬→𝜑𝜓→¬→𝜑𝜓→𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→𝜒¬→𝜑𝜓, 𝜒↗→𝜒¬→𝜑𝜓] into ax-2 | |
| 17301 | →→¬→𝜑𝜓→𝜒¬→𝜑𝜓→¬→𝜑𝜓→𝜒¬→𝜑𝜓 | Modus ponens 17299, 17300 | |
| 17302 | →→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 17303 | →¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Modus ponens 17097, 17302 | |
| 17304 | →¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 17305 | →→¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗→¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜓↗¬¬¬→𝜒¬→𝜑𝜓] into ax-1 | |
| 17306 | →¬¬¬→𝜒¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Modus ponens 17304, 17305 | |
| 17307 | →→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗¬¬¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓, 𝜒↗→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓] into ax-2 | |
| 17308 | →→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Modus ponens 17306, 17307 | |
| 17309 | →¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Modus ponens 17100, 17308 | |
| 17310 | →→¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓, 𝜒↗¬→𝜒¬→𝜑𝜓] into ax-2 | |
| 17311 | →→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Modus ponens 17303, 17310 | |
| 17312 | →→→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗→→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜓↗¬¬¬→𝜒¬→𝜑𝜓] into ax-1 | |
| 17313 | →¬¬¬→𝜒¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Modus ponens 17311, 17312 | |
| 17314 | →→¬¬¬→𝜒¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗¬¬¬→𝜒¬→𝜑𝜓, 𝜓↗→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜒↗→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓] into ax-2 | |
| 17315 | →→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Modus ponens 17313, 17314 | |
| 17316 | →¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬¬¬→𝜒¬→𝜑𝜓] into ax-1 | |
| 17317 | →→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓 | Subs [𝜑↗→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 17318 | →¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓 | Modus ponens 17316, 17317 | |
| 17319 | →→¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓] into ax-2 | |
| 17320 | →→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓 | Modus ponens 17318, 17319 | |
| 17321 | →→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗¬¬¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗¬→𝜒¬→𝜑𝜓] into ax-2 | |
| 17322 | →→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Modus ponens 17309, 17321 | |
| 17323 | →→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 17324 | →¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Modus ponens 17322, 17323 | |
| 17325 | →→¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓, 𝜒↗→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓] into ax-2 | |
| 17326 | →→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Modus ponens 17324, 17325 | |
| 17327 | →¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Modus ponens 17316, 17326 | |
| 17328 | →→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1 | |
| 17329 | →¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓 | Modus ponens 17125, 17328 | |
| 17330 | →→¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓→→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜒↗→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓] into ax-2 | |
| 17331 | →→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓 | Modus ponens 17329, 17330 | |
| 17332 | →¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓 | Modus ponens 17327, 17331 | |
| 17333 | →→¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓→→¬→𝜑𝜓→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→𝜒¬→𝜑𝜓, 𝜒↗¬¬→𝜒¬→𝜑𝜓] into ax-2 | |
| 17334 | →→¬→𝜑𝜓→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓 | Modus ponens 17332, 17333 | |
| 17335 | →¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓 | Modus ponens 17291, 17334 | |
| 17336 | →→¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓] into ax-3 | |
| 17337 | →¬→𝜒¬→𝜑𝜓→𝜑𝜓 | Modus ponens 17335, 17336 | |
| 17338 | →→¬→𝜒¬→𝜑𝜓→𝜑𝜓→⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→¬→𝜒¬→𝜑𝜓→𝜑𝜓, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1 | |
| 17339 | →⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑𝜓 | Modus ponens 17337, 17338 | |
| 17340 | →→⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑𝜓→→⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑𝜓 | Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2 | |
| 17341 | →→⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑𝜓 | Modus ponens 17339, 17340 | |
| 17342 | →↔⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓↔¬→𝜒¬→𝜑𝜓⋀𝜒→𝜑𝜓 | Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓] into bicom1 | |
| 17343 | ↔¬→𝜒¬→𝜑𝜓⋀𝜒→𝜑𝜓 | Modus ponens 17045, 17342 | |
| 17344 | →↔¬→𝜒¬→𝜑𝜓⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓⋀𝜒→𝜑𝜓 | Subs [𝜑↗¬→𝜒¬→𝜑𝜓, 𝜓↗⋀𝜒→𝜑𝜓] into biimp | |
| 17345 | →¬→𝜒¬→𝜑𝜓⋀𝜒→𝜑𝜓 | Modus ponens 17343, 17344 | |
| 17346 | →→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→¬→𝜒¬→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓] into ax-1 | |
| 17347 | →¬→𝜒¬→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens pm5.31r, 17346 | |
| 17348 | →→¬→𝜒¬→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→→¬→𝜒¬→𝜑𝜓⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗¬→𝜒¬→𝜑𝜓, 𝜓↗⋀𝜒→𝜑𝜓, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2 | |
| 17349 | →→¬→𝜒¬→𝜑𝜓⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17347, 17348 | |
| 17350 | →𝜒→→𝜑𝜓¬→𝜒¬→𝜑𝜓 | Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜓] into pm3.2im | |
| 17351 | →→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 17352 | →→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17135, 17351 | |
| 17353 | →→→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓→→→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2 | |
| 17354 | →→→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17352, 17353 | |
| 17355 | →→→→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓→𝜒→→→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗→→→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗𝜒] into ax-1 | |
| 17356 | →𝜒→→→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17354, 17355 | |
| 17357 | →→𝜒→→→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜒→→𝜑𝜓¬→𝜒¬→𝜑𝜓→𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜒↗→→𝜑𝜓→𝜑⋀𝜒𝜓] into ax-2 | |
| 17358 | →→𝜒→→𝜑𝜓¬→𝜒¬→𝜑𝜓→𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17356, 17357 | |
| 17359 | →→→𝜑𝜓→𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→𝜒→𝜑𝜓, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1 | |
| 17360 | →⋀𝜒→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓 | Modus ponens 39, 17359 | |
| 17361 | →→⋀𝜒→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓→→⋀𝜒→𝜑𝜓→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜒→𝜑𝜓 | Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜒→𝜑𝜓] into ax-2 | |
| 17362 | →→⋀𝜒→𝜑𝜓→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜒→𝜑𝜓 | Modus ponens 17360, 17361 | |
| 17363 | →⋀𝜒→𝜑𝜓→𝜒→𝜑𝜓 | Modus ponens 16967, 17362 | |
| 17364 | →→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→⋀𝜒→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓 | Subs [𝜑↗→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1 | |
| 17365 | →⋀𝜒→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓 | Modus ponens 17033, 17364 | |
| 17366 | →→⋀𝜒→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→→⋀𝜒→𝜑𝜓→𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓 | Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗→𝜒→𝜑𝜓, 𝜒↗→𝜒→𝜑⋀𝜒𝜓] into ax-2 | |
| 17367 | →→⋀𝜒→𝜑𝜓→𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓 | Modus ponens 17365, 17366 | |
| 17368 | →⋀𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓 | Modus ponens 17363, 17367 | |
| 17369 | →𝜒→⋀𝜒→𝜑𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1 | |
| 17370 | →→𝜒→⋀𝜒→𝜑𝜓𝜒→𝜒→𝜒→⋀𝜒→𝜑𝜓𝜒 | Subs [𝜑↗→𝜒→⋀𝜒→𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1 | |
| 17371 | →𝜒→𝜒→⋀𝜒→𝜑𝜓𝜒 | Modus ponens 17369, 17370 | |
| 17372 | →→𝜒→𝜒→⋀𝜒→𝜑𝜓𝜒→→𝜒𝜒→𝜒→⋀𝜒→𝜑𝜓𝜒 | Subs [𝜑↗𝜒, 𝜓↗𝜒, 𝜒↗→⋀𝜒→𝜑𝜓𝜒] into ax-2 | |
| 17373 | →→𝜒𝜒→𝜒→⋀𝜒→𝜑𝜓𝜒 | Modus ponens 17371, 17372 | |
| 17374 | →→⋀𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2 | |
| 17375 | →→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17368, 17374 | |
| 17376 | →→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→𝜒→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗𝜒] into ax-1 | |
| 17377 | →𝜒→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17375, 17376 | |
| 17378 | →→𝜒→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜒→⋀𝜒→𝜑𝜓𝜒→𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗𝜒, 𝜓↗→⋀𝜒→𝜑𝜓𝜒, 𝜒↗→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓] into ax-2 | |
| 17379 | →→𝜒→⋀𝜒→𝜑𝜓𝜒→𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17377, 17378 | |
| 17380 | →𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17369, 17379 | |
| 17381 | →→𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→⋀𝜒→𝜑𝜓→𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗→𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1 | |
| 17382 | →⋀𝜒→𝜑𝜓→𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17380, 17381 | |
| 17383 | →→⋀𝜒→𝜑𝜓→𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓] into ax-2 | |
| 17384 | →→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17382, 17383 | |
| 17385 | →⋀𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 16968, 17384 | |
| 17386 | →⋀𝜒→𝜑𝜓⋀𝜒→𝜑𝜓 | Subs [𝜑↗⋀𝜒→𝜑𝜓] into id | |
| 17387 | →→⋀𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→→⋀𝜒→𝜑𝜓⋀𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓 | Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗⋀𝜒→𝜑𝜓, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2 | |
| 17388 | →→⋀𝜒→𝜑𝜓⋀𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓 | Modus ponens 17385, 17387 | |
| 17389 | ↔→⋀𝜓𝜒¬𝜑→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜑] into con2b | |
| 17390 | →↔→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→𝜑¬⋀𝜓𝜒, 𝜓↗→⋀𝜑𝜓¬𝜒] into biimp | |
| 17391 | →↔→⋀𝜓𝜒¬𝜑→𝜑¬⋀𝜓𝜒→→⋀𝜓𝜒¬𝜑→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→⋀𝜓𝜒¬𝜑, 𝜓↗→𝜑¬⋀𝜓𝜒] into biimp | |
| 17392 | →→⋀𝜓𝜒¬𝜑→𝜑¬⋀𝜓𝜒 | Modus ponens 17389, 17391 | |
| 17393 | →→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒→→⋀𝜓𝜒¬𝜑→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒, 𝜓↗→⋀𝜓𝜒¬𝜑] into ax-1 | |
| 17394 | →→⋀𝜓𝜒¬𝜑→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒 | Modus ponens 16961, 17393 | |
| 17395 | →→→⋀𝜓𝜒¬𝜑→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒→→→⋀𝜓𝜒¬𝜑→𝜑¬⋀𝜓𝜒→→⋀𝜓𝜒¬𝜑→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→⋀𝜓𝜒¬𝜑, 𝜓↗→𝜑¬⋀𝜓𝜒, 𝜒↗→⋀𝜑𝜓¬𝜒] into ax-2 | |
| 17396 | →→→⋀𝜓𝜒¬𝜑→𝜑¬⋀𝜓𝜒→→⋀𝜓𝜒¬𝜑→⋀𝜑𝜓¬𝜒 | Modus ponens 17394, 17395 | |
| 17397 | →→⋀𝜓𝜒¬𝜑→⋀𝜑𝜓¬𝜒 | Modus ponens 17392, 17396 | |
| 17398 | →↔→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒↔→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→𝜑¬⋀𝜓𝜒, 𝜓↗→⋀𝜑𝜓¬𝜒] into bicom1 | |
| 17399 | →↔→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒→→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒 | Subs [𝜑↗→⋀𝜑𝜓¬𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒] into biimp | |
| 17400 | →↔→⋀𝜓𝜒¬𝜑→𝜑¬⋀𝜓𝜒↔→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗→⋀𝜓𝜒¬𝜑, 𝜓↗→𝜑¬⋀𝜓𝜒] into bicom1 | |
| 17401 | ↔→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑 | Modus ponens 17389, 17400 | |
| 17402 | →↔→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑→→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗→𝜑¬⋀𝜓𝜒, 𝜓↗→⋀𝜓𝜒¬𝜑] into biimp | |
| 17403 | →→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑 | Modus ponens 17401, 17402 | |
| 17404 | →→→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑→→⋀𝜑𝜓¬𝜒→→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗→→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑, 𝜓↗→⋀𝜑𝜓¬𝜒] into ax-1 | |
| 17405 | →→⋀𝜑𝜓¬𝜒→→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑 | Modus ponens 17403, 17404 | |
| 17406 | →→→⋀𝜑𝜓¬𝜒→→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑→→→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒→→⋀𝜑𝜓¬𝜒→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗→⋀𝜑𝜓¬𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒, 𝜒↗→⋀𝜓𝜒¬𝜑] into ax-2 | |
| 17407 | →→→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒→→⋀𝜑𝜓¬𝜒→⋀𝜓𝜒¬𝜑 | Modus ponens 17405, 17406 | |
| 17408 | →→⋀𝜑𝜓¬𝜒→⋀𝜓𝜒¬𝜑 | Modus ponens 16948, 17407 | |
| 17409 | →→→⋀𝜓𝜒¬𝜑→⋀𝜑𝜓¬𝜒→→→⋀𝜑𝜓¬𝜒→⋀𝜓𝜒¬𝜑↔→⋀𝜓𝜒¬𝜑→⋀𝜑𝜓¬𝜒 | Subs [𝜑↗→⋀𝜓𝜒¬𝜑, 𝜓↗→⋀𝜑𝜓¬𝜒] into impbi | |
| 17410 | →→→⋀𝜑𝜓¬𝜒→⋀𝜓𝜒¬𝜑↔→⋀𝜓𝜒¬𝜑→⋀𝜑𝜓¬𝜒 | Modus ponens 17397, 17409 | |
| 17411 | ↔→⋀𝜓𝜒¬𝜑→⋀𝜑𝜓¬𝜒 | Modus ponens 17408, 17410 | |
| 17412 | →↔→⋀𝜓𝜒¬𝜑→⋀𝜑𝜓¬𝜒↔→⋀𝜑𝜓¬𝜒→⋀𝜓𝜒¬𝜑 | Subs [𝜑↗→⋀𝜓𝜒¬𝜑, 𝜓↗→⋀𝜑𝜓¬𝜒] into bicom1 | |
| 17413 | ↔→⋀𝜑𝜓¬𝜒→⋀𝜓𝜒¬𝜑 | Modus ponens 17411, 17412 | pm4.15 |
| 17414 | ↔→↔𝜑𝜓↔𝜑𝜓↔⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓 | Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into pm5.32 | |
| 17415 | →↔→↔𝜑𝜓↔𝜑𝜓↔⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓→→↔𝜑𝜓↔𝜑𝜓↔⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓 | Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜓, 𝜓↗↔⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓] into biimp | |
| 17416 | →→↔𝜑𝜓↔𝜑𝜓↔⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓 | Modus ponens 17414, 17415 | |
| 17417 | ↔⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓 | Modus ponens 1651, 17416 | |
| 17418 | ↔⋀𝜑↔𝜑𝜓⋀↔𝜑𝜓𝜑 | Subs [𝜓↗↔𝜑𝜓] into ancom | |
| 17419 | ↔⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜓 | Subs [𝜑↗𝜓, 𝜓↗↔𝜑𝜓] into ancom | |
| 17420 | →↔⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜓↔⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓 | Subs [𝜑↗⋀𝜓↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜓] into bicom1 | |
| 17421 | ↔⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓 | Modus ponens 17419, 17420 | |
| 17422 | →↔⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓 | Subs [𝜑↗⋀↔𝜑𝜓𝜓, 𝜓↗⋀𝜓↔𝜑𝜓] into biimp | |
| 17423 | →⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓 | Modus ponens 17421, 17422 | |
| 17424 | →↔⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓→⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓 | Subs [𝜑↗⋀↔𝜑𝜓𝜑, 𝜓↗⋀↔𝜑𝜓𝜓] into biimp | |
| 17425 | →⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓 | Modus ponens 17417, 17424 | |
| 17426 | →→⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜑→⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓 | Subs [𝜑↗→⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜑] into ax-1 | |
| 17427 | →⋀↔𝜑𝜓𝜑→⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓 | Modus ponens 17423, 17426 | |
| 17428 | →→⋀↔𝜑𝜓𝜑→⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓→→⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓 | Subs [𝜑↗⋀↔𝜑𝜓𝜑, 𝜓↗⋀↔𝜑𝜓𝜓, 𝜒↗⋀𝜓↔𝜑𝜓] into ax-2 | |
| 17429 | →→⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓 | Modus ponens 17427, 17428 | |
| 17430 | →⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓 | Modus ponens 17425, 17429 | |
| 17431 | →↔⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓↔⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜓 | Subs [𝜑↗⋀↔𝜑𝜓𝜓, 𝜓↗⋀𝜓↔𝜑𝜓] into bicom1 | |
| 17432 | →↔⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜓→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜓 | Subs [𝜑↗⋀𝜓↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜓] into biimp | |
| 17433 | →⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜓 | Modus ponens 17419, 17432 | |
| 17434 | →↔⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓↔⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑 | Subs [𝜑↗⋀↔𝜑𝜓𝜑, 𝜓↗⋀↔𝜑𝜓𝜓] into bicom1 | |
| 17435 | ↔⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑 | Modus ponens 17417, 17434 | |
| 17436 | →↔⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑→⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑 | Subs [𝜑↗⋀↔𝜑𝜓𝜓, 𝜓↗⋀↔𝜑𝜓𝜑] into biimp | |
| 17437 | →⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑 | Modus ponens 17435, 17436 | |
| 17438 | →→⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑→⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑 | Subs [𝜑↗→⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑, 𝜓↗⋀𝜓↔𝜑𝜓] into ax-1 | |
| 17439 | →⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑 | Modus ponens 17437, 17438 | |
| 17440 | →→⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑→→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜓→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑 | Subs [𝜑↗⋀𝜓↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜓, 𝜒↗⋀↔𝜑𝜓𝜑] into ax-2 | |
| 17441 | →→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜓→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑 | Modus ponens 17439, 17440 | |
| 17442 | →⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑 | Modus ponens 17433, 17441 | |
| 17443 | →→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓→→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑↔⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓 | Subs [𝜑↗⋀↔𝜑𝜓𝜑, 𝜓↗⋀𝜓↔𝜑𝜓] into impbi | |
| 17444 | →→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑↔⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓 | Modus ponens 17430, 17443 | |
| 17445 | ↔⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓 | Modus ponens 17442, 17444 | |
| 17446 | →↔⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓 | Subs [𝜑↗⋀↔𝜑𝜓𝜑, 𝜓↗⋀𝜓↔𝜑𝜓] into biimp | |
| 17447 | →↔⋀𝜑↔𝜑𝜓⋀↔𝜑𝜓𝜑→⋀𝜑↔𝜑𝜓⋀↔𝜑𝜓𝜑 | Subs [𝜑↗⋀𝜑↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜑] into biimp | |
| 17448 | →⋀𝜑↔𝜑𝜓⋀↔𝜑𝜓𝜑 | Modus ponens 17418, 17447 | |
| 17449 | →→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓→⋀𝜑↔𝜑𝜓→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓 | Subs [𝜑↗→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓, 𝜓↗⋀𝜑↔𝜑𝜓] into ax-1 | |
| 17450 | →⋀𝜑↔𝜑𝜓→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓 | Modus ponens 17430, 17449 | |
| 17451 | →→⋀𝜑↔𝜑𝜓→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓→→⋀𝜑↔𝜑𝜓⋀↔𝜑𝜓𝜑→⋀𝜑↔𝜑𝜓⋀𝜓↔𝜑𝜓 | Subs [𝜑↗⋀𝜑↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜑, 𝜒↗⋀𝜓↔𝜑𝜓] into ax-2 | |
| 17452 | →→⋀𝜑↔𝜑𝜓⋀↔𝜑𝜓𝜑→⋀𝜑↔𝜑𝜓⋀𝜓↔𝜑𝜓 | Modus ponens 17450, 17451 | |
| 17453 | →⋀𝜑↔𝜑𝜓⋀𝜓↔𝜑𝜓 | Modus ponens 17448, 17452 | |
| 17454 | →↔⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓↔⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑 | Subs [𝜑↗⋀↔𝜑𝜓𝜑, 𝜓↗⋀𝜓↔𝜑𝜓] into bicom1 | |
| 17455 | ↔⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑 | Modus ponens 17445, 17454 | |
| 17456 | →↔⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑 | Subs [𝜑↗⋀𝜓↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜑] into biimp | |
| 17457 | →↔⋀𝜑↔𝜑𝜓⋀↔𝜑𝜓𝜑↔⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓 | Subs [𝜑↗⋀𝜑↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜑] into bicom1 | |
| 17458 | ↔⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓 | Modus ponens 17418, 17457 | |
| 17459 | →↔⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓→⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓 | Subs [𝜑↗⋀↔𝜑𝜓𝜑, 𝜓↗⋀𝜑↔𝜑𝜓] into biimp | |
| 17460 | →⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓 | Modus ponens 17458, 17459 | |
| 17461 | →→⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓→⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓 | Subs [𝜑↗→⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓, 𝜓↗⋀𝜓↔𝜑𝜓] into ax-1 | |
| 17462 | →⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓 | Modus ponens 17460, 17461 | |
| 17463 | →→⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓→→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑→⋀𝜓↔𝜑𝜓⋀𝜑↔𝜑𝜓 | Subs [𝜑↗⋀𝜓↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜑, 𝜒↗⋀𝜑↔𝜑𝜓] into ax-2 | |
| 17464 | →→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑→⋀𝜓↔𝜑𝜓⋀𝜑↔𝜑𝜓 | Modus ponens 17462, 17463 | |
| 17465 | →⋀𝜓↔𝜑𝜓⋀𝜑↔𝜑𝜓 | Modus ponens 17442, 17464 | |
| 17466 | →→⋀𝜑↔𝜑𝜓⋀𝜓↔𝜑𝜓→→⋀𝜓↔𝜑𝜓⋀𝜑↔𝜑𝜓↔⋀𝜑↔𝜑𝜓⋀𝜓↔𝜑𝜓 | Subs [𝜑↗⋀𝜑↔𝜑𝜓, 𝜓↗⋀𝜓↔𝜑𝜓] into impbi | |
| 17467 | →→⋀𝜓↔𝜑𝜓⋀𝜑↔𝜑𝜓↔⋀𝜑↔𝜑𝜓⋀𝜓↔𝜑𝜓 | Modus ponens 17453, 17466 | |
| 17468 | ↔⋀𝜑↔𝜑𝜓⋀𝜓↔𝜑𝜓 | Modus ponens 17465, 17467 | pm5.36 |
| 17469 | ↔⋀𝜑𝜓¬¬⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓] into notnotb | |
| 17470 | →↔⋀𝜑𝜓¬¬⋀𝜑𝜓↔¬¬⋀𝜑𝜓⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬¬⋀𝜑𝜓] into bicom1 | |
| 17471 | ↔¬¬⋀𝜑𝜓⋀𝜑𝜓 | Modus ponens 17469, 17470 | |
| 17472 | →↔¬¬⋀𝜑𝜓⋀𝜑𝜓→𝜑↔¬¬⋀𝜑𝜓⋀𝜑𝜓 | Subs [𝜑↗↔¬¬⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 17473 | →𝜑↔¬¬⋀𝜑𝜓⋀𝜑𝜓 | Modus ponens 17471, 17472 | |
| 17474 | ↔→𝜑↔¬¬⋀𝜑𝜓⋀𝜑𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓 | Subs [𝜓↗¬¬⋀𝜑𝜓, 𝜒↗⋀𝜑𝜓] into pm5.74 | |
| 17475 | →↔→𝜑↔¬¬⋀𝜑𝜓⋀𝜑𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑↔¬¬⋀𝜑𝜓⋀𝜑𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓 | Subs [𝜑↗→𝜑↔¬¬⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗↔→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓] into biimp | |
| 17476 | →→𝜑↔¬¬⋀𝜑𝜓⋀𝜑𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓 | Modus ponens 17474, 17475 | |
| 17477 | ↔→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓 | Modus ponens 17473, 17476 | |
| 17478 | ↔→𝜑↔⋀𝜑𝜓𝜓↔→𝜑⋀𝜑𝜓→𝜑𝜓 | Subs [𝜓↗⋀𝜑𝜓, 𝜒↗𝜓] into pm5.74 | |
| 17479 | →↔→𝜑↔⋀𝜑𝜓𝜓↔→𝜑⋀𝜑𝜓→𝜑𝜓→→𝜑↔⋀𝜑𝜓𝜓↔→𝜑⋀𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑↔⋀𝜑𝜓𝜓, 𝜓↗↔→𝜑⋀𝜑𝜓→𝜑𝜓] into biimp | |
| 17480 | →→𝜑↔⋀𝜑𝜓𝜓↔→𝜑⋀𝜑𝜓→𝜑𝜓 | Modus ponens 17478, 17479 | |
| 17481 | →↔→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓 | Subs [𝜑↗→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓] into biimp | |
| 17482 | →→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓 | Modus ponens 17477, 17481 | |
| 17483 | →→→𝜑⋀𝜑𝜓→𝜑𝜓→→𝜑¬¬⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→→𝜑⋀𝜑𝜓→𝜑𝜓, 𝜓↗→𝜑¬¬⋀𝜑𝜓] into ax-1 | |
| 17484 | →→𝜑¬¬⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓 | Modus ponens 6193, 17483 | |
| 17485 | →→→𝜑¬¬⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓→→→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑¬¬⋀𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2 | |
| 17486 | →→→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑¬¬⋀𝜑𝜓→𝜑𝜓 | Modus ponens 17484, 17485 | |
| 17487 | →→𝜑¬¬⋀𝜑𝜓→𝜑𝜓 | Modus ponens 17482, 17486 | |
| 17488 | →↔→𝜑⋀𝜑𝜓→𝜑𝜓↔→𝜑𝜓→𝜑⋀𝜑𝜓 | Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into bicom1 | |
| 17489 | →↔→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓↔→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓 | Subs [𝜑↗→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓] into bicom1 | |
| 17490 | ↔→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓 | Modus ponens 17477, 17489 | |
| 17491 | →↔→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓 | Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗→𝜑¬¬⋀𝜑𝜓] into biimp | |
| 17492 | →→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓 | Modus ponens 17490, 17491 | |
| 17493 | →→→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓 | Subs [𝜑↗→→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1 | |
| 17494 | →→𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓 | Modus ponens 17492, 17493 | |
| 17495 | →→→𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓→→→𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓, 𝜒↗→𝜑¬¬⋀𝜑𝜓] into ax-2 | |
| 17496 | →→→𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓 | Modus ponens 17494, 17495 | |
| 17497 | →→𝜑𝜓→𝜑¬¬⋀𝜑𝜓 | Modus ponens ancl, 17496 | |
| 17498 | →→→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into impbi | |
| 17499 | →→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓 | Modus ponens 17487, 17498 | |
| 17500 | ↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓 | Modus ponens 17497, 17499 | |
| 17501 | ↔→𝜑↔¬¬⋀𝜑𝜓𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓 | Subs [𝜓↗¬¬⋀𝜑𝜓, 𝜒↗𝜓] into pm5.74 | |
| 17502 | →↔→𝜑↔¬¬⋀𝜑𝜓𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓↔↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→𝜑↔¬¬⋀𝜑𝜓𝜓 | Subs [𝜑↗→𝜑↔¬¬⋀𝜑𝜓𝜓, 𝜓↗↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓] into bicom1 | |
| 17503 | ↔↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→𝜑↔¬¬⋀𝜑𝜓𝜓 | Modus ponens 17501, 17502 | |
| 17504 | →↔↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→𝜑↔¬¬⋀𝜑𝜓𝜓→↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→𝜑↔¬¬⋀𝜑𝜓𝜓 | Subs [𝜑↗↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓, 𝜓↗→𝜑↔¬¬⋀𝜑𝜓𝜓] into biimp | |
| 17505 | →↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→𝜑↔¬¬⋀𝜑𝜓𝜓 | Modus ponens 17503, 17504 | |
| 17506 | →𝜑↔¬¬⋀𝜑𝜓𝜓 | Modus ponens 17500, 17505 | |
| 17507 | →↔→𝜑↔¬¬⋀𝜑𝜓𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→→𝜑↔¬¬⋀𝜑𝜓𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑↔¬¬⋀𝜑𝜓𝜓, 𝜓↗↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓] into biimp | |
| 17508 | →→𝜑↔¬¬⋀𝜑𝜓𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓 | Modus ponens 17501, 17507 | |
| 17509 | →↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→→𝜑¬¬⋀𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into biimp | |
| 17510 | →→→𝜑𝜓→𝜑¬¬𝜓→→𝜑¬¬⋀𝜑𝜓→→𝜑𝜓→𝜑¬¬𝜓 | Subs [𝜑↗→→𝜑𝜓→𝜑¬¬𝜓, 𝜓↗→𝜑¬¬⋀𝜑𝜓] into ax-1 | |
| 17511 | →→𝜑¬¬⋀𝜑𝜓→→𝜑𝜓→𝜑¬¬𝜓 | Modus ponens 4585, 17510 | |
| 17512 | →→→𝜑¬¬⋀𝜑𝜓→→𝜑𝜓→𝜑¬¬𝜓→→→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓 | Subs [𝜑↗→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑¬¬𝜓] into ax-2 | |
| 17513 | →→→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓 | Modus ponens 17511, 17512 | |
| 17514 | →→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓 | Modus ponens 17487, 17513 | |
| 17515 | →↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓↔→𝜑𝜓→𝜑¬¬⋀𝜑𝜓 | Subs [𝜑↗→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into bicom1 | |
| 17516 | ↔→𝜑𝜓→𝜑¬¬⋀𝜑𝜓 | Modus ponens 17500, 17515 | |
| 17517 | →↔→𝜑𝜓→𝜑¬¬⋀𝜑𝜓→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓 | Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑¬¬⋀𝜑𝜓] into biimp | |
| 17518 | →→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓→→𝜑¬¬𝜓→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓 | Subs [𝜑↗→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑¬¬𝜓] into ax-1 | |
| 17519 | →→𝜑¬¬𝜓→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓 | Modus ponens 17497, 17518 | |
| 17520 | →→→𝜑¬¬𝜓→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓→→→𝜑¬¬𝜓→𝜑𝜓→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓 | Subs [𝜑↗→𝜑¬¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑¬¬⋀𝜑𝜓] into ax-2 | |
| 17521 | →→→𝜑¬¬𝜓→𝜑𝜓→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓 | Modus ponens 17519, 17520 | |
| 17522 | →→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓 | Modus ponens 4598, 17521 | |
| 17523 | →→→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓→→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓 | Subs [𝜑↗→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑¬¬𝜓] into impbi | |
| 17524 | →→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓 | Modus ponens 17514, 17523 | |
| 17525 | ↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓 | Modus ponens 17522, 17524 | |
| 17526 | ↔→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓 | Subs [𝜓↗¬¬⋀𝜑𝜓, 𝜒↗¬¬𝜓] into pm5.74 | |
| 17527 | →↔→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓↔↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓 | Subs [𝜑↗→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓, 𝜓↗↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓] into bicom1 | |
| 17528 | ↔↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓 | Modus ponens 17526, 17527 | |
| 17529 | →↔↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓→↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓 | Subs [𝜑↗↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓, 𝜓↗→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓] into biimp | |
| 17530 | →↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓 | Modus ponens 17528, 17529 | |
| 17531 | →𝜑↔¬¬⋀𝜑𝜓¬¬𝜓 | Modus ponens 17525, 17530 | |
| 17532 | ↔↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓 | Subs [𝜑↗¬¬⋀𝜑𝜓, 𝜓↗¬¬𝜓] into bicom | |
| 17533 | →↔↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓→↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓 | Subs [𝜑↗↔¬¬⋀𝜑𝜓¬¬𝜓, 𝜓↗↔¬¬𝜓¬¬⋀𝜑𝜓] into biimp | |
| 17534 | →↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓 | Modus ponens 17532, 17533 | |
| 17535 | →→↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓→𝜑→↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓 | Subs [𝜑↗→↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 17536 | →𝜑→↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓 | Modus ponens 17534, 17535 | |
| 17537 | →→𝜑→↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓→→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓→𝜑↔¬¬𝜓¬¬⋀𝜑𝜓 | Subs [𝜓↗↔¬¬⋀𝜑𝜓¬¬𝜓, 𝜒↗↔¬¬𝜓¬¬⋀𝜑𝜓] into ax-2 | |
| 17538 | →→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓→𝜑↔¬¬𝜓¬¬⋀𝜑𝜓 | Modus ponens 17536, 17537 | |
| 17539 | →𝜑↔¬¬𝜓¬¬⋀𝜑𝜓 | Modus ponens 17531, 17538 | |
| 17540 | →↔¬¬𝜓¬¬⋀𝜑𝜓→¬¬𝜓¬¬⋀𝜑𝜓 | Subs [𝜑↗¬¬𝜓, 𝜓↗¬¬⋀𝜑𝜓] into biimp | |
| 17541 | →→↔¬¬𝜓¬¬⋀𝜑𝜓→¬¬𝜓¬¬⋀𝜑𝜓→𝜑→↔¬¬𝜓¬¬⋀𝜑𝜓→¬¬𝜓¬¬⋀𝜑𝜓 | Subs [𝜑↗→↔¬¬𝜓¬¬⋀𝜑𝜓→¬¬𝜓¬¬⋀𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 17542 | →𝜑→↔¬¬𝜓¬¬⋀𝜑𝜓→¬¬𝜓¬¬⋀𝜑𝜓 | Modus ponens 17540, 17541 | |
| 17543 | →→𝜑→↔¬¬𝜓¬¬⋀𝜑𝜓→¬¬𝜓¬¬⋀𝜑𝜓→→𝜑↔¬¬𝜓¬¬⋀𝜑𝜓→𝜑→¬¬𝜓¬¬⋀𝜑𝜓 | Subs [𝜓↗↔¬¬𝜓¬¬⋀𝜑𝜓, 𝜒↗→¬¬𝜓¬¬⋀𝜑𝜓] into ax-2 | |
| 17544 | →→𝜑↔¬¬𝜓¬¬⋀𝜑𝜓→𝜑→¬¬𝜓¬¬⋀𝜑𝜓 | Modus ponens 17542, 17543 | |
| 17545 | →𝜑→¬¬𝜓¬¬⋀𝜑𝜓 | Modus ponens 17539, 17544 | |
| 17546 | →¬¬𝜓→𝜑¬¬𝜓 | Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 17547 | →→¬¬𝜓→𝜑¬¬𝜓→¬¬𝜓→¬¬𝜓→𝜑¬¬𝜓 | Subs [𝜑↗→¬¬𝜓→𝜑¬¬𝜓, 𝜓↗¬¬𝜓] into ax-1 | |
| 17548 | →¬¬𝜓→¬¬𝜓→𝜑¬¬𝜓 | Modus ponens 17546, 17547 | |
| 17549 | →→¬¬𝜓→¬¬𝜓→𝜑¬¬𝜓→→¬¬𝜓¬¬𝜓→¬¬𝜓→𝜑¬¬𝜓 | Subs [𝜑↗¬¬𝜓, 𝜓↗¬¬𝜓, 𝜒↗→𝜑¬¬𝜓] into ax-2 | |
| 17550 | →→¬¬𝜓¬¬𝜓→¬¬𝜓→𝜑¬¬𝜓 | Modus ponens 17548, 17549 | |
| 17551 | →→𝜑→¬¬𝜓¬¬⋀𝜑𝜓→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓 | Subs [𝜓↗¬¬𝜓, 𝜒↗¬¬⋀𝜑𝜓] into ax-2 | |
| 17552 | →→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓→¬¬𝜓→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓 | Subs [𝜑↗→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓, 𝜓↗¬¬𝜓] into ax-1 | |
| 17553 | →¬¬𝜓→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓 | Modus ponens 17522, 17552 | |
| 17554 | →→¬¬𝜓→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓→→¬¬𝜓→𝜑¬¬𝜓→¬¬𝜓→𝜑¬¬⋀𝜑𝜓 | Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜑¬¬𝜓, 𝜒↗→𝜑¬¬⋀𝜑𝜓] into ax-2 | |
| 17555 | →→¬¬𝜓→𝜑¬¬𝜓→¬¬𝜓→𝜑¬¬⋀𝜑𝜓 | Modus ponens 17553, 17554 | |
| 17556 | →¬¬𝜓→𝜑¬¬⋀𝜑𝜓 | Modus ponens 17546, 17555 | |
| 17557 | →→¬¬𝜓→𝜑¬¬⋀𝜑𝜓→→¬¬𝜓𝜑→¬¬𝜓¬¬⋀𝜑𝜓 | Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑, 𝜒↗¬¬⋀𝜑𝜓] into ax-2 | |
| 17558 | →→¬¬𝜓𝜑→¬¬𝜓¬¬⋀𝜑𝜓 | Modus ponens 17556, 17557 | |
| 17559 | →→→¬¬𝜓𝜑→¬¬𝜓¬¬⋀𝜑𝜓→𝜑→→¬¬𝜓𝜑→¬¬𝜓¬¬⋀𝜑𝜓 | Subs [𝜑↗→→¬¬𝜓𝜑→¬¬𝜓¬¬⋀𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 17560 | →𝜑→→¬¬𝜓𝜑→¬¬𝜓¬¬⋀𝜑𝜓 | Modus ponens 17558, 17559 | |
| 17561 | →→𝜑→→¬¬𝜓𝜑→¬¬𝜓¬¬⋀𝜑𝜓→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓¬¬⋀𝜑𝜓 | Subs [𝜓↗→¬¬𝜓𝜑, 𝜒↗→¬¬𝜓¬¬⋀𝜑𝜓] into ax-2 | |
| 17562 | →→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓¬¬⋀𝜑𝜓 | Modus ponens 17560, 17561 | |
| 17563 | →→¬¬𝜓¬¬⋀𝜑𝜓→¬⋀𝜑𝜓¬𝜓 | Subs [𝜑↗¬𝜓, 𝜓↗¬⋀𝜑𝜓] into ax-3 | |
| 17564 | →→→¬¬𝜓¬¬⋀𝜑𝜓→¬⋀𝜑𝜓¬𝜓→𝜑→→¬¬𝜓¬¬⋀𝜑𝜓→¬⋀𝜑𝜓¬𝜓 | Subs [𝜑↗→→¬¬𝜓¬¬⋀𝜑𝜓→¬⋀𝜑𝜓¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 17565 | →𝜑→→¬¬𝜓¬¬⋀𝜑𝜓→¬⋀𝜑𝜓¬𝜓 | Modus ponens 17563, 17564 | |
| 17566 | →→𝜑→→¬¬𝜓¬¬⋀𝜑𝜓→¬⋀𝜑𝜓¬𝜓→→𝜑→¬¬𝜓¬¬⋀𝜑𝜓→𝜑→¬⋀𝜑𝜓¬𝜓 | Subs [𝜓↗→¬¬𝜓¬¬⋀𝜑𝜓, 𝜒↗→¬⋀𝜑𝜓¬𝜓] into ax-2 | |
| 17567 | →→𝜑→¬¬𝜓¬¬⋀𝜑𝜓→𝜑→¬⋀𝜑𝜓¬𝜓 | Modus ponens 17565, 17566 | |
| 17568 | →𝜑→¬⋀𝜑𝜓¬𝜓 | Modus ponens 17545, 17567 | |
| 17569 | →↔¬¬⋀𝜑𝜓¬¬𝜓→¬¬⋀𝜑𝜓¬¬𝜓 | Subs [𝜑↗¬¬⋀𝜑𝜓, 𝜓↗¬¬𝜓] into biimp | |
| 17570 | →→↔¬¬⋀𝜑𝜓¬¬𝜓→¬¬⋀𝜑𝜓¬¬𝜓→𝜑→↔¬¬⋀𝜑𝜓¬¬𝜓→¬¬⋀𝜑𝜓¬¬𝜓 | Subs [𝜑↗→↔¬¬⋀𝜑𝜓¬¬𝜓→¬¬⋀𝜑𝜓¬¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 17571 | →𝜑→↔¬¬⋀𝜑𝜓¬¬𝜓→¬¬⋀𝜑𝜓¬¬𝜓 | Modus ponens 17569, 17570 | |
| 17572 | →→𝜑→↔¬¬⋀𝜑𝜓¬¬𝜓→¬¬⋀𝜑𝜓¬¬𝜓→→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓→𝜑→¬¬⋀𝜑𝜓¬¬𝜓 | Subs [𝜓↗↔¬¬⋀𝜑𝜓¬¬𝜓, 𝜒↗→¬¬⋀𝜑𝜓¬¬𝜓] into ax-2 | |
| 17573 | →→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓→𝜑→¬¬⋀𝜑𝜓¬¬𝜓 | Modus ponens 17571, 17572 | |
| 17574 | →𝜑→¬¬⋀𝜑𝜓¬¬𝜓 | Modus ponens 17531, 17573 | |
| 17575 | →→¬¬⋀𝜑𝜓¬¬𝜓→¬𝜓¬⋀𝜑𝜓 | Subs [𝜑↗¬⋀𝜑𝜓, 𝜓↗¬𝜓] into ax-3 | |
| 17576 | →→→¬¬⋀𝜑𝜓¬¬𝜓→¬𝜓¬⋀𝜑𝜓→𝜑→→¬¬⋀𝜑𝜓¬¬𝜓→¬𝜓¬⋀𝜑𝜓 | Subs [𝜑↗→→¬¬⋀𝜑𝜓¬¬𝜓→¬𝜓¬⋀𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 17577 | →𝜑→→¬¬⋀𝜑𝜓¬¬𝜓→¬𝜓¬⋀𝜑𝜓 | Modus ponens 17575, 17576 | |
| 17578 | →→𝜑→→¬¬⋀𝜑𝜓¬¬𝜓→¬𝜓¬⋀𝜑𝜓→→𝜑→¬¬⋀𝜑𝜓¬¬𝜓→𝜑→¬𝜓¬⋀𝜑𝜓 | Subs [𝜓↗→¬¬⋀𝜑𝜓¬¬𝜓, 𝜒↗→¬𝜓¬⋀𝜑𝜓] into ax-2 | |
| 17579 | →→𝜑→¬¬⋀𝜑𝜓¬¬𝜓→𝜑→¬𝜓¬⋀𝜑𝜓 | Modus ponens 17577, 17578 | |
| 17580 | →𝜑→¬𝜓¬⋀𝜑𝜓 | Modus ponens 17574, 17579 | |
| 17581 | →→¬⋀𝜑𝜓¬𝜓→→¬𝜓¬⋀𝜑𝜓↔¬⋀𝜑𝜓¬𝜓 | Subs [𝜑↗¬⋀𝜑𝜓, 𝜓↗¬𝜓] into impbi | |
| 17582 | →→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓 | Subs [𝜑↗→¬𝜓¬⋀𝜑𝜓, 𝜓↗→¬⋀𝜑𝜓¬𝜓] into ax-1 | |
| 17583 | →→→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→𝜑→→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓 | Subs [𝜑↗→→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 17584 | →𝜑→→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓 | Modus ponens 17582, 17583 | |
| 17585 | →→𝜑→→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→→𝜑→¬𝜓¬⋀𝜑𝜓→𝜑→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓 | Subs [𝜓↗→¬𝜓¬⋀𝜑𝜓, 𝜒↗→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓] into ax-2 | |
| 17586 | →→𝜑→¬𝜓¬⋀𝜑𝜓→𝜑→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓 | Modus ponens 17584, 17585 | |
| 17587 | →𝜑→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓 | Modus ponens 17580, 17586 | |
| 17588 | →→→¬⋀𝜑𝜓¬𝜓→→¬𝜓¬⋀𝜑𝜓↔¬⋀𝜑𝜓¬𝜓→→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓 | Subs [𝜑↗→¬⋀𝜑𝜓¬𝜓, 𝜓↗→¬𝜓¬⋀𝜑𝜓, 𝜒↗↔¬⋀𝜑𝜓¬𝜓] into ax-2 | |
| 17589 | →→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓 | Modus ponens 17581, 17588 | |
| 17590 | →→→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓→𝜑→→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓 | Subs [𝜑↗→→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 17591 | →𝜑→→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓 | Modus ponens 17589, 17590 | |
| 17592 | →→𝜑→→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓→→𝜑→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→𝜑→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓 | Subs [𝜓↗→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓, 𝜒↗→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓] into ax-2 | |
| 17593 | →→𝜑→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→𝜑→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓 | Modus ponens 17591, 17592 | |
| 17594 | →𝜑→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓 | Modus ponens 17587, 17593 | |
| 17595 | →→¬⋀𝜑𝜓¬𝜓→¬⋀𝜑𝜓¬𝜓 | Subs [𝜑↗→¬⋀𝜑𝜓¬𝜓] into id | |
| 17596 | →→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓 | Subs [𝜑↗→¬⋀𝜑𝜓¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 17597 | →→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓 | Subs [𝜑↗→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓, 𝜓↗→¬⋀𝜑𝜓¬𝜓] into ax-1 | |
| 17598 | →→¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓 | Modus ponens 17596, 17597 | |
| 17599 | →→→¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓→→→¬⋀𝜑𝜓¬𝜓→¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓 | Subs [𝜑↗→¬⋀𝜑𝜓¬𝜓, 𝜓↗→¬⋀𝜑𝜓¬𝜓, 𝜒↗→𝜑→¬⋀𝜑𝜓¬𝜓] into ax-2 | |
| 17600 | →→→¬⋀𝜑𝜓¬𝜓→¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓 | Modus ponens 17598, 17599 | |
| 17601 | →→𝜑→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓 | Subs [𝜓↗→¬⋀𝜑𝜓¬𝜓, 𝜒↗↔¬⋀𝜑𝜓¬𝜓] into ax-2 | |
| 17602 | →→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓 | Modus ponens 17594, 17601 | |
| 17603 | →→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓 | Subs [𝜑↗→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓, 𝜓↗→¬⋀𝜑𝜓¬𝜓] into ax-1 | |
| 17604 | →→¬⋀𝜑𝜓¬𝜓→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓 | Modus ponens 17602, 17603 | |
| 17605 | →→→¬⋀𝜑𝜓¬𝜓→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓→→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓 | Subs [𝜑↗→¬⋀𝜑𝜓¬𝜓, 𝜓↗→𝜑→¬⋀𝜑𝜓¬𝜓, 𝜒↗→𝜑↔¬⋀𝜑𝜓¬𝜓] into ax-2 | |
| 17606 | →→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓 | Modus ponens 17604, 17605 | |
| 17607 | →→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓 | Modus ponens 17596, 17606 | |
| 17608 | →→→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓→𝜑→→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓 | Subs [𝜑↗→→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 17609 | →𝜑→→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓 | Modus ponens 17607, 17608 | |
| 17610 | →→𝜑→→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓 | Subs [𝜓↗→¬⋀𝜑𝜓¬𝜓, 𝜒↗→𝜑↔¬⋀𝜑𝜓¬𝜓] into ax-2 | |
| 17611 | →→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓 | Modus ponens 17609, 17610 | |
| 17612 | →𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓 | Modus ponens 17568, 17611 | |
| 17613 | →→𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓→→𝜑𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓 | Subs [𝜓↗𝜑, 𝜒↗↔¬⋀𝜑𝜓¬𝜓] into ax-2 | |
| 17614 | →→𝜑𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓 | Modus ponens 17612, 17613 | |
| 17615 | →→→𝜑𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓→𝜑→→𝜑𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓 | Subs [𝜑↗→→𝜑𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓, 𝜓↗𝜑] into ax-1 | |
| 17616 | →𝜑→→𝜑𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓 | Modus ponens 17614, 17615 | |
| 17617 | →→𝜑→→𝜑𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓→→𝜑→𝜑𝜑→𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓 | Subs [𝜓↗→𝜑𝜑, 𝜒↗→𝜑↔¬⋀𝜑𝜓¬𝜓] into ax-2 | |
| 17618 | →→𝜑→𝜑𝜑→𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓 | Modus ponens 17616, 17617 | |
| 17619 | →𝜑↔¬⋀𝜑𝜓¬𝜓 | Modus ponens id, 17614 | |
| 17620 | ↔→𝜑↔¬⋀𝜑𝜓¬𝜓↔⋀𝜑¬⋀𝜑𝜓⋀𝜑¬𝜓 | Subs [𝜓↗¬⋀𝜑𝜓, 𝜒↗¬𝜓] into pm5.32 | |
| 17621 | →↔→𝜑↔¬⋀𝜑𝜓¬𝜓↔⋀𝜑¬⋀𝜑𝜓⋀𝜑¬𝜓→→𝜑↔¬⋀𝜑𝜓¬𝜓↔⋀𝜑¬⋀𝜑𝜓⋀𝜑¬𝜓 | Subs [𝜑↗→𝜑↔¬⋀𝜑𝜓¬𝜓, 𝜓↗↔⋀𝜑¬⋀𝜑𝜓⋀𝜑¬𝜓] into biimp | |
| 17622 | →→𝜑↔¬⋀𝜑𝜓¬𝜓↔⋀𝜑¬⋀𝜑𝜓⋀𝜑¬𝜓 | Modus ponens 17620, 17621 | |
| 17623 | ↔⋀𝜑¬⋀𝜑𝜓⋀𝜑¬𝜓 | Modus ponens 17619, 17622 | annotanannot |
| 17624 | →↔⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜓 | Subs [𝜑↗⋀𝜑𝜓] into biimp | |
| 17625 | →→↔⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜓→𝜑→↔⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜓 | Subs [𝜑↗→↔⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1 | |
| 17626 | →𝜑→↔⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜓 | Modus ponens 17624, 17625 | |
| 17627 | →→𝜑→↔⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜓→→𝜑↔⋀𝜑𝜓𝜓→𝜑→⋀𝜑𝜓𝜓 | Subs [𝜓↗↔⋀𝜑𝜓𝜓, 𝜒↗→⋀𝜑𝜓𝜓] into ax-2 | |
| 17628 | →→𝜑↔⋀𝜑𝜓𝜓→𝜑→⋀𝜑𝜓𝜓 | Modus ponens 17626, 17627 | |
| 17629 | →𝜑→⋀𝜑𝜓𝜓 | Modus ponens 8176, 17628 | |
| 17630 | →⋀𝜑𝜓→𝜑⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 17631 | →→⋀𝜑𝜓→𝜑⋀𝜑𝜓→⋀𝜑𝜓→⋀𝜑𝜓→𝜑⋀𝜑𝜓 | Subs [𝜑↗→⋀𝜑𝜓→𝜑⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 17632 | →⋀𝜑𝜓→⋀𝜑𝜓→𝜑⋀𝜑𝜓 | Modus ponens 17630, 17631 | |
| 17633 | →→⋀𝜑𝜓→⋀𝜑𝜓→𝜑⋀𝜑𝜓→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→𝜑⋀𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗→𝜑⋀𝜑𝜓] into ax-2 | |
| 17634 | →→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→𝜑⋀𝜑𝜓 | Modus ponens 17632, 17633 | |
| 17635 | →→𝜑→⋀𝜑𝜓𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓 | Subs [𝜓↗⋀𝜑𝜓, 𝜒↗𝜓] into ax-2 | |
| 17636 | →→→𝜑⋀𝜑𝜓→𝜑𝜓→⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓 | Subs [𝜑↗→→𝜑⋀𝜑𝜓→𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 17637 | →⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓 | Modus ponens 6193, 17636 | |
| 17638 | →→⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓→→⋀𝜑𝜓→𝜑⋀𝜑𝜓→⋀𝜑𝜓→𝜑𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2 | |
| 17639 | →→⋀𝜑𝜓→𝜑⋀𝜑𝜓→⋀𝜑𝜓→𝜑𝜓 | Modus ponens 17637, 17638 | |
| 17640 | →𝜑→⋀𝜑𝜓𝜑 | Subs [𝜓↗⋀𝜑𝜓] into ax-1 | |
| 17641 | →→𝜑→⋀𝜑𝜓𝜑→𝜑→𝜑→⋀𝜑𝜓𝜑 | Subs [𝜑↗→𝜑→⋀𝜑𝜓𝜑, 𝜓↗𝜑] into ax-1 | |
| 17642 | →𝜑→𝜑→⋀𝜑𝜓𝜑 | Modus ponens 17640, 17641 | |
| 17643 | →→𝜑→𝜑→⋀𝜑𝜓𝜑→→𝜑𝜑→𝜑→⋀𝜑𝜓𝜑 | Subs [𝜓↗𝜑, 𝜒↗→⋀𝜑𝜓𝜑] into ax-2 | |
| 17644 | →→𝜑𝜑→𝜑→⋀𝜑𝜓𝜑 | Modus ponens 17642, 17643 | |
| 17645 | →→⋀𝜑𝜓→𝜑𝜓→→⋀𝜑𝜓𝜑→⋀𝜑𝜓𝜓 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2 | |
| 17646 | →→⋀𝜑𝜓𝜑→⋀𝜑𝜓𝜓 | Modus ponens pm3.4, 17645 | |
| 17647 | →→→⋀𝜑𝜓𝜑→⋀𝜑𝜓𝜓→𝜑→→⋀𝜑𝜓𝜑→⋀𝜑𝜓𝜓 | Subs [𝜑↗→→⋀𝜑𝜓𝜑→⋀𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1 | |
| 17648 | →𝜑→→⋀𝜑𝜓𝜑→⋀𝜑𝜓𝜓 | Modus ponens 17646, 17647 | |
| 17649 | →→𝜑→→⋀𝜑𝜓𝜑→⋀𝜑𝜓𝜓→→𝜑→⋀𝜑𝜓𝜑→𝜑→⋀𝜑𝜓𝜓 | Subs [𝜓↗→⋀𝜑𝜓𝜑, 𝜒↗→⋀𝜑𝜓𝜓] into ax-2 | |
| 17650 | →→𝜑→⋀𝜑𝜓𝜑→𝜑→⋀𝜑𝜓𝜓 | Modus ponens 17648, 17649 | |
| 17651 | →→→𝜒𝜒→𝜓→𝜒𝜒→𝜑→→𝜒𝜒→𝜓→𝜒𝜒 | Subs [𝜑↗→→𝜒𝜒→𝜓→𝜒𝜒, 𝜓↗𝜑] into ax-1 | |
| 17652 | →𝜑→→𝜒𝜒→𝜓→𝜒𝜒 | Modus ponens 51, 17651 | |
| 17653 | →→𝜑→→𝜒𝜒→𝜓→𝜒𝜒→→𝜑→𝜒𝜒→𝜑→𝜓→𝜒𝜒 | Subs [𝜓↗→𝜒𝜒, 𝜒↗→𝜓→𝜒𝜒] into ax-2 | |
| 17654 | →→𝜑→𝜒𝜒→𝜑→𝜓→𝜒𝜒 | Modus ponens 17652, 17653 | |
| 17655 | →𝜑→𝜓→𝜒𝜒 | Modus ponens 815, 17654 | |
| 17656 | →→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒→𝜑→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒 | Subs [𝜑↗→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 17657 | →𝜑→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒 | Modus ponens 57, 17656 | |
| 17658 | →→𝜑→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒→→𝜑→𝜓→𝜒𝜒→𝜑→→𝜓𝜒→𝜓𝜒 | Subs [𝜓↗→𝜓→𝜒𝜒, 𝜒↗→→𝜓𝜒→𝜓𝜒] into ax-2 | |
| 17659 | →→𝜑→𝜓→𝜒𝜒→𝜑→→𝜓𝜒→𝜓𝜒 | Modus ponens 17657, 17658 | |
| 17660 | →→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜓 | Subs [𝜑↗→⋀𝜑𝜓𝜓, 𝜓↗→𝜓𝜒] into ax-1 | |
| 17661 | →→→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜓→𝜑→→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜓 | Subs [𝜑↗→→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1 | |
| 17662 | →𝜑→→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜓 | Modus ponens 17660, 17661 | |
| 17663 | →→𝜑→→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜑→⋀𝜑𝜓𝜓→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜓 | Subs [𝜓↗→⋀𝜑𝜓𝜓, 𝜒↗→→𝜓𝜒→⋀𝜑𝜓𝜓] into ax-2 | |
| 17664 | →→𝜑→⋀𝜑𝜓𝜓→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜓 | Modus ponens 17662, 17663 | |
| 17665 | →𝜑→→𝜓𝜒→⋀𝜑𝜓𝜓 | Modus ponens 17629, 17664 | |
| 17666 | →→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒 | Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗⋀𝜑𝜓] into imim2 | |
| 17667 | →→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒 | Subs [𝜑↗→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒, 𝜓↗→𝜓𝜒] into ax-1 | |
| 17668 | →→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒 | Modus ponens 17666, 17667 | |
| 17669 | →→→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒 | Subs [𝜑↗→𝜓𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒] into ax-2 | |
| 17670 | →→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒 | Modus ponens 17668, 17669 | |
| 17671 | →→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→𝜑→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒 | Subs [𝜑↗→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 17672 | →𝜑→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒 | Modus ponens 17670, 17671 | |
| 17673 | →→𝜑→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→𝜑→→𝜓𝜒→𝜓𝜒→𝜑→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒 | Subs [𝜓↗→→𝜓𝜒→𝜓𝜒, 𝜒↗→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒] into ax-2 | |
| 17674 | →→𝜑→→𝜓𝜒→𝜓𝜒→𝜑→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒 | Modus ponens 17672, 17673 | |
| 17675 | →𝜑→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒 | Modus ponens 869, 17674 | |
| 17676 | →→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜓, 𝜒↗→⋀𝜑𝜓𝜒] into ax-2 | |
| 17677 | →→→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 17678 | →𝜑→→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 17676, 17677 | |
| 17679 | →→𝜑→→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜓↗→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒, 𝜒↗→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2 | |
| 17680 | →→𝜑→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 17678, 17679 | |
| 17681 | →𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 17675, 17680 | |
| 17682 | →→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜓→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜓↗→→𝜓𝜒→⋀𝜑𝜓𝜓, 𝜒↗→→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2 | |
| 17683 | →→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜓→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 17681, 17682 | |
| 17684 | →𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 17665, 17683 | |
| 17685 | →↔𝜓⋀𝜑𝜓→𝜓⋀𝜑𝜓 | Subs [𝜑↗𝜓, 𝜓↗⋀𝜑𝜓] into biimp | |
| 17686 | →→↔𝜓⋀𝜑𝜓→𝜓⋀𝜑𝜓→𝜑→↔𝜓⋀𝜑𝜓→𝜓⋀𝜑𝜓 | Subs [𝜑↗→↔𝜓⋀𝜑𝜓→𝜓⋀𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 17687 | →𝜑→↔𝜓⋀𝜑𝜓→𝜓⋀𝜑𝜓 | Modus ponens 17685, 17686 | |
| 17688 | →→𝜑→↔𝜓⋀𝜑𝜓→𝜓⋀𝜑𝜓→→𝜑↔𝜓⋀𝜑𝜓→𝜑→𝜓⋀𝜑𝜓 | Subs [𝜓↗↔𝜓⋀𝜑𝜓, 𝜒↗→𝜓⋀𝜑𝜓] into ax-2 | |
| 17689 | →→𝜑↔𝜓⋀𝜑𝜓→𝜑→𝜓⋀𝜑𝜓 | Modus ponens 17687, 17688 | |
| 17690 | →→𝜒𝜒→⋀𝜑𝜓→𝜒𝜒 | Subs [𝜑↗→𝜒𝜒, 𝜓↗⋀𝜑𝜓] into ax-1 | |
| 17691 | →→→𝜒𝜒→⋀𝜑𝜓→𝜒𝜒→𝜑→→𝜒𝜒→⋀𝜑𝜓→𝜒𝜒 | Subs [𝜑↗→→𝜒𝜒→⋀𝜑𝜓→𝜒𝜒, 𝜓↗𝜑] into ax-1 | |
| 17692 | →𝜑→→𝜒𝜒→⋀𝜑𝜓→𝜒𝜒 | Modus ponens 17690, 17691 | |
| 17693 | →→𝜑→→𝜒𝜒→⋀𝜑𝜓→𝜒𝜒→→𝜑→𝜒𝜒→𝜑→⋀𝜑𝜓→𝜒𝜒 | Subs [𝜓↗→𝜒𝜒, 𝜒↗→⋀𝜑𝜓→𝜒𝜒] into ax-2 | |
| 17694 | →→𝜑→𝜒𝜒→𝜑→⋀𝜑𝜓→𝜒𝜒 | Modus ponens 17692, 17693 | |
| 17695 | →𝜑→⋀𝜑𝜓→𝜒𝜒 | Modus ponens 815, 17694 | |
| 17696 | →→⋀𝜑𝜓→𝜒𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒] into ax-2 | |
| 17697 | →→→⋀𝜑𝜓→𝜒𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→⋀𝜑𝜓→𝜒𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→→⋀𝜑𝜓→𝜒𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 17698 | →𝜑→→⋀𝜑𝜓→𝜒𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 17696, 17697 | |
| 17699 | →→𝜑→→⋀𝜑𝜓→𝜒𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→⋀𝜑𝜓→𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜓↗→⋀𝜑𝜓→𝜒𝜒, 𝜒↗→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2 | |
| 17700 | →→𝜑→⋀𝜑𝜓→𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 17698, 17699 | |
| 17701 | →𝜑→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 17695, 17700 | |
| 17702 | →→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓 | Subs [𝜑↗→𝜓⋀𝜑𝜓, 𝜓↗→⋀𝜑𝜓𝜒] into ax-1 | |
| 17703 | →→→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→𝜑→→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓 | Subs [𝜑↗→→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓, 𝜓↗𝜑] into ax-1 | |
| 17704 | →𝜑→→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓 | Modus ponens 17702, 17703 | |
| 17705 | →→𝜑→→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→𝜑→𝜓⋀𝜑𝜓→𝜑→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓 | Subs [𝜓↗→𝜓⋀𝜑𝜓, 𝜒↗→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓] into ax-2 | |
| 17706 | →→𝜑→𝜓⋀𝜑𝜓→𝜑→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓 | Modus ponens 17704, 17705 | |
| 17707 | →𝜑→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓 | Modus ponens pm3.2, 17706 | |
| 17708 | →→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒 | Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒, 𝜒↗𝜓] into imim2 | |
| 17709 | →→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒 | Subs [𝜑↗→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜒] into ax-1 | |
| 17710 | →→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒 | Modus ponens 17708, 17709 | |
| 17711 | →→→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒 | Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜒, 𝜒↗→→𝜓⋀𝜑𝜓→𝜓𝜒] into ax-2 | |
| 17712 | →→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒 | Modus ponens 17710, 17711 | |
| 17713 | →→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒 | Subs [𝜑↗→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 17714 | →𝜑→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒 | Modus ponens 17712, 17713 | |
| 17715 | →→𝜑→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→𝜑→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒 | Subs [𝜓↗→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒, 𝜒↗→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒] into ax-2 | |
| 17716 | →→𝜑→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒 | Modus ponens 17714, 17715 | |
| 17717 | →𝜑→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒 | Modus ponens 17701, 17716 | |
| 17718 | →→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒 | Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→𝜓⋀𝜑𝜓, 𝜒↗→𝜓𝜒] into ax-2 | |
| 17719 | →→→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒 | Subs [𝜑↗→→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 17720 | →𝜑→→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒 | Modus ponens 17718, 17719 | |
| 17721 | →→𝜑→→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒→→𝜑→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒 | Subs [𝜓↗→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒, 𝜒↗→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒] into ax-2 | |
| 17722 | →→𝜑→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒 | Modus ponens 17720, 17721 | |
| 17723 | →𝜑→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒 | Modus ponens 17717, 17722 | |
| 17724 | →→𝜑→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒→→𝜑→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→𝜑→→⋀𝜑𝜓𝜒→𝜓𝜒 | Subs [𝜓↗→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓, 𝜒↗→→⋀𝜑𝜓𝜒→𝜓𝜒] into ax-2 | |
| 17725 | →→𝜑→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→𝜑→→⋀𝜑𝜓𝜒→𝜓𝜒 | Modus ponens 17723, 17724 | |
| 17726 | →→→𝜓𝜒→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜒] into impbi | |
| 17727 | →→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒 | Subs [𝜑↗→→⋀𝜑𝜓𝜒→𝜓𝜒, 𝜓↗→→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-1 | |
| 17728 | →→→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒 | Subs [𝜑↗→→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 17729 | →𝜑→→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒 | Modus ponens 17727, 17728 | |
| 17730 | →→𝜑→→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→𝜑→→⋀𝜑𝜓𝜒→𝜓𝜒→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒 | Subs [𝜓↗→→⋀𝜑𝜓𝜒→𝜓𝜒, 𝜒↗→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒] into ax-2 | |
| 17731 | →→𝜑→→⋀𝜑𝜓𝜒→𝜓𝜒→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒 | Modus ponens 17729, 17730 | |
| 17732 | →𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒 | Modus ponens 4703, 17731 | |
| 17733 | →→→→𝜓𝜒→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗→→⋀𝜑𝜓𝜒→𝜓𝜒, 𝜒↗↔→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2 | |
| 17734 | →→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 17726, 17733 | |
| 17735 | →→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 17736 | →𝜑→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 17734, 17735 | |
| 17737 | →→𝜑→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜓↗→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒, 𝜒↗→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2 | |
| 17738 | →→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 17736, 17737 | |
| 17739 | →𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 17732, 17738 | |
| 17740 | →→→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→→𝜓𝜒→⋀𝜑𝜓𝜒] into id | |
| 17741 | →→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 17742 | →→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗→→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-1 | |
| 17743 | →→→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 17741, 17742 | |
| 17744 | →→→→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜒↗→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2 | |
| 17745 | →→→→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 17743, 17744 | |
| 17746 | →→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜓↗→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜒↗↔→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2 | |
| 17747 | →→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 17739, 17746 | |
| 17748 | →→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗→→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-1 | |
| 17749 | →→→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 17747, 17748 | |
| 17750 | →→→→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒→→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜒↗→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2 | |
| 17751 | →→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 17749, 17750 | |
| 17752 | →→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 17741, 17751 | |
| 17753 | →→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 17754 | →𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 17752, 17753 | |
| 17755 | →→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜓↗→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜒↗→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2 | |
| 17756 | →→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 17754, 17755 | |
| 17757 | →𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 17684, 17756 | |
| 17758 | →→𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜓↗𝜑, 𝜒↗↔→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2 | |
| 17759 | →→𝜑𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 17757, 17758 | |
| 17760 | →→→𝜑𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜑𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜑↗→→𝜑𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1 | |
| 17761 | →𝜑→→𝜑𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 17759, 17760 | |
| 17762 | →→𝜑→→𝜑𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→𝜑𝜑→𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Subs [𝜓↗→𝜑𝜑, 𝜒↗→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2 | |
| 17763 | →→𝜑→𝜑𝜑→𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens 17761, 17762 | |
| 17764 | →𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒 | Modus ponens id, 17759 | |
| 17765 | ↔→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒↔⋀𝜑→𝜓𝜒⋀𝜑→⋀𝜑𝜓𝜒 | Subs [𝜓↗→𝜓𝜒, 𝜒↗→⋀𝜑𝜓𝜒] into pm5.32 | |
| 17766 | →↔→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒↔⋀𝜑→𝜓𝜒⋀𝜑→⋀𝜑𝜓𝜒→→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒↔⋀𝜑→𝜓𝜒⋀𝜑→⋀𝜑𝜓𝜒 | Subs [𝜑↗→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗↔⋀𝜑→𝜓𝜒⋀𝜑→⋀𝜑𝜓𝜒] into biimp | |
| 17767 | →→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒↔⋀𝜑→𝜓𝜒⋀𝜑→⋀𝜑𝜓𝜒 | Modus ponens 17765, 17766 | |
| 17768 | ↔⋀𝜑→𝜓𝜒⋀𝜑→⋀𝜑𝜓𝜒 | Modus ponens 17764, 17767 | pm5.33 |